Single-peakedness and strategy-proofness of generalized median voter schemes

We identify, in a continuous multidimensional framework, a maximal domain of preferences compatible with strategy-proofness for a given generalized median voter scheme. It turns out that these domains are a variation of single-peakedness. A similar but stronger result for the discrete case and single-peakedness has been already obtained by Barberà et al. (1999). However, both results are independent and their proofs involve different arguments. Received: 27 July 1998/Accepted: 11 September 2000     

Income inequality,redistribution and the position of the decisive voter

A large literature explaining patterns of redistribution makes use of the median voter theorem. Using a novel approach, this contribution shows that in OECD countries the decisive voter, determined by the earner who sees her preferred tax rate being implemented, on average sits around the 50^th percentile in the income distribution, although significant within and between country differences exist. Under the assumption of a lognormal distribution of gross income, we derive the required tax rate to align the observed gross and net Gini coefficients in OECD countries. This estimated tax rate is compared to the tax rate preferred by the median income earner, which gives a new index capturing a nation’s deviation from the median voter position, measured as the difference between the estimated percentile position of the decisive voter and the 50^th percentile position of the median voter. We provide a comparative overview of this index over time and between countries. We also locate the positions of alternative versions of the decisive voter, among which following the ‘one dollar, one vote’ rule, in a Lorenz curve diagram.     

SELF-INTEREST REDISTRIBUTION AND THE NATIONAL FOOTBALL LEAGUE PLAYERS ASSOCIATION

The NFL Players Associations decision to seek increased collective determination of player compensation through a salary schedule in 1982 is explained in this study as being motivated by self-interest redistribution. Probit and multiple regression analysis are used to test whether the redistribution is consistent with median voter self-interest redistribution. The results indicate substantial redistribution in favor of the median voter with respect to experience. The Players Association's actions, which have been criticized as being against the players' interests, appear consistent with the interests of a majority of the players.     

Monopoly,efficient contract,and median voter models of union wage determination: A critical comparison

This article critically compares the monopoly, efficient contract, and median voter models of union wage determination. The models are first analyzed with respect to five theoretical issues: the aggregation of preferences, the principal-agent problem, strike costs, dynamics, and incentive compatibility. The models are then compared with regard to their ability to explain two features of union wage/employment determination: the asymmetric response of union wages to demand shocks and the wide variation in the presence of featherbedding restrictions in union contracts. While all three models suffer from significant short-comings, the median voter model is generally superior. The authors acknowledge the helpful comments of Hank Farber and the financial assistance received from the College of Business Administration, Georgia State University.     

THE GROWTH OF SOCIAL SECURITY: ELECTORAL PUSH OR POLITICAL PULL?

The social security program has grown more than a thousand fold since its inception. Even fnter the increased number of retired persons and inflation are accounted for, average real social security benefit levels more than tripled from the late 1940s to the early 1980s. What accounts for this growth? This paper finds that increased retirement benefit levels are generated by changes in the constraints faced by the median voter rather than by changes in the political power of special interest groups. The results suggest that the median voter has a finite planning horizon.     

Empirics of the median voter: democracy, redistribution and the role of the middle class

This paper improves the empirical investigation on the effectiveness of the median voter theorem. Using high quality data, it is possible to directly observe individual net cash transfers in several countries and to investigate the effects of taxes and transfers on different social classes and in aggregate. This allows testing of both the “redistribution hypothesis” (more inequality leads to more redistribution in aggregate) and the “median voter hypothesis” (the middle class plays a special role in policy making). Results suggest acceptance of the former and reject on, or at least questioning, of the latter. Not only the gains from redistribution are negligible for the middle class, but also the link between income and redistribution is also lower for it than for any other class of income. Moreover, the strength of the median voter seems to fall over time. Finally, the amount of redistribution targeted to the middle class is lower in more asymmetric societies, a result that contrasts strongly with the median voter theorem.     

Aggregate uncertainty in the citizen candidate model yields extremist parties

We extend the citizen candidate model of electoral competition with sincere voting to allow for k ≥ 2 states of aggregate uncertainty. We discuss and characterize the equilibrium set in this framework. We provide conditions for the existence of two-party equilibria when k = 2 and show that the policies of the two parties in any such equilibrium are not only divergent but that the parties are extremist: when the political mood is left-wing, the left-wing party wins decisively with a platform that is to the left of the left-wing median voter, while when the political mood is right-wing, the right-wing party wins decisively with a platform that is to the right of the right-wing median voter. We then provide conditions under which such equilibria remain robust for an arbitrary value of k.     

Bandwagon, underdog, and political competition: the uni-dimensional case

This article studies the effects of bandwagon and underdog on the political equilibrium of two-party competition models. We adapt for voter conformism the generalized Wittman?CRoemer model of political competition, which views political competition as the one between parties with factions of the opportunists and the militants that Nash-bargain one another, and consider three special cases of the general model: the Hotelling?CDowns model, the classical Wittman?CRoemer model, and what we call the ideological-party model. We find that the presence of voter conformism significantly affects the nature of political competition, and its effect on political equilibrium is quite different depending on the model one uses. In the Hotelling?CDowns model, political parties put forth an identical policy at the equilibrium, regardless of the type of voter conformism, and this is the only equilibrium. In both the ideological-party and classical Wittman?CRoemer models, parties propose differentiated policies at the equilibrium, and the extent of policy differentiation depends on the degree of voter conformism.     

MEDIAN VOTERS OR BUDGET MAXIMIZERS: EVIDENCE FROM SCHOOL EXPENDITURE REFERENDA

Some readers may have found these results of greater interest were we able to confirm the directional hypotheses of the certainty setter model in addition to finding that spending is "related" to the reversion – the much weaker prediction of the uncertainty model. Yet the failure of the certainty
When base elections were optional, their infrequent occurrence might be expected under either a median voter or a setter model. For those districts that did hold base elections, the observations appear consistent with a setter model, but are either inexplicable by or inconsistent with a median voter model. Finally, both (a) the relationship between the number of budget elections and the presence of base elections, and (b) the outcome of mandatory base elections in 1978 provide a set of observations that are challenging to either model.
A similar challenge was posed by our investigation of budget elections when we called attention to the inadequacy of static, full information models. Rather than resolving the question of the simple setter model against the simple median voter model, our results indicate that both may be inappropriate and that endeavors dealing with complexities omitted here are warranted.     

PRESSURE GROUPS AND PUBLIC EXPENDITURES: THE FLYPAPER EFFECT RECONSIDERED

A model of government budgeting is developed in which lobbying by interest groups can divert the allocation of funds away from the one preferred by the median voter. The model is applied to state and local governments to show that the "flypaper effect"–the tendency for lump-sum grants to increase public expenditures by more than an equivalent increase in the community's pretax income–can be explained without the customary assumption of voter fiscal illusion. Furthermore, the model predicts variation in the extent of the flypaper effect among expenditure categories, as found in previous empirical studies.     

Limiting median lines frequently determine the yolk

In two-dimensional Euclidean spatial voting models the yolk is the smallest circle which intersects all median lines. It has been assumed that limiting median lines, which intersect two voter ideal points, are sufficient to determine the yolk but recently counter examples have been reported. This note describes the impact of those findings on the results of computation of the location and size of yolk.I wish to acknowledge a number of helpful conversations with Craig Tovey and Nicholas Miller. Any errors which remain are my own.     

Social choice by majority rule with rational participation

This paper explores the social choice properties of majority rule when voters rationally participate in elections. Employing the basic model of voter behavior developed originally by Ledyard (1984) and Palfrey and Rosenthal (1985), we show that when the electorate is sufficiently large, a participation equilibrium exists and is unique. The main result of the paper shows that under these conditions the social preference ordering induced by majority rule is identical to that given by the expected utility of a randomly selected voter, implying the existence of a Condorcet point in the proposal space. A final section provides intuition for the main theorems and relates the equilibrium of this majority rule game to the median voter result.     

How does inequality aversion affect inequality and redistribution?

We investigate the effects of inequality aversion on equilibrium labor supply, tax revenue, income inequality, and median voter outcomes in a society where agents have heterogeneous skill levels. These outcomes are compared to those which result from the behavior of selfish agents. A variant of Fehr-Schmidt preferences is employed that allows the externality from agents who are “ahead” to differ in magnitude from the externality from those who are “behind” in the income distribution. We find first, that inequality-averse preferences yield distributional outcomes that are analogous to tax-transfer schemes with selfish agents, and may either increase or decrease average consumption. Second, in a society of inequality-averse agents, a linear income tax can be welfare-enhancing. Third, inequality-averse preferences can lead to less redistribution at any given tax, with low-wage agents receiving smaller net subsidies and/or high-wage individuals paying less in net taxes. Finally, an inequality-averse median voter may prefer higher redistribution even if it means less utility from own consumption and leisure.     

Modeling large electorates with Fourier series, with applications to Nash equilibria in proximity and directional models of spatial competition

 In this paper we introduce harmonic analysis (Fourier series) as a tool for characterizing the existence of Nash equilibria in two-dimensional spatial majority rule voting games with large electorates. We apply our methods both to traditional proximity models and to directional models. In the latter voters exhibit preferences over directions rather than over alternatives, per se. A directional equilibrium can be characterized as a Condorcet direction, in analogy to the Condorcet (majority) winner in the usual voting models, i.e., a direction which is preferred by a majority to (or at least is not beaten by) any other direction. We provide a parallel treatment of the total median condition for equilibrium under proximity voting and equilibrium conditions for directional voting that shows that the former result is in terms of a strict equality (a knife-edge result very unlikely to hold) while the latter is in terms of an inequality which is relatively easy to satisfy. For the Matthews [3] directional model and a variant of the Rabinowitz and Macdonald [7] directional model, we present a sufficiency condition for the existence of a Condorcet directional vector in terms of the odd-numbered components of the Fourier series representing the density distribution of the voter points. We interpret our theoretical results by looking at real-world voter distributions and direction fields among voter points derived from U.S. and Norwegian survey data. Received: 7 July 1995 / Accepted: 14 May 1996     

The Ross-Dunlop debate and union wage concessions: A median voter analysis

The Ross-Dunlop debate concerns the extent to which unions take into account the trade-off between wages and employment in formulating their wage demands. This paper develops a median voter model of union behavior that offers a new approach to resolving the Ross-Dunlop debate. The model shows that when the binding constraint on the median union member in the seniority distribution is the threat of layoff, the union will behave as a “Dunlop-type” union; when the binding constraint is the cost of striking, the union will behave as a “Ross-type” union. The model is then applied to the related issue of union wage concessions. Two questions are examined: Under what conditions will a union agree to wage concessions? How large a cut in wages will be accepted?     

VOTING, SPATIAL MONOPOLY, and SPATIAL PRICE REGULATION

Regulations often require that local public utilities engage in high rates of freight absorption. These regulations, often mandating uniform pricing, are shown to arise logically as a consequence of self-interested voting behavior. We specifically consider the case of a single-plant spatial monopoly which is regulated by consumers distributed around the plant. Consumers may change their delivered price by voting to require a rate of freight absorption which differs from the profit-maximizing rate. Voting outcomes under a median voter model predict the high rate of freight absorption often observed in practice.     

Limiting median lines do not suffice to determine the yolk

The yolk, an important concept in the spatial model of voting, is defined in two dimensions as the smallest circle intersecting all median lines. In the literature one finds the assumption that the limiting median lines, i.e., those that pass through two voter ideal points, suffice to determine the yolk. Counterex-amples are given here which invalidate this assumption.This work was done while the second author held a Research Associateship from the National Research Council at the Naval Postgraduate School, and a Presidential Young Investigator Award from the National Science Foundation, ECS-8451032.     

HAS THE MEDIAN VOTER FOUND A BALLOT BOX THAT HE CAN CONTROL?

This paper examines the appropriateness of the median voter hypothesis within an agenda control framework where the alternative to a proposed expenditure level is the existing level. Evidence from New York State school districts suggests that within this institutional setting the actual level of public service provision does not differ significantly from the median voter's preferred level. The evidence also suggests that demand function parameter estimates for educational expenditures are not sensitive to the assumption that the public service output level corresponds to the median voter's private equilibrium.     

Rational voters in a partisanship model

This paper examines a voter model for the US which is interconnected with the partisan theory. In our model, voters are rational and forward-looking. They are perfectly informed about the preferences of political parties and about the state of the economy. The predictions of our voter model differ from the predictions of conventional voter models, according to which the incumbent benefits from low unemployment and low inflation, irrespective of its political colour. In a partisan setting, the democratic party benefits from high unemployment and the republican party benefits from high inflation. Regressions of presidential approval rates indicate that the predictions of both the partisan voter model and the conventional model are consistent with the data.     

Equal representation in two-tier voting systems

The paper investigates how voting weights should be assigned to differently sized constituencies of an assembly. The one-person, one-vote principle is interpreted as calling for a priori equal indirect influence on decisions. The latter are elements of a one-dimensional convex policy space and may result from strategic behavior consistent with the median voter theorem. Numerous artificial constituency configurations, the EU and the US are investigated by Monte–Carlo simulations. Penrose’s square root rule, which originally applies to preference-free dichotomous decision environments and holds only under very specific conditions, comes close to ensuring equal representation. It is thus more robust than previously suggested.