Policy divergence in multicandidate probabilistic spatial voting

Existing models of multicandidate spatial competition with probabilistic voting typically predict a high degree of policy convergence, yet in actual elections candidates advocate quite divergent sets of policies. What accounts for this disparity between theory and empirical observation? I introduce two variations on the basic probabilistic vote model which may account for candidate policy divergence: 1) a model which incorporates candidate-specific variables, so that candidates may enjoy nonpolicy-related electoral advantages (or disadvantages); 2) a model which allows nonzero correlations between the random terms associated with voters' candidate utilities, thereby capturing situations where voters view two or more candidates as similar on nonpolicy grounds. I report candidate equilibrium analyses for each model, which show far greater policy divergence than exists under the standard probabilistic vote model. I then analyze the strategic logic which underlies these results.

     

Multiparty spatial competition with probabilistic voting

I develop a general model of multiparty competition in which parties model voters' choices by means of probabilistic choice rules. The model is specified in terms of an issue salience coefficient which varies with the importance voters attach to issues, as opposed to unmeasured nonissue motivations. I show that when the policy salience coefficient is sufficiently low, then both vote-maximizing and rank-maximizing parties have a dominant strategy: to adopt the “most popular platform,” which maximizes voter utilities over the entire electorate. This most popular platform therefore represents a convergent equilibrium when all parties are vote- or rank-maximizing. Numerical estimates suggest that this equilibrium result holds for degrees of issue voting which exceed the parameters behavioral researchers have estimated for various historical elections.     

Campaign allocations under probabilistic voting

We develop a probabilistic voting model where candidates compete by advertising in different media markets. Ads are viewed by everyone within a market and cannot be targeted to subgroups such as one candidate??s partisans. Candidates estimate the distribution of voter preference intensities in a market, and campaign ads then shift this distribution. Individuals with any intensity vote with some probability for each candidate. We derive comparative static implications of changes in a variety of factors on the advertising decisions of each candidate. Using campaign advertising data from 2002, we find these results to be consistent with actual campaign allocation behavior.     

An application of the multicandidate calculus of voting to the 1972 and 1976 German federal elections

Two important assumptions underlying the Riker-McKelvey-Ordeshook, expected-utility-based, multicandidate calculus of voting are that citizens decide whether or not and for whom to vote in a single-member district (SMD), plurality-winner electoral system and that they ignore aggregate outcomes, that is, how citizens in other districts may vote. Aranson modifies this calculus by investigating citizens' decisions in proportional-representation (PR) systems and/or situations in which aggregate outcomes require parties to form parliamentary coalitions to govern. This study operationalizes and applies the probability and utility components of this modified calculus to data on the 1972 and 1976 West German federal elections, which combine features of SMD and PR systems and of which coalition politics is an integral part. Expected-utility calculations used to predict reported voting decisions achieve reasonably good levels of aggregate accuracy. Further analysis reveals that gradations in respondents' expected utilities, as well as in their utilities and surrogate measures of the subjective probabilities of electoral outcomes, relate significantly to reported voting decisions. Also, variables that model coalition considerations are commonly the most significant.     

Systemic polarisation and spatial voting

The controversy between proximity and directional models of issue voting has not been settled. Instead of appointing an ultimate winner, this article explores the conditioning impact of the level of systemic polarisation and provides evidence that proximity is a more relevant determinant of voter behaviour in less polarised systems, whereas there is a centrifugal and directional dynamic in more polarised contexts. By so doing, the article shows how a largely forgotten notion – namely Sartori's idea of the spatial elasticity of the political spectrum – leads to different spatial viewpoints. In distinguishing between party (supply side) and voter (demand side) polarisation, this framework provides a comprehensive picture about the conditions that turn a centripetal electoral dynamic into a purely centrifugal one.     

Pareto optimality of policy proposals with probabilistic voting

This paper studies the Pareto optimality properties of policy proposals and electoral outcomes when there is probabilistic voting. Theorem 1 proves that, when the position of one candidate is taken as fixed, the other candidate will propose a Pareto optimal alternative. This implies that whenever there is an electoral equilibrium (in pure strategies) the electoral outcome is Pareto optimal. It also implies that, even if there is no such equilibrium, the electoral outcomes from a sequence of elections will be Pareto optimal (except, possibly, for an initial status quo).     

Congressional rationality and spatial voting

It is very difficult to demonstrate that representatives employ sophisticated cost-benefit calculations in evaluating constituent benefits when making many legislative decisions. This is because most modern American legislation is ambiguous about which constituencies will receive particularized benefits. This paper examines a series of locational rollcall votes in which the benefits going to constituents were obvious. In such cases representatives balance increases in voter support within their congressional districts and potential increases in their political power within Congress to be gained by vote trading. If constituency benefits are great, representatives overwhelmingly support legislation to provide such benefits. As the benefits decline, vote trading increases.     

Interest groups,campaign contributions,and probabilistic voting

This essay develops a simple model to analyze the impact of campaign contributions on electoral-policy decisions of candidates for office. Interest groups here are firms that select contributions under the assumption that candidates' policies and opposing groups' donations remain unaltered. Candidates, however, recognize that their policy choices affect contributions. Campaign contributions are used by candidates to affect policy-oriented voters' perceptions of candidates' positions. In this framework the introduction of campaign contributions may affect candidates' electoral policies, and if they do then they benefit surely exactly one of the two interest groups.     

Dealignment, spatial polarisation and economic voting

Abstract. Estimates of voting by occupational class are provided for each of 22 regions in the UK for every general election since 1964. These are analysed, using a log-linear modelling strategy, to identify the changing degree of class dealignment and spatial polarisation within the British electorate over the period. The growing regional variability is consistent with expectations regarding the increasing volume of economic voting and the pattern of uneven development in the country: the north-south and urban-rural divides have both widened.     

A spatial model of legislative voting with perceptual error

This paper presents a unidimensional spatial model of voting in which members of Congress vote based on an imprecise perception of roll-call alternatives. The model is applied to the Senate roll-call votes of 1977 to estimate the ideal points of the senators, and to examine the role of a liberal-conservative dimension in describing votes on economic issues relative to social issues. In light of the spatial model, the paper argues that “standard” models of roll-call voting are not based on a theory of choice, and hence, that it is difficult to interpret their results. Alternatives to standard models, based on the spatial model, are developed and are used to analyze the role of ideology in deciding a specific economic issue: coal strip-mining.     

A general probabilistic spatial theory of elections

In this paper, we construct a general probabilistic spatial theory of elections and examine sufficient conditions for equilibrium in two-candidate contests with expected vote-maximizing candidates. Given strict concavity of the candidate objective function, a unique equilibrium exists and the candidates adopt the same set of policy positions. Prospective uncertainty, reduced policy salience, degree of concavity of voter utility functions, some degree of centrality in the feasible set of policy locations, and restrictions on the dimensionality of the policy space are all stabilizing factors in two-candidate elections. 3. CITIZEN. We have been called so of many, not that our heads are some brown, some black, some auburn, some bald, but that our wits are so diversely colored. And truly I think if all our wits were to issue out of one skill, they would fly east, west, north, south, and their consent of one direct way should be at once to all points o' the compass. (Shakespeare, coriolanus II.iii. 19–26)     

A test of the predictive dimensions model in spatial voting theory

We model correlated voter-candidate issue data within the framework of the Enelow-Hinich spatial model of predictive dimensions. The empirical consequences of this model of the issue data are surprising and allow for an indirect test of the Enelow-Hinich spatial model. The central prediction of the correlated data model we construct, which depends critically on the underlying spatial model, is tested with issue data from the 1980 NES pre-election interview. The test results are highly supportive of the model's predictions. We conclude both that the spatial model of predictive dimensions is empirically supported and that candidate spatial locations estimated by the model are not an artifact of correlated voter-candidate issue data.     

How does ideology matter in the spatial model of voting?

In spatial voting games without a core, if candidates are constrained on one issue, they are implicitly constrained on other issues. Thus external constraints affect optimal positions for candidates. Using new solution concepts, we find the optimal position for a candidate given any linear constraint, given an opponent’s constraint, and determine conditions when constraints are sufficient to yield unbeatable positions.     

Three-candidate spatial competition when candidates have valence: stochastic voting

We study the effects of stochastic (probabilistic) voting on equilibrium locations, equilibrium vote shares and comparative statics in a setup with three heterogeneous candidates and a single-dimensional issue space. Comparing the equilibria with and without stochastic voting, we find that under an appropriate level of uncertainty about voter behavior, the model has a pure strategy Nash Equilibrium (PSNE) that is free from several non-plausible features of the PSNE under deterministic voting. This result is robust to extensions to asymmetric density and plurality maximization.     

Centripetal forces in spatial voting: On the size of the Yolk

The yolk, the smallest circle which intersects all median lines, has been shown to be an important tool in understanding the nature of majority voting in a spatial voting context. The center of the yolk is a natural ‘center’ of the set of voter ideal points. The radius of the yolk can be used to provide bounds on the size of the feasible set of outcomes of sophisticated voting under standard amendment procedure, and on the limits of agenda manipulation and cycling when voting is sincere. We show that under many plausible conditions the yolk can be expected to be small. Thus, majority rule processes in spatial voting games will be far better behaved than has commonly been supposed, and the possible outcomes of agenda manipulations will be generally constrained. This result was first conjectured by Tullock (1967).     

Evidence on the importance of spatial voting models in presidential nominations and elections

ADA scores and Nominate scores are used for the first time to examine the influence of spatial voting records on which candidate wins the party’s presidential nomination and on which nominee wins the general election. We find that the most conservative Republican candidate and moderately liberal Democrats were most likely to win their party’s nomination. For general elections we find that the candidate’s spatial record has nearly as much impact on the outcome as economic growth, which has been the focus of most past empirical research. The nominee whose voting record is more moderate is more likely to be elected.