On the (sequential) majority choice of public good size and location

This article studies majority voting over the size and location of a public good when voters differ both in income and in their preferences for the public good location. Public good provision is financed either by a lump sum tax or by a proportional income tax. We analyze both the simultaneous and the sequential determinations of the public good’s size and location. We show that, while the choice of the type of public good follows the traditional median logic, the majoritarian determination of the taxation rate need not coincide with the preferences of a median income citizen. With lump sum financing, income heterogeneity plays no role and the sequential equilibrium consists of the median location together with the public good level most-preferred by the individual located at the median distance from the median. This policy bundle also constitutes an equilibrium with simultaneous voting in the special case of a uniform bivariate distribution of individuals’ income and location. With proportional taxation, there is no policy equilibrium with simultaneous voting. We offer a complete characterization of the equations describing the sequential equilibrium in the general case and we show why and how our results depart from those most-preferred by the median income individual located at the median distance from the median. We also compare these majority voting allocations with the socially optimal one.     

Voting on redistribution with tax evasion

This paper analyzes voting on a linear income tax whose proceeds are redistributed lump sum to the taxpayers. Individuals can evade taxes, which leads to penalties if evasion is detected. Since preferences satisfy neither single peakedness nor single crossing, a voting equilibrium may not exist. When an equilibrium does exist, there are several possible outcomes. There may be ‘conventional’ equilibria where the rich are expropriated by the poor and middle class. There may be equilibria without full expropriation where redistribution is limited by the threat of evasion. Finally, there may be equilibria where redistribution goes from the middle class to the rich and poor.     

Costly voting when both information and preferences differ: is turnout too high or too low?

We study a model of costly voting over two alternatives, where agents’ preferences are determined by both (i) a private preference in favour of one alternative e.g. candidates’ policies, and (ii) heterogeneous information in the form of noisy signals about a commonly valued state of the world e.g. candidate competence. We show that depending on the level of the personal bias (weight on private preference), voting is either according to private preferences or according to signals. When voting takes place according to private preferences, there is an unique equilibrium with inefficiently high turnout. In contrast, when voting takes place according to signals, turnout is locally too low. Multiple Pareto-ranked voting equilibria may exist and in particular, compulsory voting may Pareto dominate voluntary voting. Moreover, an increase in personal bias can cause turnout to rise or fall, and an increase in the accuracy of information may cause a switch to voting on the basis of signals and thus lower turnout, even though it increases welfare. This is a substantially revised version of Department of Economics University of Warwick Working Paper 670, “Information Aggregation, Costly Voting and Common Values”, January 2003. We would like to thank B. Dutta, M. Morelli, C. Perrroni, V. Bhaskar and seminar participants at Warwick, Nottingham and the ESRC Workshop in Game Theory for their comments. We would also like to thank the editor and an anonymous referee for their comments.     

Equitable agendas: agendas ensuring identical sincere and sophisticated voting decisions

 Sophisticated voting under amendment procedure using majority rule usually results in a decision that is distinct from the decision obtained through sincere voting. In this article it is shown that the underlying majority tournament (determined by the voters’ preferences) admits an agenda so that the sincere and sophisticated decisions are identical if and only if the initial strong component of the tournament is not a 3-cycle. As a result, most tournaments, in an asymptotic sense, admit an agenda so that the sincere and sophisticated decisions are identical. Received: 31 August 1993/Accepted: 28 August 1995     

WHAT MOTIVATES POLITICAL PREFERENCES? SELF‐INTEREST,IDEOLOGY, AND FAIRNESS IN A LABORATORY DEMOCRACY

Substantial prior literature has established that subjects in laboratory experiments are typically willing to sacrifice their own well being to make financial allocations more equal among participants. We test the applicability of this result in an environment that contains some of the key contextual issues that are usually excluded from more abstract games, but which might be important in situations involving income redistribution. Our general finding is that votes for a redistributive tax are almost entirely in accordance with self‐interest: above‐average earners vote for low tax rates and below‐average earners vote for high tax rates. A measure of subjects' preferences for fairness or equality, their self‐reported economic ideology, is not directly related to their voting behavior in this experiment. Because the ideology measure should be correlated with any intrinsic preferences regarding inequality aversion, we conclude that any preferences for fairness or inequality that our subjects possess are not strong enough to overcome self‐interest in this context. We do, however, find evidence for a possible indirect effect of ideology on choice behavior in that more conservative subjects tend to be more responsive to their self‐interest than the more liberal subjects. (JEL C90, D63)     

Popular support for social evaluation functions

This paper provides sufficient conditions under which the preferences of a social decision maker accord with majority voting. We show that an additive and monotone utilitarian social evaluation function is consistent with the outcomes of majority voting for the class of income distributions that are symmetric under a strictly increasing transformation. An example is the lognormal distribution. The required symmetry condition is generally accepted employing panel data for 116 countries from the World Bank’s POVCAL database.In this manner, the proposed methodology provides the consistent degree of inequality aversion and shows that median income is a good proxy for welfare.     

A Social Choice Lemma on Voting Over Lotteries with Applications to a Class of Dynamic Games

We prove a lemma characterizing majority preferences over lotteries on a subset of Euclidean space. Assuming voters have quadratic von Neumann–Morgenstern utility representations, and assuming existence of a majority undominated (or “core”) point, the core voter is decisive: one lottery is majority-preferred to another if and only if this is the preference of the core voter. Several applications of this result to dynamic voting games are discussed.This paper was completed after Jeff Banks’s death. John Duggan is deeply indebted to him for his friendship and his collaboration on this and many other projects.     

The probability of the paradox of voting for weak preference orderings

In this paper the probability of the voting paradox for weak orderings is calculated analytically for the three-voter-three-alternative case. It appears that the probability obtained this way is considerably smaller than in the corresponding case for linear orderings. The probability of intransitive majority relations for weak orderings in the 3 × 3 case is calculated as well, both with unconcerned and with concerned voters. Basic in the calculations are three theorems which are formulated in the field of domain conditions and restricted preferences. Received: 18 February 1997 / Accepted: 21 October 1997     

The political viability of a negative income tax

This paper offers three propositions relating to the political viability of the negative income tax. One, despite its work disincentive, a majority of households would support a linear income tax that makes cash payments to low income households. However two, when government consumption is sufficiently high, a majority would favor a proportional tax over such a tax. Three, under certain conditions, a majority of households will prefer public provision of a private good or an in-kind transfer to a negative income tax. These latter two propositions offer an explanation for the public's apparent distaste for widespread cash transfers. Received: 17 September 1999/Accepted: 21 April 2000     

TAX EFFECTS VERSUS BUDGET EFFECTS ON LABOR SUPPLY

This paper analyzes the effects on labor supply of parallel changes in taxes and public spending of various types. A number of important recent developments in the labor supply behavior of households are highlighted by such a study of various types of "budget effects," rather than isolated "tax effects." This comes out in particular when considering cross substitution effects on labor supply of changes in public spending on goods and services or of the subsidization of goods and services provided by private markets. Moreover, the income effects of tax changes are often mitigated, or possibly even removed, by the income effects of the accompanying expenditure changes.     

Strategy-proofness on Euclidean spaces

 In this paper we characterize strategy-proof voting schemes on Euclidean spaces. A voting scheme is strategy-proof whenever it is optimal for every agent to report his best alternative. Here the individual preferences underlying these best choices are separable and quadratic. It turns out that a voting scheme is strategy-proof if and only if (α) its range is a closed Cartesian subset of Euclidean space, (β) the outcomes are at a minimal distance to the outcome under a specific coordinatewise veto voting scheme, and (γ) it satisfies some monotonicity properties. Neither continuity nor decomposability is implied by strategy-proofness, but these are satisfied if we additionally impose Pareto-optimality or unanimity. Received: 18 October 1993/Accepted: 2 February 1996     

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     

Inequality and education decisions in developing countries

In this paper we analyze the effect of inequality on school enrollment, preferred tax rate and expenditure per student in developing countries; when parents can choose between child labor, public schooling or private schooling. We present a model in which parents make schooling decisions for their children, weighing the utility benefit of having a child with formal public or private education versus the forgone income from child labor or household work. Parents vote over the preferred tax rate to finance freely provided public education. The utility benefit of an educated child is proportional to expenditure per student, so that there is congestion in public school. We find that when parents can send their children to work or to private school, high inequality leads to exit from public education at both ends of the income distribution. Thus high inequality reduces the support for public education, leading to a low tax rate and expenditure per student. Exit from public education results in both high child labor and a large fraction of students attending private school. In fact there is a threshold level of inequality above which there is no longer support for public education. In addition we explore the implications for the design of foreign aid. The results suggest that foreign aid policies should focus on promoting school attendance rather than increasing school resources, as the later policy might be offset by a reduction in the recipient country’s fiscal effort, with little impact on outcomes.      

On the equilibrium of voting games with abstention and several levels of approval

We study the core of “(j, k) simple games”, where voters choose one level of approval from among j possible levels, partitioning the society into j coalitions, and each possible partition facing k levels of approval in the output (Freixas and Zwicker in Soc Choice Welf 21:399–431, 2003). We consider the case of (j, 2) simple games, including voting games in which each voter may cast a “yes” or “no” vote, or abstain (j = 3). A necessary and sufficient condition for the non-emptiness of the core of such games is provided, with an important application to weighted symmetric (j, 2) simple games. These results generalize the literature, and provide a characterization of constitutions under which a society would allow a given number of candidates to compete for leadership without running the risk of political instability. We apply these results to well-known voting systems and social choice institutions including the relative majority rule, the two-thirds relative majority rule, the United States Senate, and the United Nations Security Council.     

Welfare-domination under preference-replacement: A survey and open questions

The objective of this paper is to describe various applications of a requirement of solidarity pertaining to situations in which the preferences of some of the agents may change. It says that the welfares of all agents whose preferences are fixed should be affected in the same direction: they should all weakly gain, or they should all weakly lose. We show how this condition, which we name “welfare-domination under preference-replacement”, can help in evaluating allocation rules. We discuss it in several contexts: private good allocation in classical economies, public good decision, binary choice with quasi-linear preferences, economies with indivisible goods, economies with single-peaked preferences, both in the private good case and in the public good case, and economies with time. For some of these models the implications of the property are well understood. For others, we state a number of open problems. Received: 2 January 1997/Accepted: 26 February 1998     

Sophisticated voting and equilibrium refinements under plurality rule

In this paper we show in the context of voting games with plurality rule that the “perfect” equilibrium concept does not appear restrictive enough, since, independently of preferences, it can exclude at most the election of only one candidate. Furthermore, some examples show that there are “perfect” equilibria that are not “proper”. However, also some “proper” outcome is eliminated by sophisticated voting, while Mertens' stable set fully satisfies such criterium, for generic plurality games. Moreover, we highlight a weakness of the simple sophisticated voting principle. Finally, we find that, for some games, sophisticated voting (and strategic stability) does not elect the Condorcet winner, neither it respects Duverger's law, even with a large number of voters. Received: 16 March 1999/Accepted: 25 September 1999     

Single-Crossing, Strategic Voting and the Median Choice Rule

This paper studies the strategic foundation of the Representative Voter Theorem (Rothstein in: Pub Choice 72:193–212, 1991), also called the “second version” of the Median Voter Theorem. As a by-product, it also considers the existence of strategy-proof social choice functions over the domain of single-crossing preferences. The main result shows that single-crossing constitutes a domain restriction over the real line that allows not only majority voting equilibria, but also non-manipulable choice rules. In particular, this is true for the median rule, which is found to be group strategic-proof over the full set of alternatives and over every nonempty subset. In addition, the paper also examines the relation between single-crossing and order-restriction. And it uses this relation together with the strategy-proofness of the median rule to prove that the outcome predicted by the Representative Voter Theorem can be implemented in dominant strategies through a simple mechanism. This mechanism is a two-stage voting procedure in which, first, individuals select a representative among themselves, and then the winner chooses a policy to be implemented by the planner.     

An extension of Bowen’s dynamic voting rule to many dimensions

 We ask in this paper about the effect on social decisions of limiting the size of changes that voters may propose each time in an otherwise standard dynamic social choice model. The voting rule we study can be seen as an extension of Bowen’s dynamic “majority voting” rule, and is closely related to the dynamic procedures for public good allocation in the literature (Drèze and de la Vallée Poussin 1971; Malinvaud 1971; Laffont and Maskin 1983; Chander 1993). Under general assumptions we prove existence and Pareto efficiency of equilibrium, and show that our rule motivates voters not to misrepresent preferences (more precisely, the rule is Strongly Locally Individually Incentive Compatible). Under Euclidean preferences we find that electoral cycles do not arise (i.e., the rule is convergent), that there is a unique equilibrium, and that the equilibrium coincides with the solution to an old problem of geometry, first addressed by Fermat, Torricelli, and Cavallieri. Received: 20 September 1994/Accepted: 6 August 1996     

Political–economic equilibrium when parties represent constituents: The unidimensional case

 A political–economic environment is studied in which two parties, representing different constituencies of citizens, compete over a proportional tax rate to be levied on private endowments, to finance a public good. Although parties know the distribution of citizen traits (preferences and endowments), they are uncertain about the distribution of traits among the citizens who will turn up at the polls. This uncertainty engenders an endogenously derived function π(t ₁, t ₂) giving the probability that any one tax policy t ₁ will defeat another t ₂ in the election. Equilibrium existence theorems are proved, and the nature of equilibrium is compared with the equilibrium that exists when Downsian parties (ones whose objective is to maximize the probability of victory) face uncertainty. Both constituency-representing parties and uncertainty are needed to generate equilibria in which parties propose different policies. Received: 4 April 1995/Accepted: 2 April 1996     

‘One and a Half Dimensional’ Preferences and Majority Rule

I examine a model of majority rule in which alternatives are described by two characteristics: (1) their position in a standard, left-right dimension, and (2) their position in a good-bad dimension, over which voters have identical preferences. I show that when voters’ preferences are single-peaked and concave over the first dimension, majority rule is transitive, and the majority’s preferences are identical to the median voter’s. Thus, Black’s (The theory of committees and elections, 1958) theorem extends to such a “one and a half” dimensional framework. Meanwhile, another well-known result of majority rule, Downs’ (An economic theory of democracy, 1957) electoral competition model, does not extend to the framework. The condition that preferences can be represented in a one-and-a-half-dimensional framework is strictly weaker than the condition that preferences be single-peaked and symmetric. The condition is strictly stronger than the condition that preferences be order-restricted, as defined by Rothstein (Soc Choice Welf 7:331–342;1990).