Existence of a Condorcet Winner When Voters Have Other‐Regarding Preferences

In standard political economy models, voters are “self‐interested” that is, care only about “own” utility. However, the emerging evidence indicates that voters often have “other‐regarding preferences” (ORP), that is, in deciding among alternative policies voters care about their payoffs relative to others. We extend a widely used general equilibrium framework in political economy to allow for voters with ORP, as in Fehr and Schmidt (1999) . In line with the evidence, these preferences allow voters to exhibit “envy” and “altruism,” in addition to the standard concern for “own utility.” We give sufficient conditions for the existence of a Condorcet winner when voters have ORP. This could open the way for an incorporation of ORP in a variety of political economy models. Furthermore, as a corollary, we give more general conditions for the existence of a Condorcet winner when voters have purely selfish preferences.     

POSITIVELY RESPONSIVE COLLECTIVE CHOICE RULES AND MAJORITY RULE: A GENERALIZATION OF MAY'S THEOREM TO MANY ALTERNATIVES

May's theorem shows that if the set of alternatives contains two members, an anonymous and neutral collective choice rule is positively responsive if and only if it is majority rule. We show that if the set of alternatives contains three or more alternatives only the rule that assigns to every problem its strict Condorcet winner satisfies the three conditions plus Nash's version of “independence of irrelevant alternatives” for the domain of problems that have strict Condorcet winners. We show also that no rule satisfies the four conditions for domains that are more than slightly larger.     

Equilibrium play in matches: Binary Markov games

We study two-person extensive form games, or “matches,” in which the only possible outcomes (if the game terminates) are that one player or the other is declared the winner. The winner of the match is determined by the winning of points, in “point games.” We call these matches binary Markov games. We show that if a simple monotonicity condition is satisfied, then (a) it is a Nash equilibrium of the match for the players, at each point, to play a Nash equilibrium of the point game; (b) it is a minimax behavior strategy in the match for a player to play minimax in each point game; and (c) when the point games all have unique Nash equilibria, the only Nash equilibrium of the binary Markov game consists of minimax play at each point. An application to tennis is provided.     

Heterogeneous labor skills,the median voter and labor taxes

This paper analyzes the median voter?s most preferred sequences of labor taxes in the standard neoclassical growth model. We consider an infinite horizon economy in which agents are heterogeneous with respect to both initial wealth and labor skills. We start by providing a set of sufficient conditions for the existence of a Condorcet winner. We then characterize the most preferred tax sequence by the median agent. First, we show that marginal labor taxes depend directly on the absolute value of the distance between the median and the mean value of the skills? distribution. Second, we find that in contrast to the intuition stemming from standard representative agent economies, labor taxes are more volatile and counter-cyclical taxation (e.g., increasing taxes in recession) might be optimal depending on the correlation between inequality and TFP. To assess the quantitative relevance of these findings, we calibrate the model economy to six countries and find that counter-cyclical labor taxation is optimal for all but the US.     

Decisiveness of contributors’ perceptions in elections

We consider a model of two-candidate elections with a one-dimensional policy space. Spending on campaign advertisements can directly influence voters’ preferences, and contributors give the money for campaign spending in exchange for promised services if the candidate wins. We find that the winner of the election depends crucially on the contributors’ beliefs about who is likely to win and the contribution market tends toward nonsymmetric equilibria in which one of the two candidates has no chance of winning. If the voters are only weakly influenced by advertising or if permissible campaign spending is small, then the candidates choose policies close to the median voter’s ideal point, but the contributors still determine the winner. Uncertainty about the Condorcet winning point (or its nonexistence) can change these results and generate equilibria in which both candidates have substantial probabilities of winning.     

Dominance solvable approval voting games

This work provides necessary and sufficient conditions for the dominance solvability of approval voting games. Our conditions are very simple since they depend just on the number of possible winners when voters play weakly undominated strategies. If there are at most two possible winners, then the game is dominance‐solvable and the outcome coincides with the Condorcet winner. If every candidate is a possible winner, the game is not dominance‐solvable. If none of the previous conditions holds, then the game need not be dominance‐solvable, and the outcome need not coincide with the Condorcet winner.     

On the voluntary provision of “weakest‐link” public goods: The case of private information

We characterize equilibria in a private‐provision public‐good game where individuals are allowed arbitrary contribution levels and the level of the public good equals the least contribution made by an individual. Equilibrium comparative statics are derived for the interim Pareto‐dominant equilibrium. First, improvements in the cost distribution of even only one player benefit all. Second, even with such “weakest‐link” public goods, for which greater similarity of preferences would seem to facilitate coordination, decreased heterogeneity can actually decrease payoffs. Indeed, increasing the riskiness of cost distributions has an ambiguous effect on welfare. Two mechanisms are provided for improving equilibrium payoffs: Technology transfer and cheap‐talk communication. While substantial welfare gains are possible, examples show that (a) technology transfer may be futile if a “regularity” condition is not satisfied and (b) cheap talk may be useless if the language for communication is not sufficiently rich.     

Market Entry Regulation and International Competition*

We analyze a non‐cooperative two‐country game where each government decides whether to allow free market entry of firms or to regulate market access. We show that a Pareto‐efficient allocation may result in equilibrium. In particular, if the cost difference between home and foreign production is “significant,” production will be located in the cost‐efficient country exclusively; and if this cost difference is even “substantial,” the induced allocation is also Pareto efficient. Only if the cost difference is “insignificant,” production may take place in both countries and the allocation is inefficient.     

On the undesirability of commodity taxation even when income taxation is not optimal

An important result due to Atkinson and Stiglitz (1976) [Atkinson, A.B., Stiglitz, J.E., 1976. The design of tax structure: Direct versus indirect taxation. Journal of Public Economics 6, 55–75.] is that differential commodity taxation is not optimal in the presence of an optimal nonlinear income tax (given weak separability of utility between labor and all consumption goods). This article demonstrates that this conclusion holds regardless of whether the income tax is optimal. In particular, given any commodity tax and income tax system, differential commodity taxation can be eliminated in a manner that results in a Pareto improvement. Also, differential commodity taxation can be proportionally reduced so as to generate a Pareto improvement. In addition, for commodity tax reforms that neither eliminate nor proportionally reduce differential taxation, a simple efficiency condition is offered for determining whether a Pareto improvement is possible.     

When do market games have transferable utility?

A pure exchange economy generates a “market game” in which the allocations achievable by any coalition are determined by the initial endowments of its members. Subject to certain regularity conditions, it is shown that for a market game it is possible to find utility representations for each consumer so that the game can be treated as a game with transferable utility if and only if indirect utility of all consumers can be represented in the Gorman polar form. This is the class for which aggregate demand behaves as if it were the demand of a single consumer.     

Subjective well‐being,consumption comparisons,and optimal income taxation

We introduce reference consumption into the standard utility function from optimal tax analysis. Individuals compare their consumption “narrowly” with those of the same productivity, or “broadly” with the average consumption across society. In both narrow and broad equilibria reference consumption is an increasing function of the tax parameters, so generating new theoretical results. Individual well‐being decreases with the net wage (net‐of‐tax) rate for low productivity workers under narrow (broad) comparisons, thus adjusting redistributive taxation considerations. Further, in both cases reference consumption distorts labor supply away from the social optimum level, giving a distortion‐correcting role for taxation.     

Electoral Thresholds as Coordination Devices

In this paper, we study one‐person–one‐vote parliamentary elections where voters care both about the winner of elections and about the composition of the parliament. Parties enter the parliament if and only if their vote share exceeds some predetermined threshold. We show that equilibria generically exist in which all parties obtain a non‐degenerate vote‐share and, perhaps more importantly, we show that the size of the electoral threshold acts as a coordination device, which crucially affects the win prospects of the Condorcet winner party. In particular, we argue that the win prospects of the Condorcet winner party decrease with the size of the entry threshold.     

Constant scoring rules,condorcet criteria and single-peaked preferences

Summary A constant scoring rule asks each individual to vote for a given (and constant) number of alternatives and the alternative with the most votes is elected. A sequential constant scoring rule applies this principle in a process of sequential elimination. Constant scoring rules as well as sequential constant scoring rules fail to satisfy Condorcet criteria when individual preferences are unrestricted. The purpose of this paper is to show that, if we assume that preferences are single-peaked, then some constant scoring rules satisfy the Condorcet loser criterion and some sequential constant scoring rules satisfy the Condorcet winner criterion. The results we provide make possible the identification of these rules.I thank Maurice Salles and two anonymous referees for their helpful comments. The usual disclaimers apply.     

Production Efficiency and the Direct-Indirect Tax Mix

In the design of the optimal direct/indirect tax mix, the canonical view was laid by Atkinson and Stiglitz (1976) who showed that commodity taxes are unnecessary in an economy in which there is an optimal nonlinear income tax provided that commodities are separable from labor in the utility functions of all taxpayers, that the aggregators over these commodities are ordinally equivalent and that wages are fixed. When wages are endogenous, Naito (1999) showed that this result may not hold and in addition that production efficiency may not be Pareto optimal. Given an optimal nonlinear income tax, we show that production inefficiency is Pareto optimal if the aggregate technology set is strictly concave. The Atkinson–Stiglitz condition is neither necessary nor sufficient for zero commodity taxation and commodity taxes are part of almost all Pareto optima.     

Transplants and Implants: The Economics of Self‐Improvement

This article examines equilibrium self‐improvement and marriage proposal strategies in a two‐sided search model with nontransferable utility. Singles are vertically differentiated—some make better marriage partners than others. A complete characterization of equilibrium is provided. It is shown there are two externalities to self‐improvement decisions. Further, these externalities may support multiple Pareto rankable equilibria. By encouraging everybody to self‐improve, society can create a situation where everybody is forced to improve to remain “acceptable.” But a preferred equilibrium may exist where there is less (costly) self‐improvement.     

A comparison of Dodgson's method and the Borda count

Summary. In an election without a Condorcet winner, Dodgson's Method is designed to find the candidate that is “closest” to being a Condorcet winner. In this paper, we show that the winner from Dodgson's Method can occur at any position in the ranking obtained from the Borda Count, the plurality method, or any other positional voting procedure. In addition, we demonstrate that Dodgson's Method does not satisfy the Independence of Irrelevant Alternatives axiom. Received: January 12, 2001; revised version: June 7, 2001     

A strategy-proofness characterization of majority rule

Summary. A feasible alternative x is a strong Condorcet winner if for every other feasible alternative y there is some majority coalition that prefers x to y. Let (resp., denote the set of all profiles of linear (resp., merely asymmetric) individual preference relations for which a strong Condorcet winner exists. Majority rule is the only non-dictatorial and strategy-proof social choice rule with domain , and majority rule is the only strategy-proof rule with domain . Received: August 29, 2000; revised version: November 13, 2002 RID="*" ID="*"We are grateful to Wulf Gaertner and our two referees for insightful comments on a previous draft. Correspondence to: D. E. Campbell     

The Copeland rule and Condorcet’s principle

Summary. The purpose of this note is to shed some light on the relationship between the Copeland rule and the Condorcet principle in those cases where there does not exist a Condorcet winner. It will be shown that the Copeland rule ranks alternatives according to their distances to being a Condorcet winner.Received: 30 July 2003, Revised: 31 December 2003, JEL Classification Numbers: D70, D71.Christian Klamler: I am very grateful to Daniel Eckert and Nick Baigent for their helpful comments.     

Optimal mixed taxation,public goods and the problem of high-skilled emigration

The optimal income tax model under the threat of migration of Simula and Trannoy (J Public Econ 94:163–173, 2010; Soc Choice Welf 39(4):751–782, 2012) is extended to include indirect taxes and public goods. This enables us to conclude that: (1) optimal income tax rates are higher than in the absence of indirect taxation, and may be positive at the top of the skills distribution; (2) indirect taxes, à la Corlett and Hague, may help mitigate the loss of redistributive capacity arising from income taxation caused by migration threats; (3) migration encourages the provision of the public goods preferred by the most productive workers; (4) optimal tax and public goods provision policies against the emigration of the highly-skilled are connected through the conditions for Pareto efficiency; (5) if the number of potential migrators is large, it may be desirable to violate classical tax rules to retain the most able in the home country; (6) when migration costs are exogenously given and utility is weakly separable, Simula and Trannoy’s results are restored; (7) if migration costs are endogenous, the Atkinson and Stiglitz theorem breaks down and the taxation of country-specific goods becomes desirable, even if utility is strongly separable.     

A recursion relation for the probability of the paradox of voting

For alternatives x_i, i = 1,…, m, giving rise to m! linear preference orderings of which one is selected independently by each of N voters, a recursion relation is developed which expresses the probability that x_i is the Condorcet winner when there are N voters in terms of the probability of this event when there are N ? 1 voters. Hence the probabilities of the paradox of voting when N is odd, and of Condorcet indecision when N is even may be obtained. The relationship holds for any set of probabilities, or culture, governing the selection of the preference orderings by the voters.