Information, Special Interests, and Single-Issue Voting

Information, Special Interests, and Single-Issue VotingAuthor(s): Roger D. CongletonSource: Public Choice, Vol. 69, No. 1 (1991), pp. 39-49Published by: SpringerStable URL: http://www.jstor.org/stable/30025396 .

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Public Choice 69: 39-49, 1991. © 1991 Kluwer Academic Publishers. Printed in the Netherlands.

Information, special interests, and single-issue voting

ROGER D. CONGLETON Center for Study of Public Choice, George Mason University, Fairfax, VA 22030

Submitted 29 June 1989; accepted 22 September 1989

1. Introduction

During the last twenty years, analysis of the political impact of special interest groups has become increasingly sophisticated. For example, the rent-seeking literature has developed fairly elaborate theories of interest group expenditures on political influence. Two recent collections, Buchanan, Tollison and Tullock (1980), and Rowley, Tollison and Tullock (1988) provide useful samples of the rent-seeking literature. In a related vein, Becker (1983) provides a model of interest group equilibrium which focuses attention on incentives for interest groups to exert pressure on the political process.

However, until recently, little attention has been focused on the actual mechanisms by which rent-seeking or special interest groups might be able to influence political outcomes in a democratic polity where policies can not liter- ally be bought (at least not publicly). Two recent papers by Austin-Smith (1987) and Congleton (1989) have modelled the extent to which the campaign contributions of special interest groups might allow them to influence electoral outcomes and thereby policy. These papers demonstrate that to the extent that campaign messages are persuasive and the distribution of potential donors asymmetric, candidates have incentives to alter their political platforms as a means of generating campaign contributions. In this paper, another mechan- ism by which special interest groups might be able to affect political outcomes is explored, namely single-issue voting. Single-issue voting occurs whenever one or more voters casts their ballots in a multi-dimensional policy choice as if there were only a single issue.

Although, much of the intuition behind voting models is based on models where voters cast votes on a single issue, largely because of the convenient geo- metric representations of such elections, very little attention has been focused on the implications of heterogeneous single-issue voting patterns or motiva- tions in multi-dimensioned issue spaces. For the most part, theoretical interest in single issue elections has been tangential to other topics. The literature on the stability of majoritarian elections points out that if an issue space can be mapped into a single-issue dimension in such a way that voter preferences are



40

single peaked, majority rule equilibria exist. See Black (1958) or Plott (1967). The special interest group literature is often written as if coalitions of individual's vote as a block based on some subset of the true issue space. For example, Gardner (1987) represents farmers as if they were only interested in the size of farm subsidies. However, the focus of analysis is interest group influence rather than behavior.

Yet, single-issue voting is clearly one of the tactics used by individuals and organized special interest groups. Casual observation suggests that political candidates are well aware of this, and tailor their speeches and platforms to gain support from special interest groups. For example, the posititions that candidates take on abortion, farm subsidy programs, and wilderness areas seem unlikely to generate direct gains for a voter of median (or average) age, income, and lifestyle. On the other hand, such positions clearly garner or cost votes from pro-choice and pro-life groups; farmers and rural merchants; and environmentalists and sportsmen.

This paper attempts to determine whether or not such positions might be taken simply because they generate votes. In other words, if special interest groups were unable to make campaign contributions, to what extent would special interest groups still be served by government programs? The analysis of this paper suggests that if a substantial number of voters vote as if there were only single issues, electoral outcomes may not reflect the median or mean position of the electorate but rather the median or average positions of special interest groups.

The paper is organized as follows. Section 2 demonstrates some properties of single-issue voting equilibria in the case where voters are zealots. This serves as a bench mark for other models of single-issue voting. Section 3 develops a model of special interest voting based on economies in information gathering and processing. Section 4 illustrates how strategic single-issue voting can generate stable policy outcomes for special interest groups. Section 5 summarizes results and suggests extensions.

2. Single-interest voting by zealots

Voters who vote as if there were only a single issue, behave in ways which vio- late many of the properties normally ascribed to voting behavior. A single- interest voter casts his votes as if he were a zealot whose objective function con- tains only a single argument. In a multi-dimensional issue space, he chooses candidates based entirely upon their positions along a single dimension. The rate of substitution across issues is effectively zero.

The first case to be analyzed is an election where voters actually are zealots having true single-issue preferences over the issue space of interest. Other ex-



41

Butter

B*

G-* Guns

Figure 1.

planations of single-issue voting are taken up in later sections. Two cases of zealotry are examined in this section of the paper: (1) the case where there are two homogeneous groups of single-issue voters, and (2) the case where there are two heterogeneous groups of single-issue voters. The election of interest is assumed to be a contest between two candidates who are able to freely adjust their positions in the relevant issue space to maximize votes.

Figure 1 characterizes the preferences of the two groups and the electoral equilibrium. For concreteness, the policy dimensions are labelled guns and butter. Group G zealots are concerned only about defense spending and vote as if each has vertical indifference curves in the guns-butter plane. Group B zealots place domestic programs above all others. Thus, Group B members have horizontal indifference curves in the guns-butter issue space. Group B's ideal "point", or rather ridge line, is labeled B* and Group G's ideal defense output is labelled G*. Note that a candidate who adopts position G* in the guns dimension gains the support of all the pro-defense zealots. A candidate who adopts B* in the butter dimension gains the support of the domestic program group. Thus, the ideal position for a candidate is B*, G*. It wins against any other platform, and generates a tie if both candidates adopt the same platform. Majoritarian voting, in this instance, yields the only outcome which is Pareto optimal. Both groups get what they want.1

Suppose instead of two homogeneous groups of zealots, there are two heterogeneous groups of zealots. In this case, members in each of the two subsets of the electorate agree about which issue is paramount, but disagree about ideal output levels. Such groups of zealots will not vote in unison, but will make independent choices based on a candidate's position in the relevant issue dimension.



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It turns out that candidate choices are only slightly more complicated in this case than in the previous homogeneous case. If G* is the position of the median member of defense group and B* is the ideal output of the median member of the domestic spending group, G*, B* is the dominant policy position for both candidates. G* generates majority support from the defense group against any other position, or a tie in the case where the other candidate takes the same position. B* generates similar results in the domestic spending group. The equilibrium is, again, stable and, again, Pareto optimal. (In this case, every policy outcome in the range of voter ideal points is Pareto optimal.)

However, median voter outcomes in each policy dimension do not imply a median result for the polity as a whole. To see this point, consider the case where there are three equally sized single-issue groups. In this case, two thirds of the electorate is indifferent to policy positions in each dimension. Thus, the median policy position of the electorate is not zealotry but rather a bland indifference in every issue dimension. (This, of course, is consistent with what election analysts often report about voter apathy.) The electoral outcome in this case does not reflect the median voter's position, but rather what might be called the position of the median zealot. Majoritarian outcomes do not necessarily reflect the opinions of the average or median voter when there is single-issue voting.

3. Information costs and single-issue voting

Theoretical conventions supported by empirical results suggests that zealotry is likely to be a relatively unusual sort of preference ordering. Most studies suggest that issues are substitutable. See Poole and Daniels (1985), or Enelow and Hinich (1984a). For single-issue voting to be empirically relevant, it must be motivated by something other than root tastes for policies. The next two sections of the paper demonstrate that individuals may vote in a manner similar to zealots (1) if there are economic reasons to collect only a single sort of information, or (2) if a fairly large number of voters are members of coordinated special interest groups. Special interest groups are taken up in the next section of the paper.

Individuals collect information about candidate positions partly as a means of maximizing the return to voting and partly for the stature and economic re- wards that being reasonably well-informed brings to them in their private lives. In either case, voters generally have an interest in minimizing the variance and bias of their estimates of candidate positions for a given expenditure on political information.2 This minimizes both electoral mistakes and loss of face and/or income derived from conversations with one's peers. The net advantage of better information is the difference between the gains from more accurate



43

estimates of candidate positions and the opportunity cost of gathering and processing the information.

Cast in conventional loss-minimizing terms, an individual's decision to gather and process information about a candidate's position in two issue dimensions can be represented as an attempt to minimize:

L = f (ab, I tb - tb' I, ag, I /g - g' I) + c (Ib, Ig) (1)

with

ab = el(Ib) ag = e2(Ig)

t tb - tb' I = e3(Ig) [Ig - I-g' I = e4(Ig)

Trailing lowercase letters b and g denote values for butter and guns, respectively. Thus, ab is the standard error of the estimated position of the candidate along the butter issue dimension; I /b - /tb' I is the bias of that estimate; and, ag is the standard error of the estimated position of the candidate position in the guns issue dimension; and I g - ,g' I is the bias of the guns estimate. Losses from estimation mistakes increase as any of these estimation errors increase. Estimation errors are assumed to decline monotonically as more information is gathered. Thus, the advantage of gathering information is the consequent reduction in losses from estimation errors. The cost of information used to estimate candidate positions is assumed to be a monotone increasing function of each sort of information gathered, here, Ib and Ig. Both the estimation loss function and the cost of information function are assumed to be convex.

If the voter of interest believes that there is no link between a candidate's positions on the issues of interest, then in order to be well-informed about a candidate's position, information must be gathered along each dimension of the relevant issue space. To simplify a bit, assume that voter's use unbiased estimation procedures, and therefore expected bias is zero in every case. Given this, the accumulation of information simply reduces the standard error of the estimates of the candidate's position in the issue dimension of interest without affecting the expected value of the estimate.

The voter's loss minimizing combination of information in this case satisfies the following first order conditions:

lab ObIb + CIb = 0 (2)

lab OgIg + CYg = 0 (3)

To minimize losses, the voter gathers information up to the point where the marginal reduction in losses equals the marginal opportunity cost of gathering and processing the information.



44

On the other hand, information costs and an individual's interest in gathering specific information along every dimension of a candidate's position de- clines if it is believed that candidate positions are not chosen independently of one another, but rather, are systematically connected because of ideological, regional or cultural characteristics of candidates or their constraints. Knowing that a candidate prefers a "strong" national defense provides voters with in- direct information about a candidate's position on domestic issues. Regardless of the reasons for this, if voters believe that issue positions are more or less one- to-one functions of one another, then gathering information about a candidate's position on a single issue allows one to forecast his positions on other issues as well.3

Such theories of policy positions may not be error free, but as long as total losses fall sufficiently to more than offset any consequent estimation losses, use of a theory is advantageous. To see this, assume that the voter believes that information about a candidate's position on guns implies information about his position on butter.

Ib = i(Ig) (4)

An individual who applies this theory can completely specialize in Ig information even though he remains interested in the butter position as well.

Application of this theory yields a new estimation loss function with only a single control variable, Ig, obtained by substituting equation 4 into equation 1 and setting Ib = 0 in the cost function. Differentiating this with respect to Ig yields the following first order condition for the loss minimizing amount of Ig information to gather and process:

lab abib + log "gig + CIg = 0 (5)

Again, the individual collects information up to the point where reduced losses from estimation errors in both issue dimensions equals the marginal cost of information about the candidate's position on guns. However, in this case, information about a candidate's position on national defence indirectly yields information about his position on domestic expenditures and thereby reduces the estimation losses in that dimension as well. This effect is represented by the first term of equation 5 and implies that the voter collects and processes more information about the candidate's position in the guns dimension than in the previous case.

An individual will benefit from using a theory like that represented by equation 4 if the expected loss from use of the theory is smaller than that associated with the independent information gathering strategy. Equation 5 demonstrates



45

why a theory does not have to be perfectly accurate for it to be useful. Since, equation 5 implies that more information about each candidate's position in the gun issue dimension is gathered, the standard error of the estimated candidate positions in the gun dimension is smaller than in the previous independent information gathering case. To the extent that the additional gun dimension information costs less than the previous investment in butter dimension information, information costs fall as well. On the other hand, to the extent that information about a candidate's position in the gun-issue dimension only im- perfectly generates information about his position in the butter dimension, the standard error of the estimated butter position may be larger than in the previous case. Use of this political theory is advantageous as long as any increased loss from errors in the butter dimension is more than offset by diminished losses in the gun dimension and cost savings from gathering and processing less political information.4

Use of a theory of candidate positions, implies that a voter collects political information about only a subset of the issue space, here, at the limit, along only a single-issue dimension. At the limit voters cast their ballots according to a candidate's position along a single dimension, that is, as if they were single- issue voters, even though their true interests span the issue space.

As long as candidates choose policy positions consistent with the political theories used, this form of single-issue voting has no practical implication beyond recognizing that voters tend to economize on information. Voters invest less on information, but candidates behave as if voters are aware of their complete political platform in the true issue space. On the other hand, any specialization in information gathering by individuals or organized groups of voters creates an opportunity for candidates to take popular positions on the "salient" issues while taking unpopular, but largely unknown, positions on others as a means of capturing the votes of individuals who focus on issues outside the mainstream.5

As long as various subsets of the electorate focus on different issue dimensions, the geometry of elections resembles that of the initial zealot case. The dominant candidate position is at the median of each issue dimension in which voters gather information. Moreover, the electoral equilibrium will be stable insofar as single-issue voting implies that electoral decisions in each issue dimension are made essentially independently of one another.

4. Special interest groups and single-issue voting

Individuals with an economic interest in a particular issue dimension have incentives to gather more information about positions along that dimension than



46

along others regardless of whether or not they have a specific theory of candidate positions. Their direct economic interest in a particular issue implies that estimation errors in this domain will be especially important. Their information costs may also, as Tullock (1967: 134) argues, be relatively smaller along the dimension of particular interest. Thus, individual voters with a common economic or ideological interest but no formal organization may vote as if they were an organized interest group because they make similar choices about per- tinent electoral information. The elderly are likely to be better informed about candidate positions on social security than on day-care. Social workers are likely to be more informed about candidate positions on the homeless than on space exploration. Defense contractors will know more about positions on defense expenditures than farm subsidies. This informational specialization naturally affects the manner in which they cast votes. And, to the extent that complete specialization occurs, their voting patterns would resemble the single- interest voting characterized in the last section.

Another possibility arises in coordinated special interest groups. In at least some cases, groups that vote as if they were interested in only a single-issue dimension will do better than they would have by revealing their true preferences over the issue space at issue.

Figure 2 illustrates this possibility for three homogeneous groups in the gun- butter issue space. Groups G and B are assumed to be more interested in guns and butter respectively than in the other issue. Their true underlying tastes are, thus, characterized by elliptical indifference curves rather than the conventional circular ones characterizing moderate group M. Suppose that all three groups have approximately the same membership. This implies that two of the three groups must favor a policy combination or candidate position for it to carry.

Suppose that the status quo is the ideal point of the moderate group. Since each group's ideal point lies long a straight line, by construction, this would have been the voting equilibrium had the two special interest groups had preferences with circular indifference curves. However, ellipsoid tastes in this case imply that there is no majority rule equilibrium. For example there is a cycle between M, N, and 0. On the other hand, if both interest groups vote as if they had only a single interest and revealed horizontal and vertical indifference curves along the main axis of their ellipsoid tastes, there is an equilibrium policy position, labelled E.

Both interest groups benefit from this strategy relative to the median voter position, since E is on a higher indifference curve for each group. On the other hand, E is outside the Pareto set, although E dominates most of the Pareto set for these two interest groups. In this case, what Kuran (1987) calls preference falsification by special interest group members yields a stable equilibrium but does not exhaust potential gains to trade. On the other hand, any departure



47

Butter

E

B*

N

M O

G* Guns

Figure 2.

from single-issue voting allows the possibility of electoral cycles and less de- sireable outcomes from the point of view of the two interest groups. Thus, the minor unrealized gains to trade between the two groups, area G, may be foregone as a means of ensuring stable and fairly beneficial political outcomes.7

It bears noting that, once again, single-issue voting yields an outcome which differs from that of the median or average voter. Group M's ideal point is at both the average and median of each dimension of choice. Yet there is no rea- son in this instance to expect majority elections to converge to point M in spite of the fact that voter preferences are all single peaked in the domain of interest and symmetrically distributed about M's ideal point. Here, strategic single- issue voting replaces the uncertainty of ordinary electoral politics with a stable equilibrium well beyond the median group's ideal point.8

5. Conclusion

The purpose of this paper has been to explore some of the implications of single-issue voting. In general terms, single-issue voting has been shown to be a stabilizing influence on majoritarian decision making. In each case examined,



48

stable equilibria exist under single-issue voting. On the other hand, the nor- mative properties of electoral outcomes are less clear cut. Under pure zealotry, electoral equilibria are uniformly Pareto efficient. However, electoral outcomes are not necessarily Pareto optimal in the case of strategic voting by special interest groups. The results suggest that single-issue voting can, by itself, cause electoral outcomes to depart from the center of the distribution of voter ideal points. Special interest groups might, thus, be served in the ordinary course of electoral politics even if they had no recourse to campaign contributions or rent-seeking activities which induce principal-agent problems. Voters who cast their votes as if they were single-issue voters can affect policy at both the largely ignored margins and in the mainstream of policy formation. Voting is enough.

Notes

1. It is clear that, this result extends to N-dimensioned issue spaces with N homogeneous groups, one per issue dimension.

2. In some circumstances espousing biased opinions may be privately useful. In a partisan environ- ment, one might well be more highly regarded for having overly dismal estimates of the performance of the opposition and overly exuberant estimates of one's own candidate's performance. However, uncertain estimates, e.g., high error variance, remain undesirable.

3. This parallels Enelow and Hinich's (1984b) analysis of how ideology can serve as an estimator for a candidate's position in the issue space. In the context of their model, candidate positions are linear functions of a one-dimensioned ideology parameter. This paper uses a similar charac- terization of the information problem. However, rather than going from some ideological parameter to the issue space, here one goes from information in one issue dimension to others by some ideological function. Use of such theories is consistent with the finding that linear transformations of issues spaces allow one to predict candidate and voter behavior. See Poole and Daniel (1987) or Enelow and Hinich (1984a: 175). See Sowell (1987) for a discussion of idea patterns in the political and non-political domains.

4. A third possibility is the use of butter information to infer gun-dimension information. That is to say, a voter might prefer to use the inverse function of "f" as the basis of his theory. In some cases, what might be called the direction of the theory matters. For example, even if a theory is symmetric with respect to its effect on estimation errors, losses from errors may be asymmetric.

5. Of course candidates also economize on information, time and energy. Thus, unless there are a sufficient number of voters to warrant mastering obscure issue dimensions, politicians will simply take no position on obscure issues. Only relatively large uncoordinated interest groups will attract the attention of candidates.

6. See Shepsle and Weingast (1981: 509) for a brief discussion of how voting on one dimension at a time generates stable electoral equilibria.

7. Tullock (1970) reaches a slightly different conclusion with a log rolling model of special interest group interaction. Log-rolling implies coordination between as well as within the special interest groups. As, Tullock points out, such coordination implies an equilibrium where indifference curves of the relevant special interest groups are tangent to one another. This result would be Pareto optimal. The single-issue voting method described in this section requires only coordination within each interest group.



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8. Single-issue voting can also move electoral outcomes closer to the origin than the median or average voter's position. For example, if two special interest groups have elliptical preferences similar to those depicted in Figure 2 but with a main axis perpendicular to the ones depicted, a single-issue voting strategy generates an outcome closer to the origin than the ideal point of the moderate group. The point of interest here is that single-issue voting can create incentives for politicians to take public policy positions well away from the median or average voter's ideal point, not that public programs are necessarily enlarged by the strategy of single-issue voting.

References

Austin-Smith, D. (1987). Interest groups, campaign contributions and probabilistic voting. Public Choice 54 (2): 123-140.

Becker, G.S. (1983). A theory of competition among pressure groups for political influence. Quarterly Journal of Economics 98 (3): 371-399.

Black, D. (1957/1987). The theory of elections and committees. Boston: Kluwer Academic Pub- lishers.

Buchanan, J.M. and Tullock, G. (1965). The calculus of consent. Ann Arbor: University of Michi- gan Press.

Buchanan, J.M., Tollison, R.D. and Tullock, G. (Eds.) (1980). Toward a theory of the rent- seeking society. College Station, TX: Texas A&M Press.

Congleton, R.D. (1989). Campaign finances and political platforms: The economics of political controversy. Public Choice 62 (2): 101-118.

Enelow, J. and Hinich, M.J. (1984a). The spacial theory of voting. Cambridge, MA: Cambridge University Press.

Enelow, J. and Hinich, M.J. (1984b). Ideology, issues and the spatial theory of elections. Ameri- can Political Science Review 74 (3): 279-300.

Gardner, B.L. (1987). Causes of U.S. farm commodity programs. Journal of Political Economy 95 (2): 290-310.

Kuran, T. (1987). Chameleon voters and public choice. Public Choice 53 (1): 63-78. Plott, C.R. (1967). Equilibrium and majority rule. American Economic Review 62 (4): 787-806. Poole, K.T. and Daniels, R.S. (1985). Ideology, party, and voting in the U.S. Congress,

1959-1980 (1985). American Political Science Review 79 (2): 373-399.

Rowley, C.K., Tollison, R.D. and Tullock, G. (Eds.) (1988). The political economy of rent- seeking. Boston: Kluwer Academic Publishers.

Shepsle, K. and Weingast, B. (1981). Structure induced equilibrium and legislative choice. Public Choice 37 (3): 503-519.

Sowell, T.A. (1987). A conflict of visions. New York: Morrow. Tullock, G. (1981). Towards a mathematics of politics. Ann Arbor: University of Michigan Press. Tullock, G. (1970). A simple algebraic logrolling model. American Economic Review 60: 419-426.



Documents

Information, Special Interests, and Single-Issue Voting