Dahl Power

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Dahl, Robert A., The Concept of Power , Behavioral Science, 2:3 (1957:July)p.201

TH ON EPT OF POWER

by Robert A Dahl

Department of Political Science, } ale Cniversity

What is power ? Most people have an intuitive notion of whatit means. But scientists have not yet formulated a statement of theconcept of power that is rigorous enough to be of use in the systematic study of this important social phenomenon. Power is heredefined in terms of a relation between people, and is expressedin simple symbolic notation. From this definition is developeda statement of power comparability, or the relative degree ofpower held by two or more persons. With these concepts it ispossible for example, to rank members of the United States Senateaccording to their power over legislation on foreign policy andon tax and fiscal policy.

T H T some people have more power thanothers is one of the most palpable factsof human exi::;tenee. BeeauRe of this, theconcept of power is as ancient and ubiquitousas any that social theory can boast. f theseassertions needed any documentation, onecould set up an endless parade of greatnames from Plato and Aristotle throughMachiavelli and Hobbes to Pareto andWeber to demonstrate tha t a large numberof seminal social theoriHts have devoted agood deal of attention to power and thephenomena a;-;sociated with it. Doubtlm.;;-; itwould be easy to show, too, how the wordand its Hynonyms are everywhere embeddedin the language of civilized peoples, often insubtly different wayH: power, influence, control, pouvoir, pui;-;sance, 1\Iacht, Herrsehaft,Gewalt, imperium, pote;-;ta:s, auetoritas,potentia, etc.

I shall spare the reader the fruits andmyself the labor of such a demom;tration.Reflecting on the appeal to authority tha tmight be made does, however, arouse twosuspicions: First following the axiom thatwhere there i smoke there i fire), if somany people at so many different times havefelt the need to attach the label power, orsomething like it, to some Thing they believe they have obserYed, one is tempted tosuppose that the Thing mm.;t exi:st; and notonly exist, but exiHt in a form capable of

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being studied more or less systematically.The second and more cynical suspicion isthat a Thing to which people attach manylabels with subtly or grossly different mean-ings in many different cultures and times isprobably not a Thing at all but manyThings; there are students of the subject,although I do not recall any who have hadthe temerity to say so in print, who thinkthat because of this the whole study of

power i:s a bottomle:ss swamp.Paradoxical as it may :sound, it i:s probably

too early to know whether the:se critics areright. For, curiously enough, the systematicstudy of power is very recent, precisely beeause it is only lately that serious attemptshave been made to formulate the conceptrigorou:sly enough for :systematic study fwe take a:s our criterion for the efficiency ofa s


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of systematic and empirical import, then wesimply cannot say whether rigorous definitions of the concept of power are likelyto be useful in theoretical systems with arelatively large pay-off in the hard coin ofscientific understanding. The evidence is

not yet in.I think it can be shown, however, thatto define the concept power in a way thatseems to catch the central intuitively understood meaning of the word must inevitablyresult in a formal definition that is not easyto apply in concrete research problems;and therefore, operational equivalents ofthe formal definition, designed to meet theneeds of a particular research problem, arelikely to diverge from one another in important ways. Thus we are not likely toproduce-certainly not for some consider

able time to come-anything like a single,consistent, coherent Theory of Power.We are much more likely to produce avariety of theories of limited scope, eachof which employs some definition of powerthat is useful in the context of the particularpiece of research or theory but different inimportant respects from the definitions ofother studies. Thus we may never getthrough the swamp. But it looks as if wemight someday get around it.

With this in mind, I propose first to essaya formal definition of power that will, Ihope, catch something of one's intuitivenotions as to what the Thing is. By formalI mean that the definition will presupposethe existence of observations of a kind thatmay not always or even frequently bepossible. Second, I should like to indicatehow operational definitions have been ormight be modelled on the formal one for

subject . The comments of Jacob Marschak on thispaper have also been most helpful. There are , ofcourse, approaches radically different from theone employed here and in the works mentioned

above. John R. P. French, Jr. (2), has developed amodel t h a t assumes a unidimensional continuumof opinion which can be measured with a ratioscale, and he defines the power of A over B(with respect to a given opinion) [to be] equal tothe maximum force which can induce on Bminus the maximum resisting force which B canmobilize in the opposite direction. Game theoryprovides still another approach. Cf. References 4,5, 9.

some specific purposes, and the actual orpossible results of these operational d, -nitions.

I should like to be permitted one liberty. :There is a long and honorable history at - ltached to such words as power, influence,

control, and authority. For a great manypurposes, it is highly important that adistinction should be made among them;thus to Max Weber, Herrschajt ist . einSonderfall von Macht, Authority is a specialcase of the first, and Legitimate Authoritya subtype of cardinal significance (11) .In this essay I am seeking to explicate theprimitive notion that seems to lie behindall of these concepts. Some of my readerswould doubtless prefer the term influence, :while others may insist that I am talkingabout control. I should like to be permittedto use these terms interchangeably whenit is convenient to do so, without denyingor seeming to deny that for many otherpurposes distinctions are necessary anduseful. Unfortunately, in the English language power is an awkward word, for unlike

influence and control i t has no convenient verb form, nor can the subject andobject of the relation be supplied with nounforms without resort to barbaric neologisms.

POWER AS A RELATION AMONG PEOPLE

What is the intuitive idea we are trying

to capture? Suppose I stand on a streetcorner and say to myself, I command allautomobile drivers on this street to driveon the right side of the road ; supposefurther that all the drivers actually do as I

command them to do; still, most peoplewill regard me as mentally ill if I insist thatI have enough power over automobiledrivers to compel them to use the right sideof the road. On the other hand, suppose apoliceman is standing in the middle of anintersection at which most traffic ordinarilymoves ahead; he orders all traffic to turnright or left; the traffic moves as he orders 1it to do. Then it accords with what I conceive to be the bedrock idea of power tosay that the policeman acting in this particular role evidently has the power to makeautomobile drivers turn right or left ratherthan go ahead. My intuitive idea of power,then, is something like this: has power

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P ujv) Probabili ty that u happenswhen v happens.

Then a relatively complete and concisestatement would be symbolized:

P a, xjA, w) P

P a, xlA, w) P2

Suppose now, that P 0.4 and P2 0.1.Then one interpretation might be: Theprobability that the Senate will vote toincrease taxes if the President makes anationwide television appeal for a taxincrease is 0.4. The probability that theSenate will vote to increase taxes if thePresident does not make such an appeal is0.1.

PROPERTIES OF THE POWER RELATION

Now let us specify some properties of thepower relation.1. A necessary condition for the power

relation is that there exists a t ime lag,however small, from the actions of theactor who is said to exert power to the re-sponses of the respondent. This require-ment merely accords with one s intuitivebelief that can hardly be said to havepower over a unless A's power attemptsprecede a's responses. The condition, ob-vious as it is, is critically important in theactual study of power relations. Who runs

the XYZ Corporation? Whenever thepresident announces a new policy, he im-mediately secures the compliance of the topofficials. But upon investigation it turnsout that every new policy he announces hasfirst been put to him by the head of the salesdepartment. Or again, suppose we had afull record of the times at which each one ofthe top Soviet leaders revealed his positionson various issues; we could then deduce agreat deal about who is running the showand who is not. A good bit of the mysterysurrounding the role of White House figureslike Sherman Adams and Harry Hopkinswould also be clarified by a record of thiskind.

2. A second necessary condition is, likethe first, obvious and nonetheless importantin research: there is no action at a dis-tance. Unless there is some connectionbetween and a then no power relation

can be said to exist. I shall leave the con-cept of connection undefined, for I wishonly to call attention to the practical sig-nificance of this second condition. In lookingfor a flow of influence, control, or power from

to a one must always find out whether .

there is a connection, or an opportunity for aconnection, and if there is not, then one needproceed no further. The condition, obviousas it is, thus has considerable practicalimportance for it enables one to screen outmany possible relations quite early in aninquiry.

3. In examining the intuitive view of thepower relation, I suggested that it seemedto involve a successful attempt by A toget a to do something he would not other-wise do. This hints at a way of stating athird necessary condition for the power :

relation. Suppose the chances are about one rout of a hundred that one of my students, ;.Jones, will read The Great Transformationduring the holidays even if I do not mentionthe book to him. Suppose that if I mentionthe book to him and ask him to read it, thechances that he will do so are still only oneout of a hundred. Then it accords with myintuitive notions of power to say thatevidently I have no power over Jones withrespect to his reading The Great Trans-formation during the h o l i d y s ~ tleastnot if I restrict the basis of my action tomentioning the book and asking him (po-litely) to read it. Guessing this to be thecase, I tell Jones that if he does not read thebook over the holidays I shall fail him inmy course. Suppose now that the chanceshe will read the book are about 99 out of100 Assume further that nothing else inJones's environment has changed, at leastnothing relevant to his reading or not read-ing the book. Then it fully accords with myintuitive notions of power to say that Ihave some power over Jones's holiday read-ing habits. The basis of my power is theright to fail him in his course with me, andthe means I employ is to invoke this threat.

Let me now set down symbolically whatI have just said. Let

D, w my threat to fail Jones if he doesnot read The Great Trans-formation during the holidays.

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o N c E P T OF P o w E R 205

(D, w)(J, .r)

Further, let

no action on my part..Jones reads The Oreal Transfor-

mation during the holidays.

Pt = P (. , x D, w) the probability that

.Jones will read TheGreat l ransforma-tion if I threaten tofail him.

pz P J, :riD, w) the probability that.Jones will read thebook if I do notthreaten to fail him.

Kow let us define the amount of power.To avoid the confusion that might arise fromthe letter p, let us use the symbol M (fromMacht) to designate the amount of power.Then, in accordance with the ideas set outin the illustration above, we define A's powerover a, with respeet to the response x, bymeans of w, as 111 or, more fully:

M ~ :w, x ) = P a, :rIA, w)

- P (a, x I A, w) = Pt - P2

Thus in the ease of myself and .Jones, 1f,my power over .Jones, with respect to reading a book during the holidays, is 0.98.

We can now specify some additionalproperties of the power relation in terms ofM:

a. If P = P2 then = 0 and no powerrelation exists. The absence of power is thusequivalent to ;;tatistieal independence.

b. M i;; at a maximum when Pt = 1 andp 2 = 0. Thi;; is roughly equivalent to sayingthat A unfailingly gets B to do somethingB would never do otherwise.

c. M is at a minimum when p1 = 0 andp 2 = l If negative values of are to beineluded in the power relation at a l l - andsome readers might object to the idea- then

we shall have a concept of negative power.This is not as foolish as it may seem, although one must admit that negative control of this kind is not ordinarily conceivedof as power. If, whenever I ask my son tostay home on Saturday morning to mowthe lawn, my request has the inevitableeffect of inducing him to go swimming,when he would otherwise have stayed home,

I do have a eurious kind of negative powerover him. The Legion of Decency sometimesseems to have this kind of power over moviegoers. Stalin was often said to wield negativepower over the actions on appropriations forforeign aid by the American Congress. Astudy of the Senate that will be discussedlater suggested that at least one Senatorhad this kind of effect on the Senate on somekinds of issues.

Note that the concept of negative power,and JYI as a measure, are both independentof the intent of A . The measure does, tobe sure, require one to a;;;;ign a positive andnegative direction to the responses of therespondent; what one chooses as a criterionof direction will depend upon his researchpurposes and doubtless these will often include some idea as to the intent of the actorsin a power relation. To take a specific ease,Pt could mean the probability that Congresswill defeat a bill if it is contained in thePresident's legislative program, and P2could mean the probability that Congresswill defeat such a bill if it is not contained inthe President's legislative program. Byassigning direetion in this way, positivevalues of l would be associated with whatordinarily would be interpreted as meaninga negative influence of the President overCongress. The point of the example is to

show that while the measure docs requirethat direction be specified, the intent of Ais not the only criterion for a;;signing direction.

POWER COMPARABILITY

The main problem, however, is not todetermine the existence of power but tomake comparisons. Doubtless we are allagreed that Stalin was more powerful thanRoosevelt in a great many ways, thatMcCarthy was less powerful after hiscensure by the Senate than before, etc.

But what, precisely, do we mean? Evidentlywe need to define the concepts more powerthan, less power than, and equal power.

Suppose we wish to compare the power oftwo different individuals. We have at leastfive factors that might be included in acomparison: 1) differences in the basis oftheir power, (2) differences in means ofemploying the basis, (:3) differences in the

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scope of their power, i.e., in type of response evoked, (4) differences in the numberof comparable respondents, and (5) differences in the change in probabilities, or M

The first two of these may be convenientlythought of as differences in properties of the

actors exercising power, and the last threemay be thought of as differences in theresponses of the respondents. Now it isclear that the pay-off lies in the last t h r e ethe responses. When we examine the firsttwo in order to compare the power of individuals, rulers, or states, we do so on thesupposition that differences in bases andmeans of actors are very likely to producedifferences in the responses of those theyseek to control.

As I have already indicated, much of themost important and useful research andanalysis on the subject of power concernsthe first two items, the properties of theactors exercising power, and there is goodreason to suppose that studies of this kindwill be as indispensable in the future as theyhave been in the past. But since we areconcerned at the moment with a formalexplication of the concept of power, andnot with an investigation of research problems, (some of these will be taken up lateron) it is important to make clear thatanalysis of the first two items does not,strictly speaking, provide us with a comparison of the power of two or more actors,except insofar as it permits us to makeinferences about the last three items. I f wecould make these inferences more directly,we should not be particularly interested inthe first two i t ems-a t least not for purposesof making comparisons of power. On theother hand, given information about theresponses, we may be interested in comparingthe efficiency of different bases or means;in this case, evidently, we can make acomparison only by holding one or both ofthe first two factors constant, so to speak.In general, the properties of the powerwielder that we bring into the problem aredetermined by the goals of one s specificresearch. For example, one might be interested in the relative power of differentstate governors to secure favorable legislative action on their proposals by meansof patronage; or alternatively, one might be

interested in the relative effectiveness of thethreat of veto employed by different governors.

In whatever fashion one chooses to definethe relevant properties of the actors whosepower he wishes to compare, strictly speak

ing one must compare them with respect tothe responses they are capable of evoking.Ideally, it would be desirable to have asingle measure combining differences inscope, number of comparable respondentscontrolled, and change in probabilities.But there seems to exist no intuitivelysatisfying method for doing so. With anaverage probability approaching one, Ican induce each of 10 students to come toclass for an examination on a Friday afternoon when they would otherwise prefer tomake off for New York or Northampton.With its existing resources and techniques,the New Haven Police Department canprevent about half the students who parkalong the streets near my office from stayingbeyond the legal time limit. Which of us hasthe more power? The question is, I believe,incapable of being answered unless we areready to treat my relationships with mystudents as in some sense comparable withthe relations of the Police Department toanother group of students. Otherwise anyanswer would be arbitrary, because there isno valid way of combining the three variables-scope, number of respondents, andchange in probabilities-into a single scale.

Let us suppose, for a moment, that withrespect to two of the three variables theresponses associated with the actions oftwo (or more) actors we wish to compareare identical. Then it is reasonable to definethe power of as greater than the powerof if, with respect to the remaining variable, the responses associated with A s actsare greater than the responses associatedwith B s acts. I t will be readily seen, however, that we may have jumped from thefrying pan into the fire, for the term greaterthan is still to be defined. Let us take upour variables one by one.

To begin with, we may suppose that theprobability of evoking the response being thesame for two actors and the numbers ofcomparable persons in whom they can evokethe response also being the same, then if the


.,


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o N c E P T OF P o w E R 207

scope of responses evoked by A is greaterthan that evoked by B A's power is greaterthan B's. But how can we decide whetherone scope is larger than another? Supposetha t I could induce my son to bathe everyevening and to brush his teeth before goingto bed and that my neighbor could inducehis son to serve him breakfast in bed everymorning. Are the two re8ponses I can control to be counted as greater than the oneresponse my neighbor can control? Evidently what we are willing to regard as a

greater or lesser scope of responses willbe di


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oxcEPT o PowEH 209

But this is not a very helpful definition.For the important question is whether wecan specify some properties that will insurecomparability among aetors, respondents,means, and scopeti. The answer, alas, is no.So far as an explication of the term poweris concerned, power comparability must betaken as an undefined term. That is, powercomparability will have to be interpreted inthe light of the speeifie requirements ofresearch and theory, in the same way thatthe decision as to whether to regard anytwo objeets-animals, plants, atomH, orwh a t n o t -a s comparable depends upongeneral considerations of classification andtheoretical import. To this extent, and tothis extent only, the deeiHion is arbitrary ;but it is not more arbitrary than otherdecisions that establish the criteria for aclass of objects.

To political scientists it might seem farfetched to compare the power of a Britishprime minister over tax legiHlation in theHouse of Commons with the power of thePresident of the l;nited States over foreignpolicy decision::; in the Senate. t would seemfarfetched because the theoretical advantage:,; of such a comparison are not atall clear. On the other hand, it would notseem quite : ;o farfetched to compare thetwo institutional positions with respect tothe same kind of poliey-Hay tax legislation or foreign policy; indeed, political::;cientists do make comparisom; of thiskind. Yet the decision to regard tax legif'lation in the House of Commons as comparable in Home sense to tax legiHlation inthe Senate is arbitrary. Even the decisionto treat as comparable two revenue measurespassed at different times in the UnitedStates Senate iH arbitrary. 'Vhat :,;aves acomparison from being genuinely arbitraryis, in the end, i ts scientific utility. Some kindsof comparisons will seem more artificial

than others; Horne will be theoretically moreinteresting and more productive than other:,;.But these are criteria derived from theoretical and empirical considerations independentof the fundamental meaning of the termpower.

On what grounds, then, can one criticizethe study mentioned a moment ago? Be-

cause the use of undiseriminating questionsproduced results of very limited theoreticalsignificance. By chom;ing a relatively weakcriterion of power comparability, the authorinevitably robbed his inquiry of much ofit: ; potential richness. Considerations ofcomparability are, therefore, eritical. Butthe criteria employed depend upon theproblem at hand and the general state ofrelevant theory. The only way to avoid anarbitrary and useless definition of powercomparability ~ to r:onsider carefully thegoals and substance of a particular piece ofresearch in view of the theoretical constructs one has in mind. Thu;-; in the ea:-;e ofthe Senate, i t may be :-;atisfactory for onepiece of research to define all Senate roll-callvotes on all issue:-; as comparable; for another, only vote,; on foreign policy issueswill be comparable; and for still another,only votes on foreign policy issues involvinglarge appropriations; etc. In a word, theresearcher himself must define what hemeans by comparability and he must do soin view of the purpose of the ranking he isseeking to arrive at, the information available, and the relevant theoretical constructsgoverning the n'seareh.

APPLICATIONS OF THE CONCEPT OFPOWER COMPARABILITY

Assuming that one has power comparability, the next problem is b rank everyaetor whose rank is relevant to the research.Here we run into practical problPm:-; ofgreat magnitude.

Suppose we wish to rank a number ofSenators IYith respect to their inftuence overthe Senate on que:-;ticm .; of foreign affairs.Specifically, the respondent and responseare defined as all Senate roll-call voteH onmeasures that have been referred to theForeign Hdatiom; Committee. To beginwith, lPt ti take two Senators. What we

wish to find out i;-; the relative inftuenr:e onthe Senate vote of the activities of the twoSenator:-; for or against a measure prior tothe roll call. For and against must bedefined by referenee to some standard

direetion. Passage of the measure is onepossible direction in the sense that aSenator can he for passing the measure,



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against it, or without a position for or againstpassage. This is not, however, a particularlysignificant or meaningful direction, and onemight wish to determine the direction of ameasure by reference to the President'sposition, or by content, or by some other

standard. For this discussion, I shall assumethat for and against are defined byreference to the first standard, i.e., passingthe measure.

Let us now assume that a Senator doesone of three things prior to a roll-call vote.He works for the measure, he works againstit, or he does nothing. (The assumption,although a simplification of reality, is by nomeans an unreasonable simplification). Letus further assume (what is generally true)that the Senate either passes the measure ordefeats it. With respect to a particular

Senator, we have the following conditionalprobabilities:

WorksFor

The SenatorWorks

AgainstDoes

Nothing

Passes P1 P2 Pa

The S e ~ ~ : e a t s; = ; ~ ~ ; = ;; = ;

Since the bottom row provides no additional information we shall, in future, ignoreit.

Followingthe

earlier discussion ofthe

concept M the measure of power, it isreasonable to define

Mt = P t P3

JJ 2 = P3 - P2

M 1 is a measure of the Senator's power whenhe works for a measure and JJ 2 a measureof his power when he works against a measure; in both cases a comparison is madewith how the Senate will act if the Senatordoes nothing. There are various ways in

which we might combine 1 and 2 intoa single measure, but the most useful wouldappear to be simply the sum of M and M2.To avoid confusion with the earlier andslightly different measure which we are nowapproximating, let us call the sum of JJ tand M 2, M . Like M, it is at a maximumof 1 when the Senate always passes the billsa given Senator works for and always

defeats the bills he works against; it is at aminimum of 1 when the Senate alwaysdefeats the bills he works for and alwayspasses the bills he works against; and it isat 0 when there is no change in the outcome,no matter what he does.

In addition, there is one clear advantageto M . t is easily shown that it reduces to

M = P t P2

In a moment we shall see how advantageoussuch a simple measure is.

The theoretical problem, then, is clear-cutand a solution seems reasonably well defined.

t is at this point, however, that practicalresearch procedures begin to alter thesignificance of a solution, for the particularoperational means selected to breathe lifeinto the relatively simple formal conceptsoutlined so far can produce rather differentand even conflicting results.

Let me illustrate this point by drawingon a paper by Dahl, March, and Nasatir (1)on influence ranking in the United StatesSenate. The aim of the authors was to rankthirty-four Senators according to theirinfluence on the Senate with respect to twodifferent areas, foreign policy and tax andeconomic policy. The 34 Senators were allthose who had held office continuously fromearly 1946 through late 1954, a long enough

period, it was thought, to insure a reasonablylarge number of roll-call votes. The classification of measures to the two areas wastaken from the Congressional QuarterlyAlmanac, as were the votes themselvesThus the subject was well defined and thenecessary data were available.

No such systematic record is maintainedof course, for the positions or activities ofSenators prior to a roll-call vote, and whatis more it would be exceptionally difficultto reconstruct the historical record evenover one session, not to say over an eight

year period. Faced with this apparentlyinsuperable obstacle, it was necessary toadopt a rather drastic alternative, n 1melyto take the recorded roll-call vote of aSenator as an indication of his position andactivities prior to the roll-call. While thisis not unreasonable, it does pose one majordifficulty: a vote is necessarily cast eitherfor or against a measure and hence the roll=



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call provides no way of determining when aSenator does nothing prior to the roll-call.But the very essence of the formal conceptof power outlined earlier hinges on a comparison of the difference between what theSenate will do when a Senator takes a given

position and what it does when he takes noposition.

I t is at this point that the advantages ofthe measure JY[ reveal themselves. Forprovided only that one is prepared to takethe Senator's recorded vote as a fair indication of his prior position and activities,the data permit us to estimate the followingprobabilities, and hence *

The Senator

Works WorksFor Against

The Senate Passes I _ - - - - - - p _ , _ . . . J

One could, therefore, estimate i l l foreach of the 34 Senators and rank all of them.

The validity of this method rankingwould appear to be greatest, however, whenall Senators are ranked on precisely thesame set of bills before the Senate. To theextent that they vote on different (althoughmostly overlapping) sets of bills, the comparability of 1 ~ f *from one Senator to another will be reduced, conceivably to thevanishing point.

For a number of reasons, including aslightly different interpretation of thecharacteristics of an ideal measure, theauthors chose a rather different approach.They decided to pair every Senator againstevery other Senator in the following way.The number in each cell is an estimate ofthe probability that the Senate will pass aproposal, given the positions of the twoSenators as indicated; the number is infact the proportion of times that the Senatepassed a foreign policy (or tax) measure inthe

period 194()-54, giventhe

recordedvotes of the two Senators as indicated.s,

Favors Opposesthe the

motion motion

Favors the motion

[

tt P 2~ I

P2l I P22s,

Opposes the motion

With ;)4 Senators, ;)()1 possible pairs of thiskind exist; but only 158 pairs were tabulatedfor foreign policy and 20G for tax andeconomic policy over the whole period.The measure used to enable comparisons tohe made between the two Senators in eachpair might be regarded a: ; an alternative toM . This measure-let us call it - restsupon the same basic a:-;sumption, namelythat we can measure a Senator's influenceby the difference between the probabilitythat the Senate will pass a measure theSenator opposes and the probability thatit will pass a measure he supports. However, there are two important differences.First, the authors deeided not to diHtinguishbetween negative and positive power;consequently they used absolute values only.Second, in estimating the probability of ameasure pasHing the Senate, the positions oftwo Senators were Himultaneously comparedin the manner shown in the table. Thus theinfluence of 81 over the Senate was measuredas the difference between the probabilitythat a bill will pass the Senate when 81favors it and the probability that it willpass when 81 opposes it. However, thisdifference in probabilities was measuredtwice: ( l) when s2 favors the motionsbefore the Senate; and (2) when 82 opposesthe motions. In the same way, 82 s influencewas memmred twice. Thus:

~ S1) IPn - P12l ,

that is, the change in probabilities,given Sz in favor of the bill.

V [ ~81) IP21 - Pzzl ,

that is, the change in probabilities,giVen 82 in oppoHition to the bill.

I,ikewise,

J l l ~ ( 8 2 ) IPn - P21l

. M ~(Sz) IP12 - Pd The influence of 8 was said to be greater

than the influence of Sz only if ~ 81) >NI; (Sz) and J v ~81) > i l l ~(Sz). That is, if

IPn - P12l > IPn - P21l and

IP21 - P22l > IP12 - P22l.

Except for the rare cm;e of what wouldordinarily be regarded as negative



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power-which, as I have already said, thisparticular measure was not intended todistinguish from positive power- theabsolute values are the same as the algebraicones. Where the algebraic differences canbe taken, and this will normally be the case,

both inequalities reduce toP2 > Pl

In the ordinary case, then, using the measureM we can say that the power of SenatorGeorge is greater than that of Senator Knowland if the probability that the Senate willpass a measure is greater when SenatorGeorge favors a bill and Senator Knowlandopposes it than when Senator Knowlandfavors a bill and Senator George opposes it.

TABLE 1

T H I RT Y- F O U R U . S . S EN ATO RS R A N K E D A c c o R D I N GTO P O W E R O V ER S E N AT E D E C I S I O N S

o N F o R E I G N P o L I C Y, 1946-54

HI GH

Hayden (tie) MagnusonChavezSmith (N.J . )**George**May bankGreen**Hill*

Aiken (tie) Wiley**HoeyKilgore

Ferguson*Murray*Know and*Morse

Fulbright** (tie) Saltonstal lJohnstonCordonHickenlooper**Ellender

Millikin (tie) McClellanEastlandRussellBridges*Johnson (Colo.)ByrdButler (Nebr.)

Langer*YoungCapehart*McCarran

LOW

m ~ m e rof Foreign Relations Committee five or moreyears

member of Foreign Relatins Committee one to fouryears

The results, some of which are shown inTables 1 to 3, are roughly consistent withexpectations based on general knowledge.

Note how the formal concept of power ~has been subtly altered in the process ofresearch; it has been altered, moreover,

not arbitrarily or accidentally but becauseof the limitations of the data available,limitations that appear to be well-nighinescapable even in the case of the UnitedStates Senate, a body whose operations arerelatively visible and well recorded over along period of time.

The most important and at first glancethe most innocent change has been to acceptthe roll-call position of a Senator as anindication of his position prior to the roll- .:call vote. This change is for most practicalpurposes unavoidable, and yet it generates a

serious consequence which I propose tocall the problem of the chameleon. Supposea Senator takes no prior position on any

TABLE 2T H I RT Y- F O U R U . S . S EN ATO RS R A N K E D A c c o R D I N G

TO P o W E R OVER SE NAT E DE CISIONS ON

TA X AND E c o N O M I C POL ICY, 1946-54

HIGH

GeorgettMillikinttEllenderBy rd t tSal ons all tCordonMcCarranYoungHoeyt tMay bank

Johnson (Colo.) t t (tie) McClellanHickenlooperEastlandRussellSmith (N . J . )Know andAikenCapehartJohnstonBridges

Hayden (tie) ChavezButler (Nebr.)tt (tie) Wiley (tie) Ferguson

Langer (tie) Hill (tie) Murray (tie) Magnuson(tie) Fulbright (tie) Green

Morse (tie) Kilgore

LOW

tt member of Finance Committee five or more yearst member of Finance Cotntnittee one to four years

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TABLE 3T n i R T Y- F o U R U. S. S EX ATO RS CLA t- \S I F I ED A c c o R D I N G TO ' P o w E R o v E R SE: - [ATE D E c r s r o x , ; o FoR

E I G N P o L I C Y A N D T A x P o L I C Y, 1946-54Foreign Policy

High influence Medium influence Low influence

Highinfluence

George**ttHoeyt t:VIaybank

EllenderSaltonstal l tCordon

l \ I i l l ikinttByrd t tl \ leCarranYoungJohnson (Colo.)ttMcClellan

Tax and EconomicPolicy

Mediuminfluence

Smith (K . . .)**Aiken*

Hickenlooper**Knowland*Johnston

East landH.ussellCapehart*Bridges*

Lowinfluence

HaydenChavez

Wilev**Hill*.

MagnusonGreen**

Ferguson*Murray*Fulbright**

MorseKilgore

Butler (Xebr.) t t

Langer*

**member of Foreign l lelat ions Committee five or more years*member of Foreign Relations Committee one to four years

t t member of Finance Committee five or more yearst member of Finance Committee one to four years

bill and always deeides how to vote byguetlsing how the Senate majority willvote; then, if he is a perfeet guesser, according to the ranking method used he willbe plaeed in the highest rank. Our commonsense tells us, however, that in this ease it is

the Senate that has power over the Senator,whereas the Senator has no influence on thevotes of other Senators.

l f the reader will tolerate an unnaturalcompounding of biological and eelec;tialmetaphorR, a special case of the chameleonmight be called the satellite. Although Ihave no evidenee that this waR so, let usRUppose that Senator Hoey took no priorpoo;itions on issues and always followed thelead of Senator George (Table :i). Let usaHsume that on foreign policy and taxpolicy, Senator George was the most power

ful man in the Senate-a indeed nearlyevery seasoned observer of the Senate docsbelieve. By following George, Hoey wouldrank a:; high as Cieorge; yet, aceording toour hypothetical a:,;sumptionH, he had noinfluence at all on George or any otherSenator.

The problem of the ehameleon (and the

satellite) is not simply an artifact created bythe method of paired comparisons employed.I t i: ; easy to see that ranking according tothe meaHure * would be subject to theRame difficulties giuen the same data Theformal eoncept of pmver, that iR to ,;ay,

presuppoHes the existence of data that in thiscase do not seem to be available---certainlynot readily available. I f one had the kindsof observations that permitted him toidentify the behavior of the chameleon orsatellite then no serious problem \vould ari:;e.One could treat chameleon a


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needs observations of the behavior ofSenators prior to the roll-calls. But if it istrue, as I have been arguing, that observations of this kind are available onlywith great difficulty, rarely for past sessions,and probably never in large numbers, then

in fact the data needed are not likely toexist. But if they do not exist for the Senate,for what institutions are they likely to exist?

CONCLUSIONS: A DIALOGUE BETWEEN ACONCEPTUAL THEORETICIAN AND

AN OPERATIONALIST

The conclusions can perhaps best bestated in the form of a dialogue between a

conceptual theoretician and a strictoperationalist. I shall call them and 0.

C The power of an actor, A would seemto be adequately defined by the measure M

which is the difference in the probability ofan event, given certain c t i o ~by A andthe probability of the event given no suchaction by A Because the power of anyactor may be estimated in this way, at leastin principle, then different actors can beranked according to power, provided onlythat there exists a set of comparable subjectsfor the actors who are to be ranked.

0 What you say may be true in principle,but that phrase in principle covers up ahost of practical difficulties. In fact, ofcourse, the necessary data may not exist.

C That is, of course, quite possible. WhenI say in principle I mean only that nodata are demanded by the definition thatwe cannot imagine securing with combinations of known techniques of observationand measurement. The observations may beexceedingly difficult but they are not inherently impossible: they don't defy thelaws of nature as we understand them.

0 True. But the probability that we canactually make these observations on., .say,the U. S. Senate is so low as to be neghgible,at least if we want relatively large numbers

of decisions. t seems to me that from astrict operational point of view, your conceptof power is not a single concept, as you haveimplied; operationally, power would ~ p p e rto be many different concepts, dependmg onthe kinds of data available. The way inwhich the researcher must adapt to the

almost inevitable limitations of his datameans that we shall have to make do with agreat many different and not strictly com-parable concepts of power. .

C I agree with all you have said. Inpractice, the concept of power will have to ,

be defined by operational criteria that willundoubtedly modify its pure meaning.

0 In that case, it seems wiser to dispensewith the concept entirely. Why pretend thatpower, in the social sense, is a concept thatis conceptually clear-cut and capable ofrelatively unambiguous operational definitions-like mass, say, in physics? Indeed,why not abandon the concept of poweraltogether, and admit that all we have or canhave is a great variety of operational concepts, no one of which is strictly comparablewith another? Perhaps we should label them:Power 1, Power 2, etc.; or better, let'sabandon single, simple, misleading wordslike power and influence , except whenthese are clearly understood to be a part ofa special operational definition explicitlydefined in the particular piece of research.

C I 'm afraid that I must disagree withyour conclusion. You have not shown thatthe concept of power as defined by themeasure M is inherently defective or that i tis never capable of being used. t is true, ofcourse, that we cannot always make theobservations we need in order to measure 'power perhaps we can do so only infreq u e n t ~ .But the concept provides us with astandard against which to compare theoperational alternatives we actually employ.In this way it helps us to specify the defectsof the operational definitions as measures ofpower. To be sure, we may have to use defective measures; but at least we shall knowthat they are defective and in what ways.More than that, to explicate the concept ofpower and to pin-point the deficiencies of theoperational concepts actually employedmay often help us to invent alternative concepts and research methods that producea much closer approximation in practice tothe theoretical concept itself.

REFERENCES

1. Dahl, R. A., March, J., & Nasatir, D. Influence ranking in the United States Senate.

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