Dispatch: May 4, 2011 CE: N/A Journal MSPNo. No.ofpages...

ajps˙519 ajps2010v2.cls (1994/07/13 v1.2u Standard LaTeX document class) May 4, 2011 20:57

AJPS ajps˙519 Dispatch: May 4, 2011 CE: N/A

Journal MSP No. No. of pages: 18 PE: Martha1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

The Three As of Government Formation:Appointment, Allocation, and Assignment

Torun Dewan London School of EconomicsRafael Hortala-Vallve London School of Economics

How does the Prime Minister organize her government so that she can implement her policy agenda? In our model, a PrimeMinister appoints individuals to her cabinet, allocates their portfolios, and assigns their policy tasks—that is, she decidesthe relevant jurisdiction of departments and the type of proposals a minister can make. Upon appointment ministers obtainexpertise on policies specific to their jurisdiction and strategically communicate this information to the Prime Ministerbefore a policy is implemented. Assignment allows the Prime Minister to implement her agenda even when she is constrainedto appoint ministers whose policy preferences are far from her own. A Prime Minister weakly prefers a diverse cabinet. Inequilibrium, the Prime Minister is indifferent between delegating policy or implementing policy herself.

The standard view of relations in parliamen-tary democracy, certainly under the Westminstermodel, is of a dominant Prime Minister whose

power is nevertheless constrained by cabinet government.But what are the sources of the Prime Minister’s influence?How effective are the instruments at her disposal in al-lowing her to implement her policy agenda? And does adiverse cabinet act as an effective constraint on the exer-cise of Prime Ministerial power? In this article we developa formal model that provides answers to these questionsand that builds on key structural features of parliamentarygovernment, which are most developed in the Westmin-ster system in which the Prime Minister is usually leaderof a majority party. Our focus is on the way that a PrimeMinister organizes her government in such a system. Wehighlight three instruments at her disposal: (1) the ap-pointment of her ministers—the Prime Minister chooseswho will serve under her and who will remain on theback-benches; (2) the allocation of portfolios—the PrimeMinister decides which ministers will run which govern-ment departments and (3) the assignment of a ministersresponsibilities within her department. With reference tothe latter we suppose that the Prime Minister can activelydefine her minister’s brief: the set of issues over which the

Torun Dewan is Professor of Political Science, Department of Government London School of Economics, Houghton Street, London WC22AE ([email protected]). Rafael Hortala-Vallve is a Lecturer in Political Science and Public Policy, Department of Government, HoughtonStreet, London WC2 2AE ([email protected]).

We thank Michael Bechtel, Gary Cox, Keith Dowding, Patrick Dunleavy, Pohan Fong, Michael Laver, Iain Maclean, David Myatt, ThomasPluemper, Kenneth Shepsle, Francesco Squintani, Anne White, seminar participants at LSE, Trinity, and the MPSA, and anonymousreferees at the AJPS, for helpful comments, discussions, and suggestions.

minister can decide (which we define as his jurisdiction)and the type of proposals that a minister can make.

The appointment of ministers is the most well-understood instrument at the Prime Minister’s disposaland has been analyzed by Huber and Martinez-Gallardo(2008), Dewan and Myatt (2007), and Thies (2001),amongst others. The allocation of ministerial portfolios iscentral to the seminal models by Laver and Shepsle (1996)and Austen-Smith and Banks (1990). The key insight ofthe portfolio allocation models is that, once we considerthe parliamentary procedures by which the rights to makeand implement policy on specific issues are allocated, wecan find equilibria of a well-defined government forma-tion game in multiple policy dimensions. These modelstreat a minister’s responsibilities as fixed: upon being ap-pointed (and allocated a portfolio) he implements theparty’s preferred policy on a set of issues aligned on a sin-gle policy dimension over which he has jurisdiction. Westart from the premiss that defining ministerial responsi-bilities is a critical element of a Prime Minister’s strategicplan and should be considered alongside the other instru-ments at her disposal.

Following standard models of delegation we assumethat the Prime Minister cannot formulate policy on all

American Journal of Political Science, Vol. 0, No. 0, xxx 2011, Pp. 1–18

C© 2011 Midwest Political Science Association DOI: 10.1111/j.1540-5907.2011.00519.x

1


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

2 TORUN DEWAN AND RAFAEL HORTALA-VALLVE

dimensions. The consequent division of labor involvesstrategic appointment of cabinet members, allocation ofministerial portfolios, and assignment of ministerial re-sponsibilities. We explore how a Prime Minister organizesher government in a multidimensional policy space andshow that the existence of a such a policy space createsstrategic opportunities for the Prime Minister to defineministerial responsibilities in a way that aligns ministers’incentives with her own. Surprisingly, this holds evenwhen she is constrained to appoint ministers with idealpolicies far from her own preferred ones.

We develop this insight in a model with imperfect in-formation: ministers have known policy biases but haveexpertise on policies under their jurisdiction. Specificallyministers have private information which they can revealtruthfully or otherwise to the Prime Minister. We showthat when the Prime Minister assigns responsibilities opti-mally (from her perspective) then she is able to obtain thesame outcomes as if she were perfectly informed and im-plemented policy directly. In fact, we show that when thePrime Minister optimally chooses ministerial responsibil-ities then she is strictly indifferent between implementingpolicy herself or delegating to her ministers. This is trueeven when her cabinet is ideologically diverse; in fact weshow that a Prime Minister (weakly) prefers diversity.

The article is organized as follows. We first offer adiscussion of the related literature before providing someempirical motivation for our model. We introduce ourmodeling framework, and we analyze a two ministermodel that allows us to explore the relative effectivenessof the three instruments that the Prime Minister has ather disposal and to establish some baseline results. Inthe remainder of the article we provide a more generalanalysis, first exploring the process of appointment, allo-cation and assignment in large cabinets and then takingaccount of the size of adjustments required to status quojurisdictions. We then explore the robustness of our find-ings in different institutional environments: we considerthat the Prime Minister is elected by some subsection ofparty members; consider different ways of conceptual-izing the cabinet; allow for collusion between ministers;and finally consider a world where ministers not onlyhave policy biases but also hold expertise on issues (thatmay be correlated with these biases). Finally, we considerthe novel empirical implications of our analysis and thenconclude. All proofs are contained in the appendix.

Related Literature

Our model relates to a growing literature that usesprincipal agent theory to understand the multiple rela-

tions in parliamentary democracies (Martin and Vanberg2004; Strøm, Muller, and Bergstrom 2003; Thies 2001).Our analysis of aggregation of dispersed informationby cabinet members is circumscribed in the cheap talkliterature (Crawford and Sobel 1982) that analyzes strate-gic communication by an agent to a principal who im-plements policy. Whilst this literature has been used toexplore information transmission in Congress (Baron2000; Gilligan and Krehbiel 1987; Patty 2009), to ourknowledge our work is the first to apply this machin-ery to parliamentary democracies. In the classic modelof committee organization in the U.S. House (Gilliganand Krehbiel 1987), the parent body chooses the proce-dural rules that, in turn, provide incentives for commit-tee members to acquire information in a unidimensionalpolicy space. In our model of Westminster government,a Prime Minister assigns a minister’s task by defininghis jurisdiction and responsibilities. Ministers acquire in-formation (costlessly) on policy issues over which theyhave jurisdiction, and so, and in contrast to the classicmodel, expertise is endogenously assigned by the PrimeMinister.

The fact that departmental jurisdictions overlap,means that a multidimensional model is appropriate toour setting. Our framework and initial results (proposi-tions 1 and 2) applies the multidimensional cheap talkmodel introduced by Battaglini (2002) and highlights theimportance of these results toward understanding gov-ernment organization. Whereas Battaglini shows that ina multidimensional cheap-talk setting there is a fully re-vealing truth-telling equilibrium where jurisdictions areorthogonal to the biases of senders, we show that in ourworld this is true of any truth-telling equilibrium. Usingthis framework our results can clearly be distinguishedfrom those of the unidimensional model that has beenused to analyze Congress: whereas in that model infor-mation transmission improves when the (median) pref-erence of the committee and the parent body are not farapart, in our model diversity does not undermine thepower of a Prime Minister and can sometimes benefither. Jurisdictional assignments as equilibrium phenom-ena has been studied previously by Ting (2002) who ana-lyzes optimal assignments in the presence of moral hazardwhen the legislature controls the agency budget and con-tractual rewards; he shows conditions under which a leg-islature would wish to consolidate bureaucratic tasks ina single agency. Indridason and Kam (2008) also look atmoral hazard in a situation where the budget resourcesa minister can claim for a given portfolio may be trans-ferred to a rival minister following a reshuffle. In contrastto these models asymmetric information due to exper-tise. A similarity arises between the work of Indridason


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

THREE AS OF GOVERNMENT FORMATION 3

and Kam and ours in that the Prime Minister can exploitdifferences between her ministers and align their incen-tives with her own.

Finally, a critical question that we address is the opti-mal assignments when the Prime Minister is constrainedto making only small adjustments to ministerial respon-sibilities. The political situation we analyze is a specialcase of the assignment problem studied in mathematics(Burkhard, Dell’Amico, and Martello 2009).

Adapting Ministerial Jurisdictions

Our key contribution is in exploring the ways that a PrimeMinister uses the tools that are available to her in orderto align the incentives of her ministers with her own. Animplication of our analysis, that we explore more fully be-low, is that by carefully selecting ministers’ tasks a PrimeMinister is better able to draw on their advise. An illus-trative case is the first cabinet of Margaret Thatcher thatincluded Tory “wets,” such as William Whitelaw, JamesPrior, Iain Gilmour, and Lord Carrington, who opposedher monetary policies. The inclusion of these ministersin Thatcher’s cabinet reflects their considerable experi-ence, expertise, and standing within the party.1 But thisis not the whole story. Whitelaw, for example, havingstood against Thatcher in the 1975 Conservative Partyleadership contest, served as Thatcher’s Home Secretaryand then as Leader of the House of Lords and becameher most loyal lieutenant. The successful relationship be-tween them—Thatcher acknowledged Whitelaw’s role inher now famous accolade “every Prime Minister needsa Willie”—is often put down to Whitelaw’s character,pragmatism, and commitment to public service. A keyfactor in the relationship was, however, that Whitelawwas not consulted on matters over which he disagreedwith the Premier and thus was at ease in providing ad-vise on other issues. Young (1999) writes of Whitelaw’sactions: “He was operating on a different plane, mak-ing his own analysis, which told him that blind obedi-ence punctuated by sage advice on matters outside theeconomic realm, was the only rational course of action”(1999, 235).

The key general insight that we offer is that a PrimeMinister can astutely manage her cabinet, and in par-ticular the dimensionality of the policy space, in a waythat policy relevant information can be effectively aggre-gated and in line with the Prime Minister’s objectives.

1 King (1994) has argued that some ministers—whom he terms“the big beasts of the jungle”—are by their standing too importantto be left out of the cabinet.

In the case of Whitelaw, the Prime Minister was able torestrict the policy space on which she adhered to his ad-vice so that she could benefit from his experience andexpertise on issues where they were aligned. This elementis important to understanding the nonconflictual work-ing relationship between such erstwhile rivals to the Toryleadership.

Our analysis goes further in exploring how a PrimeMinister can manipulate the machinery of governmentin order to illicit information from her ministers. Arecent report by the Institute of Government into thechanging structure of Whitehall states that the abilityof the Prime Minister to rearrange departments servesas “such an important tool that only one new PrimeMinister since 1950 has chosen not to reconfigure de-partments in some way after assuming the leadership”White and Dunleavy (2010, 1). Such reconfiguration typ-ically takes one of two forms: new departments are cre-ated from a rearrangement of existing departmental re-sponsibilities; or the department structure remains thesame but ministerial responsibilities are reassigned acrossdepartments.

An example of the first comes with the creation of theDepartment of Energy and Climate Change in October2008 taking over energy functions from Department forBusiness, Enterprise and Regulatory Reform and takingover climate change functions from the Department forEnvironment, Food and Rural Affairs. A further exampleconcerns the recent overhaul of the Home Office, thatincluded the setting up of a new Ministry of Justice anda new Office for Security and Counter-Terrorism withinthe Home Office. A still recent example is the setting up ofthe Department for International Development in 1997following a transfer of responsibilities from the Foreignand Commonwealth Office.

Major organizational changes are typically takenwithout a major change to the departmental structureand involve a simple transfer of policy responsibilities.The history of the Home Office is particularly interest-ing with a plethora of policy functions being transferredand withdrawn from its jurisdiction over the course of itshistory. At different points in time it has been responsi-ble for sport, broadcasting, and adoption and child carewhich it received following a transfer of responsibilitiesfrom the Ministry of Health in 1947 with the same pol-icy powers being transferred back to the Department ofHealth and Social Security in 1971 (the DHSS was itself,a department that merged functions previously held byother departments). More recently in 2007 criminal jus-tice, prisons, probation, and legal affairs were transferredto the Ministry of Justice while counterterrorism strategywas brought under the Home Office’s remit. These are


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53


a few of more than forty changes made in the twentiethcentury.2

Such changes, which amount to a major reorganiza-tion of the policy responsibilities and functions of Britishgovernment, fall under the Royal Prerogative which isexercised by the Prime Minister.3 No primary legisla-tion is required and changes are made in the absenceof an objection from either House.4 Indeed a recent re-port of the House of Commons Public AdministrationSelect Committee, stated that “it is anomalous that itis so procedurally straightforward for the Prime Min-ister to reorganize the Civil Service by amending thefunctions of the ministers it serves, when reorganiz-ing other public services may often involve statutoryconsultation, parliamentary approval, or even primarylegislation.”5

An important and previously uninvestigated conse-quence of these organizational changes is that there isconsiderable overlap in the jurisdictions of different de-partments. To provide some examples from the currentassignment of Whitehall departments: policies on Health,whilst part of the domain of the Ministry for Health, arealso dealt with in the Department of Education; poli-cies on terrorism, counterterrorism, and security, comeunder the purview of the Foreign and CommonwealthOffice and the Home Office; international relations fallsunder the jurisdiction of the Secretary of State for De-fence and the Minister for Environment, Food and RuralAffairs.

The ability to strategically adapt the government ma-chine has an important consequence: in so doing, a PrimeMinister is able to manipulate a minister’s jurisdiction inways not afforded to her when able only to allocate portfo-

2 A full record of all such changes to British government from 1964to 1992 gathered by Iain McLean is held at http://www.nuffield.ox.ac.uk/politics/whitehall/; Chester and Wilson (1968) look atchanges from 1960 to 1983.

3 Relatedly, in the German Federal Republic the reassignment ofpolicy competencies ultimately falls under the Richtlinienkompe-tenz of the Chancellor according to Article 65 of the Basic Law.

4 In response to the question made on February 6, 2006 byLord Stoddart of Swindon, who asked Her Majesty’s Government“whether they will issue a Green Paper on the proposed reorgani-sation and splitting of the Home Office, and allow for a period ofpublic debate and consultation and the issuing of a White Paperbefore any Bill to implement such reorganization is presented toParliament”, the Minister of State for the Home Office, BaronessScotland of Asthal, replied unequivocally: “questions of changes tothe machinery of government are decided by the Prime Minister.”By contrast, it was Congress that set up the Homeland SecurityDepartment in response to the 9/11 terrorist attacks.

5 Seventh Report of Sessions 2006–2007 of the House of CommonsPublic Administration Select Committee: Machinery of Govern-ment Changes.

lios with preexisting and well defined policy boundaries.Government reorganization can be used to a Prime Minis-ter’s advantage, in particular when she is constrained withregard to the personnel in her cabinet. A contemporaryexample involves Vincent Cable the Business Secretary inthe current British government, who until recently wasresponsible for media regulation. In this role, Cable wasresponsible for investigating the plans of News Corpo-ration’s boss Rupert Murdoch to take over all of BritishSky Broadcasting. Cable was, however, secretly recordedby undercover journalists stating that he had “declaredwar” on the media tycoon with the Daily Telegraph pub-lishing the story on December 21, 2010. This statementof his ideological position brought into question his im-partiality and put him at odds with government policy.The consequence of his gaffe was not resignation, de-spite Opposition calls, for as a senior Liberal figure inthe fledgling coalition he could not be replaced. InsteadPrime Minister Cameron transferred aspects of media andtelecoms policy from Cable’s department, (along with 70civil servants), to the Department of Culture Media andSport headed by Jeremy Hunt the Culture Secretary. Inour terminology there was no change in terms of thePrime Minister’s appointments or allocations, butthe assignment varied. The final implication was that thepolicy outcome–government approval of News Corpora-tion’s plans on March 2, 2011— was different to the out-come that would likely have prevailed under the initialassignment.

Our notion of assignment described earlier also ac-counts for the fact that the Prime Minister can limit thetypes of proposals that a minister can make. Ministersmust make policy proposals, within the area of their ju-risdiction, that accord with guidelines set down by thePrime Minister. A leading example is where the PrimeMinister provides direction over spending priorities. Astark and currently very relevant case is where the PrimeMinister wishes to ring-fence or prioritize certain areasof spending over others. Such ringfencing protects bud-gets according to policy priorities identified by the PrimeMinister. For example, in a recent announcement DavidCameron committed to increase the Foreign Aid budget,administered by the Department for International De-velopment, by 0.7% of gross national income by 2013despite overall public spending cuts totalling 83 billionpounds. Other examples include the budget for the De-partment of Education which is due to rise year on year,though capital spending has been slashed by 60%. Theseexamples are indicative of the ways in which the PrimeMinister can limit the type of proposals that a ministerbrings to cabinet and introduces to the floor of the Houseof Commons.


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53


A Formal Analysis of theWestminster Model

We develop a formal model that explores a situation inwhich an executive leader organizes her cabinet. Her or-ganizational strategy has three elements: she selects thepersonnel who will serve in her cabinet; she allocates theirportfolios; and she then assigns ministerial responsibili-ties in a way in which we make precise below. The strategicactors in our model are then a Prime Minister and herministers who are motivated by policy. Outcomes are de-termined by strategic interaction between ministers whoreport to the Prime Minister on their assignment andthe Prime Minister who organizes her cabinet and imple-ments policy.

Payoffs

We initially restrict to a government that consists of twoministerial posts, though we later extend our analysis toa larger cabinet. The preferences of ministers are definedover policy outcomes x ∈ R

2 and are single peaked andquadratic with bliss points at mi and i ∈ {1, 2} so thatpayoffs are defined as ui (x) = − ∑2

n=1(xn − mni )2.6 We

write the Prime Minister’s ideal point as pm∗ and, fornotational simplicity, normalize so that it is located at theorigin pm∗ = (0, 0). This implies that the ministers’ biaswith respect to the Prime Minister is (mi − pm∗) = mi.

The Prime Minister’s Instruments

The Prime Minister must appoint ministers, allocate aportfolio to each and then assign their responsibilities.The first element of assignment is the set of policies overwhich the minister reports to cabinet. This is what weterm a ministers “jurisdiction.” For two policy dimen-sions it is possible that a Prime Minister would assignall issues related to dimension X to the portfolio of oneminister, and the other Y to the other minister. As wehave seen, however, there may be a degree of overlap inthe jurisdictions of different departments. So we allow forthe fact that a Prime Minister might give some influenceover issues on X and Y to both ministers.

The second element of a ministers assignment is thetype of proposal that a minister can make within his juris-diction. As we have seen, although ministers are respon-sible for their own departments, the Prime Minister setsimportant policy guidelines that constrains the type of

6 This is without loss of generality. More specifically, we require thatutility functions are continuous, quasi-concave, and differentiable.

FIGURE 1 Defining aMinister’sAssignment

Policy X

Policy Y

m1

A1

α

proposals ministers can make. To illustrate consider Fig-ure 1 that depicts a two dimensional policy space involv-ing policy X and policy Y . We indicate by m1 a minister’spolicy bias relative to that of the Prime Minister (recallthat the Prime Minister’s ideal policy lies at the originand so in this example the minister’s bliss point is to thenorth-east of that point). If the minister had influence onboth policies, then he would wish to implement a policythat is greater than pm∗ on both policy dimensions. Con-sider, for example a situation where the minister coulddecide how much money should be allocated to policiesX and Y . The minister would like to spend more on bothrelative to the Prime Minister. If, however, the ministerwere forced to choose a level of spending along the linegiven by A1 then her preferred allocation on that line isthe same as that of the Prime Minister: her indifferencecurve is tangent to A1 at the origin.7

An implication of this example, that we explore morefully, is that by carefully defining ministerial responsibil-ities a Prime Minister may be able to align the incentivesof her ministers with her own. A critical aspect is that ju-risdictional overlap creates a multidimensional problemthat provides the Prime Minister greater strategic leeway.To return to our spending example, if the Prime Minis-ter were only able to define her minister’s responsibilitiesalong a single dimension, then she could constrain his

7 The analysis extends to any continuous multidimensional policyspace where preferences are strictly convex. Consider for examplethe case where the minister is, relative to the Prime Minister, in favorof stricter regulation of environmental standards, via a carbon taxfor example, and greater provision for nuclear power. He mightthen be required to couple any proposed plan to increase nuclearcapacity, via state support for capital investment in nuclear plants,with a reduction in carbon taxes.


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53


proposals in a very stark fashion: by, for example, settinga maximum (or minimum) level of spending. In multipledimensions, however, the Prime Minister can define theministerial brief in a way that provides her with strategicadvantage.8

The Prime Minister and Her Cabinet

To complete our formal setting we now describe morefully the relationship between the Prime Minister and herteam of ministers, the timing of our game, what ministersknow, and how they know it.

Information. The source of a minister’s influence in ourmodel is an informational asymmetry. We assume thatthere are underlying social, economic, and political fun-damentals that are (initially) not directly observed byeither the Prime Minister or her ministers. We capturethese fundamentals via the vector � ∈ � = R

2. Once aminister has been allocated a department and its juris-diction is assigned, however, he acquires all informationrelevant to policymaking in that jurisdiction. An impli-cation of our assumption is that in assigning responsi-bilities the Prime Minister decides which of her ministerwill become informed and on which set of issues. Havingdefined a minister’s jurisdiction the Prime Minister com-pletes the assignment by specifying the minister’s task:the minister, upon receiving the policy-relevant informa-tion in their jurisdiction, must report a single dimensionalvariable to the PM, si : � → R. An assignment, however,restricts ministers to reporting on one of two directionsAi ∈ R

2, i = {1, 2} that span the whole policy space (i.e.A1 �= �A2, ∀� ∈ R).

Timing . In the first stage of our model the Prime Minis-ter appoints her ministers, allocates their portfolios andassigns their responsibilities. In the second stage minis-ters bring a proposal to the Prime Minister that conformswith the responsibilities assigned to them. Finally, andupon receiving the minister’s proposal the Prime Minis-ter implements policy which we denote as y ∈ R

2. Herchosen policy may depend on the declarations made byministers so that y((s1(�), s2(�))). We write the policyoutcomes as x, which depends on both the chosen policyy and the underlying fundamentals �. Specifically the fi-nal outcome satisfies x = y + �. The policy that the PrimeMinister chooses depends upon her beliefs about thesefundamentals given the declarations of her ministers. We

8 We are saying nothing new here. This insight was developed inthe seminal article by Austen-Smith (1993).

write the posterior belief of the PM on the possible statesof the world as � : R × R → P (�).

Solution Concept

Our solution concept is Perfect Bayesian Equilibrium.Loosely speaking, this requires that the actions of thePrime Minister and her ministers be sequentially rationalgiven their beliefs, that their beliefs be consistent withrational play and Bayes rule along the equilibrium path,and with some beliefs off the equilibrium path. We focusattention on the existence of a truthful and fully revealingequilibrium: ministers adopt a truthful strategy, that isthey report the true state of the world within their min-isterial responsibility and, in combining her ministers’joint declarations, the Prime Minister learns all there is toknow about the true state of the world. In game theoreticterms a fully revealing equilibrium is defined by posteriorbeliefs cumulated on the true state of the world, �(s1(�),s2(�))(�) = 1. Of course an equilibrium may not be truth-ful and yet still be fully revealing. This occurs, for example,if the ministers systematically misreport: it may be com-mon knowledge that a minister exaggerates by adding abias to his report and that the Prime Minister takes thisinto account by discounting such reports. Applying rea-soning akin to the revelation principle, it can be shownthat there is no loss of generality in restricting attentionto fully revealing equilibria that are at once truthful andinvolve degenerate out of equilibrium beliefs.9 The intu-ition behind this result is that cabinet members only careabout final outcomes: when a fully revealing equilibriumexists they may as well report truthfully (they need neverconstruct complicated out-of-equilibrium beliefs, as thepreferred policy of the Prime Minister is an equilibriumoutcome in either case).

Three A’s in a Two Member Cabinet

In this section we establish our core results in a simpletwo member cabinet. We develop our results by lookingat two distinct and extreme cases. In the first, assignmentsare given by the policy axis and the only instrument thePrime Minister can use in order to implement her policyagenda is to choose which individuals sit in her cabinetand to allocate a portfolio to each. In the second case, weassume the Prime Minister has no discretion over whoto appoint but is able to allocate portfolios and assignministerial responsibilities.

9 See Lemma 1 of Battaglini (2002).


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53


Appointing Ministers

We begin our analysis by focussing on the simplest sce-nario in which departmental jurisdictions are fixed, butthe Prime Minister has complete discretion to appointher ministers. To make things interesting we make a slightrestriction on the type of ministers that are available as-suming that there will always be some ideological conflict.That is, a Prime Minister is unable to appoint ministerswho share her ideal point.

As a toy example that helps illustrate some of themain ideas and introduces our basic notation, considera situation where the ideal points satisfy pm∗ = (0, 0),m1 = (0, 1) and m2 = (1, 0), respectively (the first co-ordinate represents the ideal point on policy X , and thesecond coordinate the ideal point on policy Y ). In thissituation the Prime Minister has perfectly aligned prefer-ences with m1 on policy X, (both the Prime Minister andher minister would like the policy outcome to be as closeas possible to the origin) whilst, analogously, on policy Y,the Prime Minister and m2 are perfectly aligned.

Under these circumstances, and given any underlyingvalue of �, the Prime Minister can strategically appointher ministers so that ministers reveal their informationtruthfully. Consider a situation where m1 is appointed tothe department that has full jurisdiction over policy X ,so that his assignment is A1 = (1, 0), or any proportionalvector to this one, and agent 2 has full jurisdiction onthe second policy dimension so that he reports on A2 =(0, 1). Now imagine that m2 truthfully reveals her infor-mation to the Prime Minister (so that s2(�) = �2). Armedwith this information the Prime Minister will implementa policy (y2 = −�2) such that x2 = 0. In order to com-pute Minister 1’s best response to truthful revelation byminister 2 we can draw the indifference curve tangentto his assignment: the point of tangency coincides withthe ideal point of the Prime Minister. Thus minister 1delivers a report that yields a policy outcome x1 = 0. Ina truthful equilibrium, the minister reports s1(�) = �1

and the Prime Minister implements y1 = −s1(�). In thisexample the Prime Minster elicits all the information rel-evant to full implementation of her agenda: si(�) = �i

for mi is a best response for minister i when the otherminister reveals her information truthfully. It remains tobe shown that this is in fact part of a (perfect Bayesian)equilibrium.

Proposition 1. When ministerial responsibilities co-incide with policy dimensions and each minister’s assign-ment is orthogonal to his bias then there is an equilibriumwhere each minister reports truthfully the state of the worldgiven his assignment. The Prime Minister believes these

statements, and the policy that is implemented yields anoutcome coinciding with the Prime Ministers ideal point.

This first result shows that, without specifying theagents’ messages nor the response of the Prime Ministerto these messages, there is an equilibrium in which thepreferred policy of the Prime Minister is implemented.10

One such equilibrium is both truthful and fully reveal-ing .11

Allocating Portfolios and AssigningMinisterial Responsibilities

The results of the previous section reveal conditions un-der which cabinet selection acts as an instrument allowingthe Prime Minister to implement her agenda. Of course,there are limitations to the use of this tool. A Prime Min-ister may be forced to select on some individual trait otherthan the political preferences of her appointee—for ex-ample, talent, experience, or following in the party—andmay find that those best able to serve under her do notshare her political opinions.12 This might suggest thenthat the Prime Minister’s position is weakened. Indeedthe view that a Prime Minister’s power is both limitedand contextual due to restrictions on her ability to ap-point is commonly held.

This viewpoint overlooks the fact that the Prime Min-ister has other instruments at her disposal, and that theiruse may also influence the policies that are implemented.In particular she can decide which policies form part ofa minister’s jurisdiction and the type of proposals a min-ister can make. In the previous section we looked at asituation where assignments are aligned with the policyaxis and so a department is the only one with jurisdictionin a given policy area. Although analytically convenient,as we have seen, usually there is some overlap in the

10 As usual in these environments there are many more equilibria(e.g., a babbling equilibrium where no information is revealed andthe messages are never used by the Prime Minister).

11 As noted earlier, there may be other fully revealing equilibria(not truthful) where ministers systematically overstate the truestate of the world (si(�) = �i + �), but where the Prime Minister,taking such behavior into account, implements the policy (y(s) =−(s1 − �, s2 − �)). When the Prime Minister is able to appoint aminister whose bias is orthogonal to the jurisdiction, then she canobtain full information and so implement her preferred policy.

12 An alternative explanation is that the Prime Minister prefers tohave her opponents in the cabinet. John Major was unwilling tosack three staunch opponents of his policies arguing that “we don’twant another three bastards out there. What’s Lyndon Johnson’smaxim? . . . ” Johnson had famously declined to sack FBI directorEdgar Hoover on the basis that “it’s probably better to have himinside the tent pissing out than outside pissing in.”


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53


jurisdictions of different departments. Figure 1 depicts asituation where the minister’s policy bias relative to thatof the Prime Minister is given by m1 and the assignmentA1 involves both policy X and policy Y . Recall that thePrime Minister’s ideal policy lies at the origin and so inthis example the minister’s bliss point is to the north-eastof that point. Ideally, from his perspective, the minis-ter would recommend a policy that is greater than pm∗

on both policy dimensions. Suppose however, that theminister’ assignment is given by A1: then he must ac-knowledge a trade-off in which he can increase X only bydecreasing Y . A natural way to think of this trade-off re-gards policies over distribution, where X and Y involvespending on particular policies and/or targeted distribu-tion to specific constituencies. For example, a report onA1 to the northwest of the origin ties an increase in spend-ing on policy Y to a decrease in spending on policy X ,relative to the Prime Minster’s ideal point; the oppositespending pattern is implied by a report to the southeast ofthe origin. Thus, although relative to the Prime Minister,the minister would like to spend more on both policies(constituencies), he is forced into a trade-off between thetwo. The Prime Minister has the power to determine thistrade-off by defining his minister’s brief. In our modelthis is achieved by determining the slope of A1. She willdo so optimally given her knowledge of the minister’sbias. We are now ready to show that in any fully revealingequilibrium (in which the Prime Minister implements herpreferred policy) each minister’s assignment needs to beorthogonal to his own bias.

Lemma 1. Fix the ideal points of ministers and allowthe Prime Minister to choose their assignment. In a fullyrevealing equilibrium, a ministers assignment is orthogonalto his bias and not affected by the ideal point of the remainingcabinet ministers. Multiplying a minister’s bias by a constantdoes not change his assignment.

The implication of this result is that, when the PrimeMinister is constrained to appoint a minister with a givenand known bias then she can always define a minister’sresponsibilities assign in such a way that he reports truth-fully. This result is not affected by the size of the minister’sbias relative to the Prime Minister’s ideal point, nor thedistribution of ideal points in the cabinet. The followingproposition shows that a set of orthogonal assignmentsform part of a fully-revealing perfect-Bayesian equilib-rium.

Proposition 2. Assume that the biases of the ministerswith respect to the the ideal point of the Prime Minister arelinearly independent. Allow the Prime Minister to choose

ministerial assignments. She then elicits full informationfrom her ministers and so can fully implement her policyagenda.

A technicality in the wording of the proposition de-serves further attention: the biases of the ministers withrespect to the ideal point of the Prime Minister need tobe linearly independent . By Lemma 1 we know that ina fully revealing equilibrium each assignment needs tobe orthogonal to its minister’s bias. If biases are linearlydependant, assignments would coincide and the PrimeMinister would no longer be able to infer the true state ofthe world in our two-dimensional policy space. Instead,linear independence ensures that both assignments spanthe whole policy space and the Prime Minister is thenable to illicit all information she needs to implement herpreferred policy.

According to one prominent and widely held view,the Prime Minister’s control over policy is limited by theneed to include ministers who (1) do not share her policypreferences and (2) are either too senior, talented, or wellsupported in the party, to be overlooked.13 Our analy-sis suggests that these are necessary though not sufficientconditions. According to our view the Prime Minister isconstrained, that is she is unable to fully implement heragenda, only when each of the following conditions holdwith respect to a particular minister: the Prime Minister isforced to appoint the minister even though the ministerspreferences are not aligned with her own; the ministerhas veto power over his/her appointment to a particularministry; the minister has veto-power over any changesto his assignment; in such circumstances, the minister’sreport cannot yield implementation of the Prime Minis-ter’s preferred policy. In all other situations, even when thePrime Minister is constrained to appoint ministers whosepreferred policies are very far from her own, she neverthe-less is able to implement her desired policies. Moreover,and perhaps surprisingly, this does not depend on the as-sumption that the Prime Minister implements policy aswe show in the following corollary to proposition 2.

Corollary to Proposition 2. When the configurationof tasks is optimally designed from the Prime Minister’sperspective, the Prime Minister is strictly indifferent betweenchoosing policy herself or fully delegating the task to herminister.

The implication of this result is stark. As long asthe Prime Minister has full control over assignment, her

13 King (1994) argued that a few “big beasts of the jungle” main-tained such stature as to be able to impose their views on policyoutcomes in their departments (see also Laver and Shepsle 2000).


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53


influence is undiminished even when she allows policyto be chosen and implemented by her ministers. Thuswhat Lupia (2003) has referred to as the “perils of delega-tion” in parliamentary democracies are avoided so longas the Prime Minister has full control over the allocationof ministerial tasks. When policy decisions are delegatedto ministers they implement precisely those policies thePrime Minister would implement in the event that shehad full and perfect information.

As we noted earlier our model is related to the clas-sic application of the cheap talk literature to Congress(Gilligan and Krehbiel 1987). There it is well known thatthe legislative body can extract more information whencommittee members have biases that are small relativeto the Floor median. Do the insights from the Congres-sional literature on information transmission carry overin our multidimensional setting more suited to Westmin-ster? Here we observe that our results do not hinge on thedistance of ministers ideal points from the preferred out-comes of the Prime Minister. Given any bias, however big,the Prime Minister can design a ministerial brief such thatthe minister will report truthfully and given the optimalassignments to all cabinet members the Prime Ministerextracts all relevant information. In fact the Prime Minis-ter is never worse off when the cabinet is more diverse.

Three A’s in a Large Cabinet

In the remainder of the article we consider how robustour findings are to different assumptions about the insti-tutional environment. Thus far our analysis has relied ona two-member cabinet. It is natural to consider the impli-cations of analyzing a fully fledged cabinet consisting ofan arbitrary number of ministers deciding over multiplepolicy issues and so extend our model to consider a mul-timember cabinet with n > 2 distinct policy issues relatedto the same number of government departments.

Proposition 3. Consider a situation where the numberof policy issues decided by the government is n > 2 so thatthe cabinet consists of n ministers with fixed ideal points.Allowing the Prime Minister to choose the assignment ofeach of her ministers, and assuming that the biases of at leasttwo ministers with respect to the ideal point of the PrimeMinister are linearly independent, the Prime Minister elicitsfull information from her agents and so can fully implementher policy agenda.

Perhaps surprisingly, when moving to the generalcase we can use less restrictive assumptions about theideal points of the ministers. In particular, for n > 2, we

FIGURE 2 Portfolio AllocationWhen n = 3

Polic

yZ

Policy X

Policy Y

m1 m2

m3

only need two ministers’ ideal points to be linearly inde-pendent (i.e., the orthogonal hyperplanes to their biasesspan the whole policy space). This can be shown with athree minister example as illustrated in Figure 2. Herenote that the ideal points of m1 and m2 are linearly de-pendent: both ministers agree with the Prime Minister ontwo of the three policy dimensions. Following our earlierlogic, it is straightforward to see that the Prime Ministercan elicit all of the relevant information when assigningjurisdiction over policy X to m3, jurisdiction over policy Yto m1, and jurisdiction over policy Z to m2; each ministerneeds to report on the assignment formed by the policyaxis. This is not the only way in which the Prime Minis-ter can organize her government and be in a position toimplement her agenda: she could, for instance, obtain thesame outcome by switching the jurisdictions of m1 andm2. In fact she could give overlapping jurisdiction on pol-icy Y and Z as long as these were linearly independent.We note that in such a situation both minister acquireinformation on policies Y and Z but not on X , whereasminister 3 only acquires information on policy X . Thisshows that in dimensions n > 2 a minister’s expertise canbe limited to policies over which he has jurisdiction. Thusthe Prime Minister, as part of the assignment process, en-dogenously determines the expertise of her ministers.

Adjusting Assignments

A key innovation in our analysis is that we consider theassignment of ministerial departments as being part ofa Prime Minister’s strategic plan. As we have seen, whenthe Prime Minister can create departments with overlap-ping jurisdictions and optimally assign tasks then she canobtain her desired outcomes even when constrained with


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53


regard to the appointments she makes to cabinet. Mostmodels of government formation do not consider this as-pect. In the portfolio allocation models, for example, eachminister’s jurisdiction involves a single policy dimension.An interesting theoretical question then is the extent thatthe optimal assignment from the Prime Minister’s per-spective deviates from a status quo where ministers’ as-signments are given by the policy axis as in Figure 1. Ourfocus is in the angular move �, defined as the necessaryadjustment making a minister’s assignment orthogonalto his bias, when starting from this status quo. Our inter-est in this parameter can be motivated from the followingthought experiment. Imagine that ministers enter gov-ernment with the expectation that they will be given fullcontrol over a well defined portfolio with jurisdictionover a given policy area (i.e., the policy axis X in Figure 1)How much must the Prime Minister adjust this portfolioto correct for the bias of her minister and in order to alignhis incentives with her own. We know that, in any fullyrevealing equilibrium, the Prime Minister will adjust un-til Ai is orthogonal to mi (as illustrated in figure 1 for i =1 and A = 1). Thus, for example, when mi = (1, 1), themove is 45◦.

To explore our question we ask how does � respondto the size of government.14 The political implications ofincreasing the size of the government are the following:on the one hand, an increase in the size of government im-plies an increase in the number of possible assignments,and this is associated with an increase in the complex-ity of the Prime Minister’s assignment problem; on theother, an increase in the size of government increases thepossibility, that for a given set of ministers, and on anyparticular assignment, the Prime Minister can find a min-ister with an ideal point that is orthogonal to the statusquo assignments in which case he need make no adjust-ments to that portfolio. We look at the extreme case wherethe Prime Minister has no appointment power, thus wetreat each minister’s ideal point as a random draw froma known distribution. We assume that the size of theadjustment(the angle �)that produces an assignment or-thogonal to a minister’s bias is independently drawn froma distribution F with density f . We call AAn as the averagesize of adjustment when assigning n ministers. We analyzehow this average adjustment responds to increasing thesize of government (i.e., as n grows large).

Proposition 4. When there is a strictly positive proba-bility that the adjustments required to existing portfolios are

14 Recall that we need as many ministers as policy dimensions sothat in our analysis an increase in the number of policy dimensionsis equivalent to an increase in the size of government.

FIGURE 3 Average Adjustment ofReorganizing Assignments

0 7 14 21 280

10

20

30

Size of Cabinet

Ave

rage

Adj

ustm

ent

(ang

ular

mov

e)

arbitrarily small (i.e., F(�) > 0 for all � > 0), the averageadjustment of the optimal assignment tends to zero as thenumber of policy dimensions increases (limn→∞AAn = 0).

In the limit, as the size of the government grows large, thenecessary adjustments from the status quo provisions inorder for the Prime Minister to implement her agenda goto zero. Pushing further we analyze the same parameterin commonly sized cabinets (i.e., n just below 30). An im-mediate concern is how fast the average adjustment AAn

converges to zero and whether, in commonly sized cab-inets these are also negligible. We analyze this questionnumerically by assuming that there are n ministers whosebias with respect to the Prime Minister on each policydimension is drawn from a normal distribution with zeromean and unit variance. As for our our earlier results, sta-tus quo jurisdictions are the coordinate axis. We computethe minimum angular move so that each assignment isorthogonal to the bias of each minister. For each of the500 simulations we run, we find the optimal assignmentthat minimizes the size of the required adjustment. Wecompute the average adjustment among all our simula-tions. Full details of our algorithm can be found in theappendix, here we concentrate instead on our substantiveresults represented by Figure 3.

The upper (red) line in Figure 3 shows the rate ofconvergence when the Prime Minister has no freedom toappoint who sits in her cabinet, but can make assignmentsin such a way that ministers will report truthfully. We seethat, as the number of jurisdictions increases, the averageadjustments to the status quo fall rapidly toward zero.15

15 Here we depict the average results from 500 simulations.


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53


When n = 2 the (average) necessary angular move awayfrom the status quo jurisdictions is � = 29.832◦. This fallsto � = 0.722◦ as the government size increases to n =29.16 The lower (gray) line in Figure 3 shows a situationwhere the Prime Minister has some discretion over ap-pointments and has twice as many ministerial options asjurisdictions. As might be expected, convergence is muchfaster as under these circumstances the Prime Ministercan seat in her cabinet those ministers with the smallestbiases. These graphs provide an indication as to how theinstruments at the Prime Minister’s disposal, namely herability to appoint ministers, allocate portfolios, and as-sign tasks, interact to allow her to implement her agenda.Moreover they show that for these particular parameters,the adjustments required to the status quo assignments(i.e., those that coincide with the policy axis) in a reason-ably sized government are negligible.

Changing the InstitutionalEnvironment

Our results are based upon a somewhat stylized and re-duced form view of the Westminster Model. Here weconsider how robust are our findings to the addition ofsome institutional detail. First we consider what wouldhappen if the Prime Minister were to be held accountablevia an electoral mechanism, that is she could be replacedby some section of the polity. Next we consider alter-native views of the cabinet: in one, ministers deliberateover outcomes; in another they are able to collude be-fore providing their reports to the Prime Minister. Finallywe consider a world where ministers are distinguished bytheir expertise as well as by their policy preferences.

Choosing the Prime Minister

Thus far we have not considered any mechanism by whichthe Prime Minister can be held to account for the orga-nization of her government and the decisions that arereached given her organizational strategy. In some sensewe might view the Prime Minister as the agent of her partywho is endowed with the powers to appoint ministers, al-locate them to portfolios, and assign tasks. The questionthen arises: which agent would the party choose? Our keyresults reveal that when the Prime Minister has controlover assignments, even though she may be constrainedwith regard to appointments, she can implement poli-cies as if she were fully informed on the relevant issues.

16 In all our numerical simulations, total costs also go to zero.

An implication of these findings is that it straightforwardto extend our analysis to a world in which the PrimeMinister were selected by the party of some subset ofits membership. For example, we could extend our anal-ysis to a world where there was an open entry contestto become the Prime Minister, in which eligible citizens(however defined) cast their votes between competingcandidates. A straightforward application of the citizen-candidate framework (Besley and Coate 1997), yields thefollowing: when voters anticipate the final implementedpolicies, there is an equilibrium in which at least onecandidate stands for the office of Prime Minister; theequilibrium is Pareto efficient; if there exists an individ-ual amongst the polity whose ideal point is a Condorcetwinner then that citizen is elected unopposed. Thus thereis a normative justification for providing a Prime Ministerwith the tools to implement her agenda.

Cabinet Deliberations

One objection to our analysis, with its focus on allocationand assignment, is that a Prime Minister might not needsuch powerful instruments at her disposal in order to im-plement her agenda. Instead she could use cabinet delib-erations as a mechanism for learning the true state of theworld before making policy decisions. One way she coulddo this is to have ministers report everything they knowrather than limiting the type of proposals that they canmake. Then any discrepancy between their reports wouldimmediately reveal that at least one minister did not re-port truthfully. In such a world, Ambrus and Takahashi(2008) show that there is a fully revealing equilibrium,so long as off the equilibrium path actions can be appro-priately punished. Applied to our world the intuition isstraightforward: when the Prime Minister can commit toimplementing a policy commonly disliked by her min-isters in the event their statements do not match, thenministers’ willingness to conceal information is avoided.This logic yields an outcome—full implementation of thePrime Minister’s agenda—that is observationally equiva-lent to ours.

We provide some reasons for why the mechanismthat we highlight offers a more compelling account. Themain reason we highlight is that a model that focussedon cabinet deliberations, unlike ours, can not accountfor observed changes to ministerial assignments that aredue to government reorganization. A further argumentrelies on the theoretical robustness of the equilibriumof our model. Suppose that, instead of perfectly observ-ing �i, a minister’s observation of the state is noisy. Aslong as such noise is of a particular type–independentand symmetrically distributed across the various policy


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53


FIGURE 4 Collusive AgreementsDo Not Constitute anEquilibrium

J1J2

Jc Policy X

Policy Y

m1

m2

xc

xc

dimensions—equilibria of the sort we have constructedin Proposition 2 remain.17 This is not the case, however,for the truth-telling equilibrium that can emerge due tocabinet deliberation. To see why, note that when reportscontain error the Prime Minister is unable to draw com-parisons between them and so is unable to punish devia-tions accordingly.

Collusion Between Ministers

A final theoretical concern is collusion-proofness. Askingministers to report on the whole dimensionality intro-duces scope for collusion between ministers. They mayjointly agree to report in a way that yields a final outcomecloser to their bliss point. To see this recall that the equi-librium constructed in Proposition 2 allows each ministerto determine the coordinate on his own jurisdiction. Thesituation described there may, however, induce minis-ters to collude and thereby arrive at mutually beneficialoutcomes. Figure 4 depicts a situation where they do so.Figure 4 depicts a policy outcome xc that lies in the thePareto set of m1 and m2. Given the declaration of minis-ter 1, minister 2 can send any message such that the finalpolicy outcome is anywhere along Jc (orthogonal to min-ister 2’s bias through policy xc). Note that minister 2 has aprofitable deviation: he can choose a report such that thefinal policy is xc . Thus collusive agreements will prove un-stable in the absence of an enforcement mechanism. Westate this formally in a note to the Proof to Proposition2 in the appendix. Whilst the equilibrium constructed

17 This follows from the analysis of Battaglini (2004); Levy andRazin (2007) show the limitations of the fully revealing equilibriumwhen the signals received on each dimension are not independent.

here is collusion-proof in the sense that, although Paretoimprovements from the ministers’ perspective are alwayspossible, they do not form part of an equilibrium in theabsence of a commitment mechanism, it remains an openquestion whether ministers are able to forge an agreement(an enforceable side-contract a la Laffont and Martimort1997) that avoids unilateral deviations.

Expertise

A Prime Minister may consider motives other than thedesire to counter ministers biases when organizing hergovernment. In particular, she may wish to account fora minister’s expertise when allocating his portfolio. Untilnow we have considered only a world where all ministersare experts (they are perfectly informed) on the issuesover which they have jurisdiction. Here we consider aworld where this is no longer so for all ministers: someministers are better informed on some issues than areothers. The question we ask is whether the Prime Ministercan organize her cabinet so that (in equilibrium) sheobtains truthful reports from her ministers.

When potential cabinet members have a known biason a policy where their expertise lies, the Prime Ministerneeds to trade-off receiving a biased report from an anexpert, or a noisy report (on an assignment orthogonalto the sender’s bias) from a relatively less well-informedminister.18 In this circumstance the Prime Minister willgenerally be unable to aggregate information efficiently.To illustrate this point we develop a numerical examplewhere the Prime Minister delegates the implementationof policy to two ministers on Ai.19

We consider a situation with a two-dimensional pol-icy space where two ministers have biases (m1, 0) and (0,m2). The true state of the world is unknown but its priordistribution is common knowledge, �i ∼ N(0, �2) for i =1, 2 and �1 and �2 are independent. Minister 1 perfectlyobserves the true state of the world in the first dimen-sion but privately observes a noisy signal on the seconddimension: s1 ∼ N(�2, � 2). By contrast, minister 2 can

18 When bias and expertise are negatively (and perfectly) correlated,the previous analysis applies: by assigning an orthogonal assign-ment to a minister’s bias, the Prime Minister not only avoids thebias in her report but assignments coincide with the dimensionwhere ministers are experts.

19 Adding expertise to our primitive model with strategic infor-mation transmission in a multidimensional model (instead of thePrime Minister delegating the implementation of policies) is nottrivial. The problem lies in characterizing equilibrium reports whenjurisdictions are not orthogonal: using a similar rational to the onein Crawford and Sobel (1982), we know that the message space willbe partitioned; characterizing those partitions in a multidimen-sional space remains an open question in the theoretical literature.


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53


perfectly observe the second dimension but privately ob-serves a noisy signal in the first one: s2 ∼ N(�1, � 2) (bothsignals are independent).Upon receiving the relevant in-formation, ministers implement a policy constrained bytheir ministerial brief: (A1, 1) for minister 1 and (1, A2)for minister 2. In other words, minister i needs to decidea real value ri and the overall implemented policy is equalto r1 · (A1, 1) + r2 · (1, A2).

In the appendix we provide step by step calculationsproviding equilibrium declarations of ministers given anypair of assignments. We then look at the optimal assign-ment by the Prime Minister when taking into account theministers’ best responses. In order to illustrate our pointwe give particular values to the biases and the variance ofthe signals (we consider the case where biases and vari-ances of posterior beliefs on the true state of the worldare all equal to one, m1 = m2 = 1 and var(�i | s j ) = 1 fori �= j). We find that the (unique) optimal assignment isnot orthogonal to the ministers’ biases. This result showsthat the Prime Minister will prefer extracting better in-formation by utilizing a minister’s expertise even whenthis implies that the assignments are not orthogonal tothe ministers’ biases. This of course implies that ministerswill no longer report truthfully (the ministers’ indiffer-ence curves are no longer tangent to their jurisdictionsat the origin—the preferred policy of the Prime Minis-ter) and so the final policy implemented will not be thePrime Minister’s ideal one. Analyzing the way in whichthe Prime Minister modifies assignments according to therelative expertise of her ministers and their biases consti-tutes ongoing work.

Empirical Consequences andImplications of Our Model

Before concluding we provide a brief overview of ourresults and discuss their empirical relevance. We havestudied an abstract model of government formation thathighlights the importance of jurisdictional assignmentsas part of a Prime Minister’s organizational strategy. Animmediate empirical payoff of our model is that we canuse the fully revealing equilibrium described in Proposi-tion 2 to derive a number of comparative static results thatshow how jurisdictions change according to differencesin the composition of cabinet (according to membersideal points). It is straightforward to show that, when thePrime Minister is constrained to changing assignments,then any exogenous shift in a minister’s bias will lead toa change in his (orthogonal) assignment. It is difficult toconstruct an empirical test of these claims. In particular,

although some steps have been taken to put together datathat details how jurisdictions have altered in the Britishcase, we as yet have no independent measures of min-isterial ideal points. Since ministers are bound by theconvention of collective responsibility, and in any eventpartisan votes are enforced by government whips, we can-not obtain measures of variance in ministers ideal pointsthat would allow us to test our ideas.20 We note of coursethat any model (or claim or conjecture) about how as-signments varied with the ideal points of ministers wouldface the same common problem: we can not always obtainexogenous variation on the variables of interest; and, asfamously pointed out by Krehbiel (1993), this is in par-ticular the case where the variable of interest concerns thepreferences of political actors.

Of course, it would be desirable to directly test someof the implications of our model. It is possible to gener-ate (uncontaminated) data from a suitable experimentalsetting. Here we discuss ongoing work that provides thefirst test of our theory. In that work we analyze whethera subject acting as Prime Minister can offset the bias of asubject acting as minister by allowing the latter to choose(implement a policy) on a particular set of outcomes. Wesimplify our model and focus on the relationship betweenthe Prime Minister and a single minister (by assuming anonstrategic second minister). We allow the subject actingas Prime Minister to choose among a menu of ministe-rial briefs (each corresponding to a different trade-off).Knowing the true state of the world, the subject acting asa minister then chooses a final allocation from the menuassigned to him. This simple experimental design allowsus to analyze whether assignments are made optimallyand the “minister” responds truthfully. More elaborateexperiments should introduce the strategic interactionthat arises between two ministers and on aspects such ascollusion or expertise.

Given the problems of measurement and identifica-tion that arise when exploring the phenomenon at hand,our formal model does proves useful and nonobvious in-sights into the consequences of the organizational powersof the Prime Minister which we elaborate upon here. Thefirst key insight—one that we believe has been overlookedby analysts who have focussed entirely on the composi-tion of cabinets and turnover of ministerial positions—is that the allocation of tasks is a powerful tool for the

20 Some recent studies have used MPs positions on nonwhippedvotes to test party strength and to provide an indication of theaverage dispersion of ideal points amongst groups of MPs (Dewanand Spirling 2010). Such data is not helpful, however, since werequire a measure of the distance between the Prime Minister andher Minister on those policies over which she has jurisdiction; thenumber of unwhipped votes in that category are likely to be smalland the sample unrepresentative.


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53


chief of the executive to have at her disposal. Contrary toconventional wisdom we show that the Prime Minister’sability to implement her desired policies is not necessar-ily diminished when she is unable to fully determine whosits in her cabinet; when she is able to assign ministerialjurisdictions and responsibilities then she can still imple-ment her agenda. Would the Prime Minister neverthelessprefer a cabinet in which the views of her colleagues arealigned with her own? Our model shows that, whilst thisview may be correct in a unidimensional world, wherethe ministers acted as either veto players or agents of thePrime Minister, such an inference is incorrect in a multi-dimensional setting in which ministers are the providersof information.

A further empirical insight stems from our analysis ofrelations between the Prime Minister and her ministers.One of our key results is that when the Prime Minis-ter designs her government optimally, then she is strictlyindifferent between implementing policy herself or hav-ing her minister do so. The conventional view of Britishpolitics is that ministers are not autonomous: Prime Min-isters regularly intervene in the running of departmentsand there is no constitutional enshrined protection forministerial autonomy as provided under German BasicLaw, for example. Our analysis allows us to explore a rele-vant counterfactual: what would happen if ministers werefree to implement their desired policy, as the principal ofministerial autonomy implies, though are constrained toact only on those policies over which they are grantedjurisdiction and according to the responsibilities definedby the Prime Minister? We show then that the same pol-icy outcomes prevail irrespective of whether the PrimeMinister or her minister implements policy.

Conclusion

Although the analysis of strategic information transmis-sion has been central to the formal literature on Congres-sional committees and their relationship to the U.S. Houseof Representatives, these models have not, until now, beenapplied in a parliamentary setting. We analyze how minis-terial appointments, responsibilities, and the structure ofgovernment departments, can be adapted strategically bya Prime Minister who aggregates information providedby (biased) ministers who are experts in their brief. In as-signing a ministers’ responsibilities optimally, the PrimeMinister is able to extract all of the relevant informationso that she can implement her preferred policies. In fact,once she has organized her government optimally, thePrime Minister is indifferent between implementing pol-icy herself or delegating this task to her ministers. Perhaps

surprisingly this result does not depend on the extent ofministers’ biases relative to the Prime Minister. We alsoprovide an example where ministers have exogenouslygiven expertise that is correlated with their biases andshow that then the Prime Minister is unable to imple-ment her desired policies.

We end by suggesting other avenues for future re-search on this topic. Although our model captures someof the critical features of Westminster democracy, we usesimplifying assumptions. In our basic model civil ser-vants are both perfectly informed and perfect agents ofministers, and so we abstract from the agency problembetween a Prime Minister and her ministers and the in-centives required for a bureaucrat to obtain information(Bawn 1995). However our model does extend to thebasic agency problem between a minister and her civilservants. Indeed the permanency of officials in most par-liamentary systems means that the assignment of tasks islikely to be used by a ministerial principle to extract infor-mation from her agents. Whilst our model provides usefulinsights to Westminster democracy, it abstracts from is-sues of party competition and coalition formation andthe basic framework developed here could be extended toinclude variations on this institutional architecture. Nev-ertheless, as our earlier example of Telecoms regulationin the United Kingdom (page 8) makes clear, our insightscarry over to coalition scenarios: in that case the PrimeMinister was unable to fire the minister responsible, orallocate him a different portfolio, due to the constraintsof the coalition agreement; but obtained a more desirableoutcome by reassigning ministerial tasks.

Appendix

Proof of Proposition 1. Assignments are the coordi-nate axis (A1 = (1, 0) and A2 = (0, 1)) and the Prime Min-ister chooses two ministers with preferences m1 = (0, m2

1)and m2 = (m1

2, 0). We can show that there exists a truthfulfully revealing equilibrium where a minister with prefer-ences m1(m2) has jurisdiction on the first (second) policydimension. This equilibrium has the following features:each minister reports the true state of the world given theirministerial brief si(�)=�i, i =1, 2; the Prime Minister fol-lows the ministers’ advice in implementing policy so thaty(s1(�), s2(�)) = −(A1 · s1(�) + A2 · s2(�)) and, finally,the Prime Minister’s beliefs accumulate all mass on thejointly reported state of the world, �(s1(�), s2(�))(�) = 1.

We show that these strategies and beliefs con-stitute an equilibrium. The interim utility of minis-ter i is ui (y(s1(�), s2(�))) = −(−s1(�) + �1 − m1

i )2 −(−s2(�) + �2 − m2

i )2. Ministers want to send the report


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53


that maximizes their interim utility. Taking as given thebehavior of minister 2, the optimal behavior of minister1 is to report s1(�) = �1 (i.e., the prescribed behaviorin a truthful and fully revealing equilibrium). Minister2’s optimal behavior can analogously be proved. Beliefsare consistent with equilibrium behavior as they accu-mulate all mass on the true state of the world. Finally, thePrime Minister’s behavior is optimal given these beliefs:the Prime Minister implements a policy, y = −�, thatyields his preferred policy outcome x = (0, 0), and so hasno incentive to deviate. �

Proof of Lemma 1. Given minister j’s report, ministeri’s optimal report should lead to pm∗ when the equilib-rium is fully revealing. As can be observed in figure 1,this can only happen when minister i’s indifference curveover pm∗, is tangent to the set of policies from which hecan choose, i.e., his own assignment. Indifference curvesof quadratic utilities are circles, and any tangent line toa circle is orthogonal to the radius of the circle on thetangency point. This implies that the direction of the as-signment is orthogonal to the bias between the ministerand the Prime Minister, (mi − pm∗) · Ai = 0. It followsthat an assignment is orthogonal to a minister’s bias andthus is invariant with respect to changes in another minis-ter’s bias; and, multiplying a minister’s bias by a constantdoes not change the optimal assignment as the orthogonaldirection remains unchanged. �

Proof of Proposition 2. We show that when the PrimeMinister chooses orthogonal assignment to the minis-ters’ biases, agents report the true state of the world inthe new coordinate system induced by their assignments.The Prime Minister then holds beliefs that allow the im-plementation of her preferred policy. Consider two ar-bitrary bliss points m1, m2 ∈ R

2. Lemma 1 implies that,without loss of generality, we can restrict attention tobliss points of the form: m1 = (m1

1, 1) and m2 = (m12, 1).

Two orthogonal assignments read as A1 = (−1, m11) and

A2 = (−1, m12). It is useful to first express the true state

of the world in the new set of coordinates given by A1 andA2.21

A necessary and sufficient condition for this set ofequations to have a solution is that the biases need to belinearly independent. By solving these two equations wecan describe the truth-telling equilibrium strategies andbeliefs. In this equilibrium each minister reports the co-

21 We need to find x and y to solve x · A1 + y · A2 = �. That is, weneed to solve the following system of equations −x − y = �1 andxm1

1 + ym12 = �2.

ordinate of the true state of the world in their assignment:

s1 (�) = �2 + �1m12

m11 − m1

2

and s2 (�) = −�2 − �1m11

m11 − m1

2

.

In a truthful and fully revealing equilibrium, thePrime Minister follows her ministers’ advice and so imple-ments policy following the expression for y(s1(�), s2(�))in the proof of Proposition 1, and, as in that earlier result,her beliefs put all weight on the jointly reported state of theworld. In order to prove the optimality of the prescribedstrategies we compute the interim utility of minister 1given minister 2’s behavior:

u1(y(s1, s2(�)) = −(x1s1 + s2 (�) + �1︸︷︷︸

x1

− m11

)2

−(x2−s1m1

1 − s2 (�) · m12 + �2︸︷︷︸

x2

− 1)2

which we use to find the optimal response of the firstminister by computing the first order condition of theoptimization problem is. Its solution yields

s1

(1 + (

m11

)2) = 1(m1

1 − m12

)(1 + (

m11

)2)�2

+((m1

1

)2 + 1)�1m1

2

which is precisely the behavior prescribed above. Minister2’s optimal behavior is analogously proved. Beliefs areconsistent with equilibrium behavior as they accumulateall mass on the true state of the world. Finally, the PrimeMinister’s behavior is optimal given beliefs: the PrimeMinister implements the policy y = −� that yields herpreferred policy outcome x = (0, 0) , thus has no incentiveto deviate. �

Note (1) on Proof to Proposition 2: While assignmentsdo not depend on any other minister’s bias, equilibriumdeclarations do depend on the other minister’s assign-ments. Assignments will generally not be given by the pol-icy axis thus the new coordinates of the state of the world(i.e., the ministers declarations) depend on both minis-terial briefs. In equilibrium then, a minister takes intoaccount the (equilibrium) messages reported by otherministers. Aggregation of truthful messages yields the ex-pected final policy.

Note (2) on Proof to Proposition 2: By looking at theobjective function of minister 1 (analogously minister2), we can see that in a fully revealing equilibrium hisbest response depends linearly on the action of the otherminister which implies that there can be (at most) oneequilibrium. In other words, when the Prime Ministeroptimally assigns ministerial tasks, the minister cannot


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53


collude on an equilibrium different than the fully reveal-ing one.

Proof of Proposition 3. The rationale of lemma 1 stillapplies when n is larger than 2: in a fully revealing equi-librium assignments need to be orthogonal to the biases.However, whereas when n = 2 the orthogonal directionis uniquely determined, when n > 2 this is no longer thecase as there are now n − 1 orthogonal directions. Thisallows the Prime Minister to elicit full information when(at least) two ministers have linearly independent biases.To see this, consider the most extreme case where n − 1ministers have exactly the same bias and the nth ministerhas a bias that is linearly independent to the rest. We canchoose n − 1 assignments in the orthogonal hyper-planeof the n − 1 ministers and an orthogonal direction for thenth minister that is linearly independent to the previoushyperplane. This set of assignments is orthogonal to eachminister’s biases and spans the whole n-dimensional pol-icy space. Once we have determined this set of orthogonaljurisdictions we can follow the proof of proposition 2 andrewrite any point in the Euclidean space using the new setof coordinates. The coordinate in the direction of each as-signment is precisely the declaration of the minister thathas been given such ministerial brief. After receiving allministers’ declarations, the posterior beliefs of the PrimeMinister are concentrated on the true state of the worldand so she implements a policy that yields her preferredpolicy outcome. �

Proof of Proposition 4. Frenk, van Houweninge, andRinnoy Kan (1987) show that the asymptotic behavior ofthe expected average cost in a random assignment prob-lem is determined by that of the smallest order statis-tic when the costs are i.i.d. and their distribution func-tion F satisfies the following two near zero conditions:(1) limn→∞ F −1( 1

n ) = 0; and (2) F is of positive decrease

at 0 (i.e., ∃a ∈ (0, 1) : limx↓0F (x)

F (ax) > 1. This implies thatwhen both these conditions are satisfied the average costof the random assignment problem tends to zero. We canapply this rationale to the average adjustment the PrimeMinister needs to incur in the optimal assignment of tasks.

When there is a strictly positive probability that therequired adjustment is arbitrarily small, F(x) > 0 for allx > 0 and the distribution is atomless in 0 we have thatlimn→∞ F −1( 1

n ) = 0. Having a strictly positive probabil-ity of arbitrarily small realizations of the random variableimplies that there exists r > 0 (possibly very small) whereF ′(x) = f (x) is bounded and f (x) > 0 for all x ∈ (0, r).Thus, limx→0f (x) > 0 or the limit of the kth derivativewhen x tends to zero should be different from 0 for afinite k. In either case, by applying Hopital’s rule (possibly

repatedly) we see that condition (2) is satisfied. Given thatboth conditions are satisfied we know that the average ad-justment goes to zero as we increase the number of policydimensions.

When there is a positive mass on 0, we can apply theresults above simply by considering the adjustments to bex = (x + ε) where x is distributed according to F and ε isuniformly distributed in [0, r], where r > 0 is arbitrarilysmall. The previous argument now applies and we knowthat the the average adjustment of the optimal assign-ment when adjustments are augmented by ε can only behigher. �

Algorithm for Numerical Simulations

In our simulation we assume there are n citizens whosebias with respect to the Prime Minister on each policydimension is drawn from a normal distribution with zeromean and unit variance. Status quo assignments are thecoordinate axis (i.e., Ai = (0, . . . , 0, 1, 0, . . . 0)). Theminimum adjustment is the angular move that is requiredto make assignments Ai orthogonal to the bias of citizenj as �(mj , Ai). We compute � using the definition ofthe scalar product between two vectors, i.e., �(m j , Ai ) =90◦ − arccos(mi

j /||m j ||2).Once we compute the minimum adjustment that is

needed to make each germane assignment orthogonal toa citizen bias, we can apply the Hungarian algorithm (seeKuhn (1955)) to find the optimal assignment, i.e., theone that minimizes the average adjustment. We iterateour simulations 500 times and report the average resultsin figure 3 (the gray line in this figure corresponds to asituation with n policy dimensions and 2n citizens).

A Model with Expertise

There are two ministers with biases (m1, 0) and (0, m2).The prior distribution of the true state of the world is�i ∼ N(0, �2) for i = 1, 2 and �1 and �2 are independent.Minister 1 perfectly observes the true state of the world inthe first policy dimension but privately observes a noisysignal in the second one: s1 ∼ N(�2, � 2). Minister 2 per-fectly observes the second policy dimension but privatelyobserves a noisy signal in the first one: s2 ∼ N(�1, � 2)(both signals are independent). Upon receiving the rele-vant information, ministers need to implement a policyfollowing their ministerial brief: (A1, 1) for minister 1 and(1, A2) for minister 2. In other words, minister i needs todecide a real value ri and the overall implemented policyis equal to r1 · (A1, 1) + r2 · (1, A2).22

22 Our setting is equivalent to the case where the Prime Ministercan commit to using ministers’ reports in a predetermined way.


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53


The Prime Minister assigns tasks in order to maxi-mize his utility while taking into account that ministerschoose a policy that most benefits themselves. His maxi-mization program reads as follows:

maxA1,A2

−E ((r1 · A1 + r2 + �1)2 + (r1 + r2 · A2 +�2)2)

subject to

⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩

r1 ∈ arg maxr1 −E ((r1 · A1 + r2 + �1−m1)2

+ (r1 + r2 · A2 + �2)2)

r2 ∈ arg maxr2 −E ((r1 · A1 + r2 + �1)2

+ (r1 + r2 · A2 + �2 − m2)2)

After observing signal si, minister i’s expected valueon the true state of the world in the second policy dimen-

sion �j is E (� j | si ) = si �2

� 2+�2 (DeGroot 1970). By takingfirst-order conditions we find the optimal decision ofminister i:

ri = 1

1+ A2i

((mi −�i )Ai − E (� j | si )−E (r j )(A1 + A2)).

The equilibrium of the simultaneous game playedby the ministers requires the computation of minister i’sexpected value of minister j’s implemented policy: E(ri|sj ,�j) for i �= j. The equilibrium given the Prime Minister’sassignments is:⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

r1 = � − �1 A2

A1 A2 − 1+ A1m1

(1 + A2

2

) − A2m2 (A1 + A2)

(A1 A2 − 1)2 ,

� = s1�2

� 2 + �2

r2 = − �2 A1

A1 A2 − 1+ A2m2

(1 + A2

1

) − A1m1 (A1 + A2)

(A1 A2 − 1)2 ,

= s2�2

� 2 + �2

The first term in the policy implemented by eachminister captures the truthful (but noisy) aspect of hisaction. The second term captures the drift included intheir implemented policy; this drift exists as long as juris-dictions are not orthogonal to biases. The Prime Ministerobjection function can now be rewritten as:

−E ((r1 · A1 + r2 + �1)2 + (r1 + r2 · A2 + �2)2)

= −1

(A1 A2 − 1)2

((1 + A2

1

)Var(X) + (

1 + A22

)Var(Y )

+ A21 A2

2

(m2

1 + m22

) + A21m2

1 + A22m2

2

− 2A1 A2m1m2(A1 + A2))

where X = � − �2 and Y = − �1.23 This expressioncaptures the trade-offs the Prime Minister faces in the

23 E (X) = E (Y ) = 0, Var(X) = Var(Y ) = �2�2

�2+�2 , andCov(X, Y ) = 0.

presence of expertise. When ministerial briefs are orthog-onal to the biases (A1 = A2 = 0) the Prime Ministerutility is equal to (−Var(X) − Var(Y )); indeed, there isno bias in the report but the implementation of policyis noisy. Instead, when the Prime Minister’s assignmentscoincide with the dimensions where each minister hasexpertise (A1, A2 → ∞) her utility is (−m2

1 − m22); she

avoids the noise in the perception of the true state of theworld but implementation of policy is biased towards theministers preferred policies. When Var(X) = Var(Y ) =m1 = m2 = 1, the objective function of the Prime Minis-ter is (−2 − 2 A1+A2

(A1 A2−1)2 (A1 + A2 − A1 A2)). By analyzingthis function we find that it is minimized at A1 = A2 = xwhere x is the unique real root of (x3 − 4x2 + 3x − 4) –thevalue is approximately 3.4675. In this case, the objectivefunction takes a value −1.4192. Instead, when the PrimeMinister assigns orthogonal jurisdictions that coincidewith the policy axis the Prime Minister’s utility is equalto −2 (so, moving assignments away from the policy axisimplies an improvement of about 30%).

References

Ambrus, A., and S. Takahashi. 2008. “Multi-Sender Cheap Talkwith Restricted State Spaces.” Theoretical Economics 3(1):1–27.

Austen-Smith, D. 1993. “Information Acquisition and theOrthogonal Argument.” In Political Economy, Institutions,Competition, and Representation, ed. W. A. Barnett, M. J.Hinich, and N. J. Schofield. Cambridge: Cambridge Univer-sity Press, 407–36.

Austen-Smith, D., and J. Banks. 1990. “Stable Governmentsand the Allocation of Policy Portfolios.” American PoliticalScience Review 84(3).

Baron, D. P. 2000. “Legislative Organization with InformationalCommittees.” American Journal of Political Science 44(3):485–505.

Battaglini, M. 2002. “Multiple Referrals and Multi-dimensionalCheap Talk.” Econometrica 70: 1379–1401.

Battaglini, M. 2004. “Policy Advice with Imperfectly InformedAgents.” Advances in Theoretical Economics 4(1).

Bawn, K. 1995. “Political Control Versus Expertise: Congres-sional Choices About Administrative Procedures.” AmericanPolitical Science Review 89(1): 62–73.

Besley, T. J., and S. Coate. 1997. “An Economic Model ofRepresentative Democracy.” Quarterly Journal of Economics112(1): 85–114.

Burkhard, R., M. Dell’Amico, and S. Martello. 2009. AssignmentProblems. Philadelphia: SIAM.

Chester, D., and F. Wilson. 1968. The Organization of BritishCentral Government 1960-83. London.

Crawford, V. P., and J. Sobel. 1982. “Strategic InformationTransmission.” Econometrica 50(6): 1431–51.

DeGroot, M. H. 1970. Optimal Statistical Decisions. McGraw-Hill.


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53


Dewan, T., and D. P. Myatt. 2007. “Scandal, Protection, andRecovery in the Cabinet.” American Political Science Review101(1): 63–77.

Dewan, T., and A. Spirling. 2010. “Cohesive Government andStrategic Opposition ion Westminster Democracies.” Paperpresented to the annual meetings of the American PoliticalScience Association.

Frenk, J., M. van Houweninge, and A. Rinnoy Kan. 1987. “OrderStatistics and the Linear Assignment Problem.” Computing9(3): 165–74.

Gilligan, T. W., and K. Krehbiel. 1987. “Collective Decisionmak-ing and Standing Committees: An Informational Rationalefor Restrictive Ammendment Procedures.” Journal of Law,Economics, and Organization 3(2): 287–335.

Huber, J. D., and C. Martinez-Gallardo. 2008. “Replacing Cabi-net Ministers: Patterns of Ministerial Stability in Parliamen-tary Democracies.” American Political Science Review 103(2):169–80.

Indridason, I., and C. Kam. 2008. “Cabinet Reshuffles andMinisterial Drift.” British Journal of Political Science 38(4):621–56.

King, A. 1994. “Ministerial Autonomy in Britain.” In Cabi-net Ministers and Parliamentary Government , ed. M. Laver,and K. A. Shepsle. New York: Cambridge University Press,203–25.

Krehbiel, K. 1993. “Where’s the Party.” British Journal of PoliticalScience 23(2): 235–66.

Kuhn, H. W. 1955. “The Hungarian Method for the As-signment Problem.” Naval Research Logistics Quarterly 2:83–97.

Laffont, J.-J., and D. Martimort. 1997. “Collusion Under Asym-metric Information.” Econometrica 65(4): 875–911.

Laver, M., and K. A. Shepsle. 1996. Making and Breaking Gov-ernments: Cabinets and Legislatures in Parliamentary Democ-racies. New York: Cambridge University Press.

Laver, M., and K. A. Shepsle. 2000. “Ministrables and Govern-ment Formation: Munchkins, Players and Big Beasts of theJungle.” Journal of Theoretical Politics 12(1): 113–24.

Levy, G., and R. Razin. 2007. “On the Limits of Communicationin Multi-dimensional Cheap Talk: A Comment.” Economet-rica 75(3): 885–94.

Lupia, A. 2003. “Delegation and its Perils.” In Delegation andAccountability in Parliamentary Democracies, ed. K. Strøm,W. Muller, and T. Bergstrom. Cambridge: Cambridge Uni-versity Press, 33–54.

Martin, L., and G. Vanberg. 2004. “Policing the Bargain: Coali-tion Government and Parliamentary Scrutiny.” AmericanJournal of Political Science 1(48): 13–27.

Patty, J. W. 2009. “The Politics of Biased Information.” Journalof Politics 71(2): 385–97.

Strøm, K., W. Muller, and T. Bergstrom. 2003. Delegation andAccountability in Parliamentary Democracies. Oxford: Ox-gord University Press.

Thies, M. 2001. “Keeping Taps on Partners: The Logic of Del-egation in Coalitions Governments.” American Journal ofPolitical Science 45(3): 580–98.

Ting, M. 2002. “A Theory of Jurisdictional Assignments inBureaucracies.” American Journal of Political Science 46(2):364–78.

White, A., and P. Dunleavy. 2010. “Making and BreakingWhitehall Departments: A Guide to Machinery of Govern-ment Changes.” Institute for Government; LSE Public PolicyGroup, London.

Young, H. 1999. One of Us. London: Pan Books.

Dispatch: May 4, 2011 CE: N/A Journal MSPNo. No.ofpages...

Documents

Transcript of Dispatch: May 4, 2011 CE: N/A Journal MSPNo. No.ofpages...