Opposition Backlash and Platform Convergence in a Spatial Voting Model with Campaign Contributions

Opposition Backlash and Platform Convergence in a Spatial Voting Model with CampaignContributionsAuthor(s): Richard BallSource: Public Choice, Vol. 98, No. 3/4 (Jan., 1999), pp. 269-286Published by: SpringerStable URL: http://www.jstor.org/stable/30024487 .

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Public Choice 98: 269-286, 1999. 269 @ 1999 Kluwer Academic Publishers. Printed in the Netherlands.

Opposition backlash and platform convergence in a spatial voting model with campaign contributions

RICHARD BALL* Department of Economics, Haverford College, Haverford, PA 19041, U.S.A.

Accepted 8 January 1997

Abstract. This paper investigates the effects of campaign contributions on candidate behavior in elections. The particular focus is on how candidates choose their platforms when they know that the positions they take will influence the level of campaign contributions that they (and their opponents) receive from concerned interest groups. The analysis is carried out in the context of a simple one-dimensional spatial voting model with two candidates and two interest groups. Since the earliest Hotelling-Downs formulations, a central issue in the literature on spatial voting has been the degree to which, under various sets of assumptions, the candidates' platforms converge in equilibrium. This paper extends that literature by examining how the introduction of interest groups making campaign contributions affects the degree of platform convergence. The paper shows that when choosing their platforms, candidates face a trade-off between generating increased support from opponents and provoking a backlash from the opposition. An example is developed to illustrate a surprising result that can occur because of the backlash effect: the introduction of two extremist interest groups may lead the candidates to moderate their platforms, resulting in a greater degree of platform convergence than would be observed in the absence of any campaign contributions.

1. Introduction

This paper investigates the effects of campaign contributions on candidate behavior in elections. The particular focus is on how candidates choose their platforms when they know that the positions they take will influence the level of campaign contributions that they (and their opponents) receive from concerned interest groups. The analysis is carried out in the context of a simple one-dimensional spatial voting model with two candidates and two interest groups. Since the earliest Hotelling-Downs formulations, a central issue in the literature on spatial voting has been the degree to which, under various sets of assumptions, the candidates' platforms converge in equilibrium. This paper

* This paper was presented at the 1996 annual meeting of the Public Choice Society. The comments received there, particularly from the discussants John Matsusaka and Michael Munger, are gratefully acknowledged. Helpful discussion and assistance were also provided by Lynne Butler, Ellsworth Digg, Marissa Golden, Picard Jannd, Miller Maley and Sid Waldman. Any remaining errors are of course the responsibility of the author.



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extends that literature by examining how the introduction of interest groups making campaign contributions affects the degree of platform convergence.

The general qualitative result of the paper is that when choosing their platforms candidates must anticipate not only the response of the allied interest groups from which they receive contributions, but also the response of the opposition interest groups that contribute to their opponents. The incentives to please allies on the one hand, but not to alienate opponents on the other, will in general pull the candidates in opposite directions. Which effect dominates - and so whether the introduction of campaign contributions leads to greater or less platform convergence - depends on the particular specification of the model. An example developed in this paper illustrates one surprising possibility: the introduction of two extremist interest groups may lead the candidates to moderate their platforms, resulting in a greater degree of platform convergence than would be observed in the absence of any campaign contributions.

The trade-off candidates face between choosing platforms that will curry the favor of like-minded interest groups versus moderating their positions to reduce the backlash from opposition interest groups has not been explicitly analyzed in previous spatial models of electoral competition with campaign contributions. This paper demonstrates, in fact, that in one well-known study (Magee, Brock and Young, 1989) the failure to incorporate the opposition backlash effect represents a serious omission in the analysis.

Section 2 of this paper presents a simple version of the probabilistic spatial voting model (PSVM) without the influence of campaign contributions by interest groups. This preliminary model serves as a benchmark for comparison with the results obtained when campaign contributions by interest groups are introduced. The version of the PSVM presented in this section closely follows the structure developed by Wittman (1983, 1990), Hansson and Stuart (1984), Calvert (1985) and Mitchell (1987).1 This model is based on the classic Hotelling-Downs formulation, with two modifications: candidates are allowed to care not only about winning the election, but also about what

policy is implemented after the election; and (from the point of view of the candidates) the outcome of the election depends stochastically rather than

deterministically on the platforms chosen by the candidates. A general result in the PSVM literature is that, with these modifications of the Hotelling- Downs model, the candidates' platforms need not completely converge in

equilibrium, and a simple example illustrating such non-convergence is also

presented in Section 2. Section 3 develops a two-stage version of the model in which the candidates'

simultaneous choices of platforms are followed by simultaneous choices of campaign contribution levels by two interest groups. An example developed in



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Section 3 illustrates the possibility of increased platform convergence arising as a result of the influence of extremist interest groups, and Section 4 explores in general the trade-off candidates face between seeking the support of allied interest groups and alienating opposition interest groups. Section 5 reviews several previous works that have studied two-stage spatial voting models with interest group campaign contributions, and Section 6 concludes.

2. A probabilistic spatial voting model without interest group influence

Consider an election between two candidates, A and B. During the campaign Candidate A announces a platform a and Candidate B announces a platform b. These platforms are simply the policies that the candidates commit to implement if elected.2 The unidimensional policy space from which a and b are chosen is normalized to the interval [0,1]. The outcome of the election depends stochastically on the candidates' platforms, with the probability that Candidate A wins the election given by a function P(a,b). (Candidate B's probability of winning is of course 1-P(a,b).) Two assumptions are made about the probability of winning function:

(Al) 0< P(a,b) 1

(A2) For a < b, P(a, b) is non-decreasing in a and non-decreasing in b, and for a > b, P(a, b) is non-increasing in a and non-increasing in b

(Al) simply states that the probability represented by P(a,b) must always be between 0 and 1. (A2) reflects the spatial nature of the competition between the candidates. It says that if one candidate moves his platform toward that of his opponent, then he does not decrease (and may increase) his probability of winning the election; if he moves his platform away from his opponent's, then he does not increase (and may decrease) his probability of winning. A particular form of P(a,b), derived from explicit micro-foundations and satisfying both of these assumptions, is introduced below in example 1.

The candidates' objective functions depend on two components. First, each places an intrinsic value on holding office; these office-motivation parameters are denoted kA and kB. In addition, each cares about the policy implemented after the election (regardless of who is in office); the policy preferences of Candidates A and B are denoted respectively as u(.) and v(.). The overall objective functions are the sum of the expected policy payoff and the expected office payoff. For Candidates A and B respectively these are

U(a, b, kA) = P(a, b)u(a) + [1 - P(a, b)]u(b) + P(a, b)kA

V(a,b, kB) = P(a, b)v(a) + [1 - P(a, b)]v(b) + [1 - P(a, b)]kB (1)



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In the one-period game with no campaign contributions, Candidates A and B simultaneously choose their platforms a and b from the interval [0,1], and their payoffs are given by U(a,b,kA) and V(a,b,kB).

A central result of the previous literature is that in this probabilistic version of the spatial voting model in which the candidates are at least partly policy-motivated, the candidates' platforms need not completely converge in equilibrium.3 This paper investigates how the degree of platform convergence observed in equilibrium is affected by the introduction of special interest groups that influence the outcome of the election by making campaign contributions. As a benchmark for comparison with the model involving campaign contributions, the following example illustrates an equilibrium with less than complete platform convergence that arises in the basic PSVM without interest group influence.

Example 1. Consider the normal form of the PSVM developed above. For simplicity of exposition, assume that the candidates are purely policy- motivated (kA = kB - 0).4 Assume that the candidates' preferences over policies z in the interval [0,1] are given by u(z) = -l(z - 1)2 and v(z) =

1 Z2, SO that the ideal points of Candidates A and B are 1 and 0, respectively. To derive the probability of winning function used in this example,5 sup-

pose that the voters' ideal points are distributed along the policy space [0,1]. Assuming that every voter's policy preferences are single-peaked (and symmetric), then each individual will vote for the candidate whose platform is closest to his ideal point.6 In this case, the winner of the election will be the candidate whose platform is closest to the ideal point of the median voter.7 The source of randomness in the model is that candidates do not know with certainty what the median voter's most preferred policy is.8 Their (common) beliefs about the location of median voter's ideal point, m, are represented by a density f(m) over the policy space [0,1]. Given the announced platforms a and b, each candidate perceives his probability of winning simply to be the probability that m is closer to his platform than to his opponent's platform (and each candidate's probability of winning is one half if the two platforms are equidistant from m). The probability of winning function will then be of the general form

a+b

f f(m)dm if0<a<b<l 0

P(a, b)= 1 if0< a = b < 1 (2)

f f(m)dm if0<b<a<1 a+b



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Suppose also that the candidates' beliefs are that the median voter's ideal point is distributed uniformly on the policy space [0,1], so that f(m) =

1 for 0<m< 0 otherwise . In this case, the probability of winning function (2) will

have the particular form

a+b for 0 < a<b < 1

P(a, b) 1 for 0< a=b <1 (3)

1- a+b for 0<b<a< 1 2

Both the general form of the probability of winning function given in (2), as well as the special case given in (3), satisfy assumptions (Al) and (A2).

As discussed in footnote (3), we know that each candidate will choose a platform that is closer to his ideal point than is his opponent's platform, so that we must have 0 < b < a < 1. Given this condition, the probability of winning function will be of the form P(a, b) - 1 - a+b, so the candidates' objective functions can be written as

U(a, b, 0) = (1 - b)[-(a - 1)2] + (a+b)[--(b

- 1)2] (4)

V(a, b, 0) =(1 -a)(-'a2)a+ ( (- b 2

The players' reaction functions are then implicitly defined by the first-order conditions9

(a,b)= (- [- (a - 1)2] -

(1 -

a+b)(a - 1) + ( )[- (b - 1)2] = 0

V(a,b,O (-)(-a 2) + (- b2) - ( a+b) (b)= 0 (5) b 2 2 (5)

These equations are solved by the pair (a* - , b* - ), which constitutes a Nash equilibrium for this game. This equilibrium illustrates the result of less than complete platform convergence in this version of the model without campaign contributions. 0

Some intuition into the candidates' choices of platforms in this example can be gained by examining the general form of the first-order condition defining Candidate A's equilibrium platform. (A symmetric analysis of Candidate B's equilibrium choice of platform would yield the same intuition.) For an interior solution with 0 < b* < a* < 1, this first-order condition will be of the form

OU(a*, b*, kA) _P(a*, b*) Ou(a*) OU(a*[u(a*) - u(b*) + kA] + a

P(a*, b*) = Oa Oa 9a

(6)



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The first term on the right-hand-side of (6) is the marginal cost to Candidate A of an increase in his platform. It consists of the decrease0o in his probability of winning resulting from diverging from Candidate B's platform, times his net benefit of winning the election (the difference between the policy payoff he receives if he wins and the policy payoff he receives if Candidate B wins, plus the intrinsic value he places on holding office). The second term shows the marginal benefit of an increase in a. This term consists of the amount by which the increase in a increases Candidate A's preference for his own platform, times the probability that Candidate A wins and that platform is actually implemented. Condition (6) states that, given Candidate B's equilibrium platform b*, Candidate A's optimal platform a* equates these marginal costs and benefits.

3. The PSVM with campaign contributions

This section extends the one-stage version of the PSVM developed in Section 2 to include a second stage in which special interest groups make campaign contributions. In the first stage, candidates A and B simultaneously choose their platforms a and b from [0,1]. In the second stage, after observing the platforms selected by the candidates, two interest groups, labeled IG A and IG B, simultaneously decide how much money to contribute to each candidate. The amount of money that IG A contributes to candidate A will be denoted a, and the amount of money that IG B contributes to candidate B will be denoted 3.11

Each candidate's probability of winning now depends not only on the locations of the platforms, but also on the amounts of money contributed to each candidate. The function P(a, b, a, /3) will represent candidate A's probability of winning (which again is equal to one minus Candidate B's probability of winning). Three assumptions are made about this generalized probability of winning function:

(A l) 0 < P(a, b, a, 3) < 1

(A2) For a<b, P(a,b,a,/) is non-decreasing in a and non-decreasing in b, and for a>b, P(a,b,a,/3) is non-increasing in a and non-increasing in b

(A3) P(a,b,a,/3) is non-decreasing in a and non-increasing in /3

(Al) ensures that P(a, b, a, /3) always gives a probability between zero and one. (A2) is a direct extension of (A2), and again reflects the spatial nature of the electoral competition. (A3) simply states that campaign contributions to a candidate increase (or at least do not decrease) his chance of winning



275

the election. The simplest way to think of this is that the candidates use the contributions they receive to buy publicity such as television advertising, and that by advertising a candidate increases his probability of winning the election. This assumption is consistent with the empirical work of Jacobson, who argues that, at least for non-incumbents in congressional elections, "the amount of money [they] spend has a large effect on the proportion of votes they receive and on their probability of winning the election" (Jacobson, 1992: 50).12 Similarly, one could think of the expenditure made by the interest group not as a contribution to the candidate's campaign, but as an "independent expenditure" made on behalf of the candidate to help him get elected.13

The major alternative explanation for why interest groups make campaign contributions is that they use them to "'buy' access to the successful candidate" (Austen-Smith, 1987: 123).14 This is the approach taken by Aranson and Hinich (1979) in their study of the effects of legislation limiting or requir- ing disclosure of campaign contributions. They make the polar assumption that contributions have no effect on the outcome of the election, and that "the contributor's sole purpose in giving is to invest in a kind of insurance policy... [T]hat insurance either provides a benefit if the recipient candidate wins, or forestalls punishment if that candidate is less than magnanimous in victory" (p. 440). Similar assumptions are maintained by Hinich and Munger (1994), who, following Welch (1974), focus on the trade-off a contributor faces between "quid pro quo" and "ideological" motivations.

The assumption maintained in the present paper, that contributions are made to affect the outcome of the election, was also adopted by Austen-Smith (1987) and Magee, Brock and Young (1989). It is appropriate here because the issue being studied is how candidates modify their positions in anticipation of contributions by interest groups; it is the fact that these contributions influence who is most likely to win the election that makes the candidates care about them and anticipate them when choosing their platforms.15

As before, the policy preferences of Candidates A and B are represented by functions u(.) and v(.), and their office-motivation parameters are kA and kB, so their payoff functions for the two-stage version of the PSVM can be written as

U(a,b, a, , kA)

P(a, b, a, P)u(a) + [1 - P(a, b, a, /3)]u(b) + P(a, b, a, p)kA (7)

V(a, b, a, , kB) =

P(a, b, a, P)v(a) + [1 - P(a, b, a, P)]v(b) + [1 - P(a, b, a, p3)]kB



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IG A has policy preferences represented by a function w(.), and IG B's policy preferences are represented by a function )(-). As in Austen-Smith (1987) and Magee, Brock and Young (1989), the interest groups' net payoffs are given by the expectation of their policy preference functions, less their campaign expenditures. For interest groups A and B, respectively, these are

(a, b, a, p) = P(a, b, a, 3)w(a) + [1 - P(a, b, a, P)]w(b) - a (8)

(a, b, a, p) = P(a, b, a, P3)(a) + [1 - P(a, b, a, P)]O(b) - p

The timing of the game is as follows. Candidates A and B simultaneously choose their platforms a and b from the interval; after observing the platforms chosen by the candidates, IGs A and B simultaneously choose non-negative contribution levels a and 3; and the payoffs are as given in (7) and (8).

The following example extends the one-shot game solved in example 1 to the two-stage version with campaign contributions outlined above. All parameter values and functional forms are consistent with those used in example 1, so that the results from the two examples are comparable. This second example illustrates the possibility of increased platform convergence resulting from the introduction of extremist interest groups.

Example 2. Assume as in example 1 that the candidates are purely policy- motivated (kA - kB = 0) and that their policy preferences are given by u(z) - -1(2 - 1)2 and v(z) =- 122. In the absence of any campaign contributions (a /3 - 0), the probability of winning function will be identical to that used in example 1: P(a, b, 0, 0) = P(a, b), where P(a, b) is of the form given in (3). When at least one of the contribution levels is positive, assume that the probability of winning function is of the form

P(a, b, a, 3)= max {

0, min {

P(a, b) + 7 (a-b/a+b),1}}

where P(a, b) is again of the form given in (3). It is easy to check that this functional form satisfies (Al), (A2) and (A3). It implies that if the interest groups make equal (positive) contributions, they have no influence on the outcome of the election, and the probability of winning reduces to P(a, b). If the contribution to Candidate A is greater than the contribution to Candidate B (a > /), then Candidate A's probability of winning is increased. The amount by which this probability increases depends not only on the absolute difference in the two contribution levels, but on this difference relative to the total amount of money contributed to both candidates. When /3 > a, Candidate A's probability of winning is decreased in a similar manner. The parameter y is assumed to be positive; the larger is 7, the greater is the impact



277

of the campaign contributions. The max and min notation simply ensures that

P(a, b, a, p) always takes on a value between 0 and 1. A polar assumption is made about the policy preferences of the interest

groups. IG A is assumed to be "allied" with Candidate A in the sense that the policy preferences of IG A are identical to those of Candidate A.16 IG B is similarly "allied" with Candidate B, so we have w(z) = u(z) = -(z - 1)2 and 0b(z) - v(z) = ½2. The interest groups (like the candidates) are thus extremists, in the sense that their ideal points are at the end-points of the policy space.

A sub-game perfect Nash equilibrium for this example can be found with the standard backward induction procedure for two-stage games.17 Given announced platforms a and b from the first stage, the objective functions of the interest groups when choosing their campaign contributions in the second period will be18

(a,b, a, 1)= [l- I+ y(a-b/a+b)

[-1/2(a-1)2] +

[a+b/2- -y(a-b/a+b)] [-12(b-1)2] -a

(a,b,a,b)= [1-a+b/2+ y(a-b)/a+b)

(-!a2) + [a+b/2- -y(a-b/a+b)] (-12b2) -b

Taking the corresponding first-order conditions and solving them simulta- neously19 yields the equilibrium campaign contributions for the second stage as functions of the platforms chosen in the first stage

a* (a, b) = 2^y(a - b) (1- a+b/2)2 (11)

P* (a, b) =2^(a-b) (1-a+b/2) (a+b/2)

In the first stage, anticipating this second-stage response from the interest groups, the candidates play an induced game with payoffs20

U(a, b, a* (a, b), /* (a, b), 0) = [1 - a+b +(1 - a - b)]

[-1/2 (a- 1)2] + [a+b - y(1 - a - b)][-l(b - 1)2 (12)

V(a, b, a* (a, b), /* (a, b), 0) = [1 - a+b/2 + y(1 - a - b)]

(-a2)+[a+b/2-y)]

The candidates' first-order conditions for the induced game are



278

OU(a,b,a* (a,b),3*

(a,b),O) =(-1/2) (1/2+y)

[(b- 1)2 (a - 1)2] _ (a- 1)[1- a+b/2 +by(l -a-b)] =0 (13)

aV(a,b,a* (a,b),0*/ob

(a,b),O) =(1/2)(1/2+y)

[a2 - b2] - b[a+b/2 - y(1( - a - b)] = 0

These equations are solved by the pair

3 + 2y 1 + 2y a** b** (14) 4 + 47 4 + 4,

These expressions show the platforms chosen by the candidates in a sub-game perfect Nash equilibrium of the game with campaign contributions. O

This example illustrates the central result of this paper: the equilibrium platforms found in the game with campaign contributions (example 2) exhibit a greater degree of platform convergence than those found in the game without campaign contributions (example 1). Indeed, the equilibrium platforms found in example 2 have the interesting property that as 'y approaches infinity, the candidates' platforms converge toward ½ (with Candidate A's platform converging from above and Candidate B's platform converging from below). That is, as the probability of winning becomes very sensitive to the influence of campaign contributions, the equilibrium tends toward (but never reaches) complete platform convergence. On the other hand, as the sensitivity of the probability of winning function vanishes (i.e., as 7 goes to zero), the candidates' platforms diverge from each other toward (a* = 3 b* = )1/4, which are the equilibrium platforms of the game with no campaign contributions found in example 1.

4. The heart of the matter

The increased platform convergence observed when interest group influence is added to the model is somewhat counterintuitive. The interest groups introduced in example 2 are extremists, in the sense that their ideal policies of 0 and 1 are at the end-points of the policy space. One might conjecture that Candidate A would move his platform closer to 1 in anticipation of a greater campaign contribution from his allied IG A, and that Candidate B would move his platform closer to 0 in anticipation of a greater campaign contribution from his allied IG B. If this intuition were correct, then the introduction of interest group influence would result in increased platform divergence.



279

Example 2, however, shows that the introduction of interest group influence can have just the opposite effect.

The intuition for this result can be gained by examining the trade-offs defining Candidate A's equilibrium choice of platform. (A symmetric analysis of Candidate B's equilibrium choice of platform would yield the same intuition.) In the induced game between Candidates A and B (where the candidates anticipate the equilibrium outcome of stage 2 that will follow their platform choices), Candidate A's objective function has the general form

U(a,b,a(a,b),= b(a,b) =

P(a,b,a(a,b), b(a,b))u(a) + P(a, b, a* (a, b), p*(a, b))]u(b)(15)

+P(a, b, a* (a, b), p* (a, b))kA

With Candidate B's platform at its equilibrium value b**, Candidate A's equilibrium choice of platform a** is defined by the first-order condition

OU(a** ,b**,a* (a**,b**),3* (a**,b**),kA) = Oa

ap/aa+ ap/aa aa(a,b)/aa+ ap/ab ap(a,b)/aa [u(a) -u(b) +ka] (16)

+au(a)=0

where the notation P* -

P(a**, b**, a* (a**, b**), p* (a**, b**)) is introduced for brevity. This first-order condition is a direct analog of condition (6) discussed following example 1. Just as in (6), the marginal benefit to Candidate A of an increase in his platform, uP*, is equal to the amount by which the increase in a increases Candidate A's preference for his own platform, times the probability that Candidate A wins and that platform is actually implemented. The marginal cost of an increase in a is again equal to the change in the probability of winning induced by this increase in platform times the net benefit of winning the election. In the case of (16), however, the change in the probability of winning depends not only on the direct effect of the change in the location of Candidate A's platform, a, but also on two indirect effects.

The terms a and a show how an increase in a changes the contribution of each interest group to its allied candidate, and how these changes in the contributions in turn affect Candidate A's probability of winning. These two effects work in opposite directions. Since IG A will want to contribute more to Candidate A as his platform gets closer to IG A's ideal point of 1, %; will be positive; since this increase in a will increase P, the entire term , will also be positive. Simultaneously, however, as Candidate A increases his



280

platform, he becomes more unattractive to IG B, whose ideal point is 0. It will therefore become more important to IG B that Candidate B win the election. IG B will consequently increase its contribution to Candidate B, so 0b*/0a will be positive. Since this increase in / will decrease Candidate A's probability of winning, the entire term 0P/0b 0b*/0a will be negative.

The introduction of interest group influence thus creates both an incentive and a disincentive for a candidate to choose a more extreme platform. By making himself more attractive to his allied interest group, he would increase the campaign contribution he receives and thereby increase his probability of winning. Simultaneously, however, he would make his position more objectionable to the opposition interest group, increasing the contribution made to his opponent, and decreasing his probability of winning. In general, either of these effects could dominate: the candidates could feel greater pressure to choose more extreme platforms to curry the favor of their allied interest groups, resulting in greater platform divergence; or they could feel greater pressure to choose more moderate platforms to avoid alienating the opposition interest group, resulting in increased platform convergence.

The fact that the latter effect dominates in example 2 can be traced to the fact that the policy preference functions specified for the interest groups are strictly concave. Since each candidate's platform is relatively close to the ideal point of his allied interest group, the concavity of the interest group's preferences mean that a movement of the platform in the direction of the interest group's ideal point will make the candidate only a little more attractive to the interest group, inducing only a small increase in the campaign contribution. On the other hand, since each candidate's platform is relatively far from the ideal point of the opposition interest group, concavity implies that a small movement of the platform away from that interest group's ideal point will make the candidate much more objectionable to the interest group, and induce a large increase in the contribution to the opponent. In equilibrium, therefore, each candidate chooses a more moderate platform, losing a bit of

support from his allied interest group, but decreasing more substantially the contribution made to his opponent.

The result of increased convergence found in example 2 is a consequence of the particular functional forms introduced there. The general point, however, is simply that in choosing their platforms, candidates face a trade-off between rallying support from their allies and fanning the flames of opposition backlash. Which of these effects will dominate will depend on the

particular specification of the model, but both effects need to be accounted for. The following section shows that in at least one well-known study of interest group influence on elections (Magee, Brock and Young, 1989), the effect of opposition backlash was entirely overlooked.



281

5. Related literature

Several previous works have studied models similar in structure to the game developed in this paper. Austen-Smith (1987), Hinich and Munger (1994), and Magee, Brock and Young (1989) all analyze games in which candidates' simultaneous choices of platforms are followed by interest groups' simultaneous choices of contribution levels. None of these works, however, explicitly analyze the issue that is central to this paper, the trade-off candidates face between pleasing their allies and alienating their opponents. In the cases of Austen-Smith and Hinich and Munger, this is a consequence not of any error or omission, but simply reflects the fact that those studies focus on different substantive issues. As shown below, however, the fact Magee, Brock and Young did not account for this trade-off reflects a critical omission in their analysis.

Austen-Smith (1987) assumes that voters have noisy perceptions about the candidates' true positions, and money received from contributors is used to clarify those positions to the public. Although that paper does consider how the candidates would adjust their positions in anticipation of the responses of the contributors, there is no explicit analysis of the trade-off between currying the favor of allies versus increasing the alienation of the opposition. In an important recent work that recasts the traditional spatial voting model in terms of ideology (as opposed to simple policy positions), Hinich and Munger (1994) extend the analysis of Austen-Smith to allow candidates to use campaign contributions not only to clarify their own positions to the public, but also to add noise to the public's perception of the opponent's platform.21 Their focus is on the negative consequences of such "mud-slinging", rather than on the question of how campaign contributions affect the candidates' choices of platforms. Indeed (for reasons appropriate in the context of the issues they study), Hinich and Munger make the polar assumptions that candidates' positions are fixed (all they can do in the campaign is clarify them to the public), and that contributors believe that their donations have no impact on the outcome of the election.

The probabilistic voting model of Magee, Brock and Young (1989; hereafter MBY) is couched in terms of trade policy, but is formally very similar to the model developed in this paper. The policy space from which the candidates choose platforms is the level of a tariff or subsidy. One of the candidates (MBY call them parties) and one of the interest groups (MBY call them lobbies) are inherently protectionist (favoring a tariff), and the other candidate and interest group are inherently proexport (favoring a subsidy). The candidates simultaneously choose platforms; the interest groups simultaneously choose contributions levels; and the candidates' probabilities of winning depend both on their platforms and on the contributions of the interest groups.



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The analysis of MBY, however, contains a critical omission: there is an implicit (and unjustifiable) assumption that changes in a candidate's platform change the contribution that he receives from his allied IG, but do not change the contribution made to his opponent by the opposition IG. This omission can be seen most clearly in the formal development of their model in the Appendix to Chapter 3 (pp. 267-270). Consider in particular their equations (3.11) and (3.12), which show the objective functions22 of the candidates in the first period induced game, incorporating the equilibrium second stage responses of the IGs. In each candidate's objective function, the contribution of the allied IG is shown to depend on the candidates' platforms, but the contribution of the opposition IG is just given as a constant. The first-order conditions (3.15) and (3.16) also reflect this omission: although these conditions take into account how the allied IG's contribution changes as a candidate changes his platform, the change in the opposition IG's contribution is implicitly assumed to be zero.

MBY thus implicitly assume away the effect of opposition backlash that is central to this paper. What they fail to consider is that although changes in a candidate's platform do not change the contribution he receives from the

opposition interest group (since that will be zero in any case), changes in his platform will change the contribution that the opposition interest group makes to the opposition candidate, and that in turn will change the candidate's probability of winning the election.

6. Conclusion

In a study of PAC influence on legislative behavior, Sabato (1984: 130) argues that "the perception on Capitol Hill is that one wrong move on a vote of major importance to a large PAC could trigger a 'max-out' to one's rival". He goes on to quote a House of Representatives member on this issue: "We're forced always to look over our shoulders and figure out whether this vote will cost us $10,000 from a PAC, or worse yet, whether it will provoke a PAC into

giving $10,000 to an opponent". In an analysis of the first Clinton presidency, Ferguson (1995) describes a similar phenomenon when he states that Clinton got into "trouble by straying too far to the left of center" (p. 6). He was saved by "senior 'centrist' advisers [like David Gergen] who could help him get back on track in the middle of the road" (p. 6). Ferguson argues that this move back to the center was a result of the pressures of campaign financing: "That Clinton strongly resembles a registered republican and might well go down in history as the most conservative Democratic president since Grover Cleveland was entirely predictable. Anyone should have seen it who had followed what might be termed the 'Golden Rule' of political analysis - to



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discover who rules, follow the gold (i.e., trace the origins and financing of the campaign... )" (p. 8).

These statements capture precisely the phenomena analyzed in this paper. When choosing how to present themselves to the public, candidates must consider not only how their own contributors will react, but how their opponents' contributors will react as well. This trade-off has not been explicitly analyzed in the previous literature, and the importance of the opposition reaction to a candidate's choice of position has not been appreciated. Indeed, Magee, Brock and Young (1989) failed entirely to account for this backlash effect in their model of elections with campaign contributions. Correctly incorporating this effect in the model does affect the results in important ways. Although in general the introduction of campaign contributions could lead either to increased or decreased platform convergence, example 2 showed that under certain conditions - chiefly concavity of the interest groups' preferences - the candidates' fear of opposition backlash could dominate their desire to increase the support of their allies, resulting in increased platform convergence and position moderation in the presence of extremist interest groups.

An interesting direction in which this work could be extended would be to examine the effects of asymmetries, either in the inherent strength of the candidates (an incumbency effect, for example) or in the power or resources of the interest groups (relaxing, for instance, the assumption made in example 2 that when two opposed interest groups make identical contributions there is no net effect on the election). Another obvious direction for further research would be to allow for more than two candidates in the election, more than two interest groups, and/or a multi-dimensional policy space. Whatever the configuration of candidates, interest groups and issues, however, the main intuition of this paper will carry over: in choosing their positions, candidates must consider not just how their friends will respond, but must also look over their shoulders to see what response they may provoke from the enemy camp.

Notes

1. The stage game of the infinitely repeated game studied by Alesina (1988) also has this structure; this game also forms the basis of the experimental work done by Morton (1993).

2. A credibility problem arises in any static version of the PSVM in which candidates have policy preferences. For a candidate's announced platform to be credible, there must be some mechanism that commits him to actually implementing that platform if he is elected, rather than reneging on his campaign promise and simply implementing his most preferred policy. Although the model developed here consists of a one-shot game, a mechanism that would in practice be effective in overcoming this credibility problem would be repeated play of the game. If candidates expect to run for office again in future elections, they would have an incentive to develop a reputation for faithful adherence to campaign promises. Alesina (1988) addresses this dynamic inconsistency problem in an infinitely repeated



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version of the PSVM, and finds that (if the candidates do not discount the future too heavily) faithful implementation of announced platforms is sustainable in a sub-game perfect equilibrium.

3. Calvert (1985: 84, Theorem 6) shows that as the weight that the candidates' objective functions place on their expected policy payoffs (relative to the weight they place on holding office) goes to zero, the degree of platform divergence observed in equilibrium goes to zero. This result, however, allows for some platform divergence when the candidates care enough about policy relative to holding office. When the candidates are only policy motivated, it is easy to show that their platforms must diverge in equilibrium, and that each chooses a platform closer to his ideal point than is his opponent's platform. For proofs and discussion of this assertion, see Wittman (1983: 144, Proposition 2), Hansson and Stuart (1984: 434, Theorem 1) and Calvert (1985: 83, Theorem 5).

4. The inclusion of positive office-motivation parameters in the examples developed in this paper would not affect the qualitative results concerning the influence of campaign contributions on candidates' choices of platforms.

5. A similar probability of winning function was derived by Alesina and Cukierman (1990, Appendix 1).

6. If some voter is indifferent between the two candidates, then assume that he flips a fair coin to decide how to vote.

7. Again, ties are resolved by a coin flip. 8. In other models, randomness in the outcome of the election is generated by (rational)

abstentions by voters. See Hinich, Ledyard and Ordeshook (1972, 1973), Hinich (1977) and Ledyard (1984).

9. It is easy to verify that for a and b in the policy space [0,1], the second-order conditions for each player's optimization problem are satisfied. This will also be true for every other optimization problem considered in this paper, so further reference to second-order conditions is omitted.

10. OP(a*,b*) Oa

is non-positive by assumption (A2), since we are considering a solution with 0 < b* < a* < 1. Since a is greater than b, an increase in a represents a divergence of Candidate A's platform from Candidate B's platform, and so decreases (or at least does not increase) Candidate A's probability of winning.

11. This formulation assumes that each interest group makes a donation to only one candidate. In general, we could allow the interest groups to contribute to both candidates simultaneously. It is easy to show, however, that in equilibrium each interest group would choose to contribute to just one candidate. This is a result demonstrated by Magee, Brock and Young (1989, Chapter 4), who call it the "Contribution Specialization Theorem". Restricting attention to each interest group contributing to only one candidate therefore entails no loss of generality, and it simplifies the exposition.

12. Jacobson (1978, 1985) and Welch (1981) consider the effects that two-way causality between the contributions a candidate receives and his probability of winning might have on empirical estimates of the influence of money on election outcomes. Jacobson (1985: 40) concludes that although the issue is not definitively settled, "the available, limited anecdotal evidence supports the idea that spending money during the campaign does indeed buy attention and support for non-incumbents". For the case of incumbents, Green and Krasno (1988) argue that the effects of spending on probabilities of winning are greater than estimated by Jacobson.

13. See Sorauf (1984: 52-55) for a discussion of the use of independent expenditures. He describes them as "a genuine alternative to direct contributions" (p. 52).

14. In this case, the Contribution Specialization Theorem discussed in footnote 11 would break down: a single interest group might "hedge its bet" by contributing to both candidates.

15. Another point to be made here is that although the direct effect of contributions is on the candidates' probabilities of winning the election, they do also indirectly affect the policy positions chosen by the candidates. This point was made by Austen-Smith (1987: 124), who argued that although there is "no explicit exchange relationship between contributors



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and politicians", it is nonetheless true that the candidates "recognize that contributions, to some degree, will depend on their policy stance, and so they will take this into account in choosing election strategies".

16. Notice that this notion of "alliance" between the interest groups and the candidates has to do only with shared policy preferences, and does not entail any personal preference on the part of the interest groups for one candidate over the other.

17. See Gibbons (1992: 71-73) for a general exposition of this method. 18. This formulation of the objective functions reflects two observations. First, it relies on the

fact that, for the reasons given in footnote (3), the platforms announced by the candidates in the first period will satisfy 0 < b < a < 1. Consequently, P(a, b) = 1 - a+b/2. Second, this formulation assumes that 0

b P(a,b)+ y (i+) 1, so that P(a, b, a,) =

P(a, b) + -y (i-) (i.e., we can ignore the max and min notation in (9)). In this example, the equilibrium campaign contributions of the two interest groups will be identical, so this condition will indeed be satisfied.

19. The mathematical details of these operations are available from the author. 20. To find these forms of the induced game objective functions, note that, for the expressions

a* (a, b) and 0* (a, b) given in (11), the expression a*

(a,b)- b* (a,b) a*

(a,b)+ b*

(a,b) simplifiesto 1 - a - b, * (ab)+b (a,b)

so that P(a, b, a* (a, b), p* (a, b)) = 1 - a+b/2 + 7(1 - a - b).

21. A similar approach is taken by Hinich and Munger (1989) and Cameron and Enelow (1992).

22. The assumption made by MBY about the objectives of the candidates is the polar opposite of the assumption made in this paper: they assume that the candidate is purely office motivated and is not concerned at all with the policy actually implemented. Regardless of the assumption made about candidate motivations, however, the opposition backlash effect that MBY omit should be included in the analysis.

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Opposition Backlash and Platform Convergence in a Spatial Voting Model with Campaign Contributions

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