Convergence Results for Unanimous Voting

This paper derives a necessary condition for unanimous voting to converge to the perfect information outcome when voters are only imperfectly informed about the alternatives. Under some continuity assumptions, the condition is also sufficient for the existence of a sequence of equilibria that exhibits convergence. The requirement is equivalent to that found by Milgrom [1979, Econometrica47, 679-688] for information aggregation in single-prize auctions. An example illustrates that convergence may be reasonably fast for small committees. However, if voters have common preferences, unanimity is not the optimal voting rule. Unanimity rule makes sense only as a way to ensure minority views are respected. Journal of Economic Literature Classification Numbers: D72, D82, D44.     

Storable votes

Motivated by the need for more flexible decision-making mechanisms in the European Union, the paper proposes a simple but novel voting scheme for binary decisions taken by committees that meet regularly over time. At each meeting, committee members are allowed to store their vote for future use; the decision is then taken according to the majority of votes cast. The possibility of shifting votes intertemporally allows agents to concentrate their votes when preferences are more intense, and although the scheme will not achieve full efficiency, storable votes typically lead to ex ante welfare gains over non-storable votes. Welfare gains can be proven rigorously in the case of 2 voters. With more voters, counterexamples can be found, but the analysis suggests that the welfare improvements should continue to hold if one of the following conditions is satisfied: (i) the number of voters is above a minimum threshold; (ii) preferences are not too polarized; (iii) the horizon is long enough.     

On the existence of equilibria in economies with infinitely many commodities and without ordered preferences

The present paper deals with the existence of equilibria in economies whose commodity space is L_∞(M, M, μ) and where the agents' preferences need not be complete or transitive. Applying a fixed point theorem of Browder, an equilibrium existence theorem for abstract economies (generalized qualitative games) is proven where each agent's choice set is contained in an arbitrary topological vector space. With the help of this theorem the existence of Walrasian general equilibrium for a suitably specified economic model is obtained. The final result is a generalization of T. F. Bewley's (J. Econ. Theory4 (1972), 514–540) equilibrium existence theorem to the case of non-ordered preferences.     

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.     

STRATEGIC CANDIDACY AND SINGLE‐PEAKEDNESS*

In elections, the voting outcomes are affected by strategic entries of candidates. We study a class of voting rules immune to strategic candidacy. Dutta et al. (2001 ) show that such rules satisfying unanimity are dictatorial if all orderings of candidates are admissible for voters’ preferences. When voters’ preferences are single‐peaked over a political spectrum, there exist non‐dictatorial rules immune to strategic candidacy. An example is the rule selecting the m‐th peak from the left among the peaks of voters’ preferences, where m is any natural number no more than the number of voters. We show that immunity from strategic candidacy with basic axioms fully characterizes the family of the m‐th leftmost peak rules.     

A note on the fundamental theorem of exact aggregation

If individual i's demands for a commodity are a function of prices, p, income M_i and a vector of attributes A_i, then aggregate demand is

This paper derives the necessary and sufficient conditions of f_i, F and a system of functions g_k(M₁,…,M_N,A₁,…,A_N) symmetric in the M's and A's such that F can be written in the form F(p, g, (M₁,…,M_n,A₁,…,A_N),…, g_n(M₁,…,M_n,A₁,… ,A_n)) for all values of its arguments.     

Redistributive policies with heterogeneous social preferences of voters

There is growing evidence on the roles of fairness and other-regarding preferences as fundamental human motives. Call voters with fair preferences, as in Fehr and Schmidt (1999), fair-voters. By contrast, traditional political economy models are based on selfish-voters who derive utility solely from “own” payoff. In a general equilibrium model with endogenous labor supply, a mixture of fair and selfish voters choose optimal policy through majority voting. First, we show that majority voting produces a unique winner in pairwise contests over feasible policies (the Condorcet winner). Second, we show that a preference for greater fairness leads to greater redistribution. An increase in the number of fair voters can also lead to greater redistribution. Third, we show that in economies where the majority are selfish-voters, the decisive policy could be chosen by fair-voters, and vice versa. Fourth, while choosing labor supply, even fair voters behave exactly like selfish voters. We show how this apparently inconsistent behavior in different domains (voting and labor supply) can be rationalized within the model.     

A progress report on Kelly's majority conjectures

LetC(m, n) be the proportion of n-voter profiles on m alternatives that have a majority winner. Jerry Kelly conjectured that C(m, n) > C(m + 1, n) for m ? 3 and n = 3 and n ? 5, and C(m, n) > C(m, n + 2) for m ? 3 and n ? 3. We prove these for special cases.     

Cyclic sets in multidimensional voting models

Simple majority rule usually does not yield an unambiguous consistent outcome. Assuming a characterization of the set of potential outcomes as Rⁿ and an odd number of voters with quasiconcave preferences, a unique, nonempty set of majority rule cycles exists. Sufficient conditions are established for the top cycle set to encompass the entire policy space. Generalized quadratic utility functions satisfy these conditions.     

Preference revelation with a limited number of indifference classes

Suppose that g is a strategy-proof social choice rule on the domain of all profiles of complete and transitive binary relations that have exactly m indifference classes. If and the range of g has three or more members, then g is dictatorial. If m = 2, then for any set X of feasible alternatives, there exist non-dictatorial and strategy-proof rules that are sensitive to the preferences of every individual and which have X as range.     

Coordinated voting in sequential and simultaneous elections: some experimental evidence

This paper studies a situation wherein a set of voters choose between two alternatives in the presence of a payoff externality. Specifically, regardless of her intrinsic preference, a voter’s payoff is maximized should she vote for the alternative that garners a majority of the votes cast. Are votes coordinated on a single alternative? Using laboratory experiments, we examine voting patterns in sequential voting and simultaneous voting elections. Across both election types, we also vary the amount of information that an individual voter has regarding the intrinsic preferences of the other voters. Our main findings are as follows. In the “low” information treatment, sequential voting elections facilitate coordinated voting. However, in the “high” information treatment, voting patterns are not dependent on how the election is structured.     

Tops-only domains

In this paper we consider the standard voting model with a finite set of alternatives A and n voters and address the following question: what are the characteristics of domains \({\mathcal D}\) that induce the property that every strategy-proof social choice function \({f: {\mathcal D}^n \rightarrow A}\) satisfying unanimity, has the tops-only property? We first impose a minimal richness condition which ensures that for every alternative a, there exists an admissible ordering where a is maximal. We identify conditions on \({\mathcal D}\) that are sufficient for strategy-proofness and unanimity to imply tops onlyness in the general case of n voters and in the special case, n = 2. We provide an algorithm for constructing tops-only domains from connected graphs with elements of A as nodes. We provide several applications of our results. Finally, we relax the minimal richness assumption and partially extend our results.     

Majority voting with stochastic preferences: The whims of a committee are smaller than the whims of its members

This note studies the volatility of the policy chosen by a committee whose members’ preferences are volatile, due to common and individual preferences shocks. It is shown that majority voting mitigates the latter but not the former. The volatility of the policy is smaller the smaller the volatility of members’ preferences, smaller the larger the size of the committee, and smaller than if it was chosen by a single member. The results hold in a context of uncertainty and with multidimensional issues.

Essential aggregation procedures on restricted domains of preferences

The restricted domains of individuals' preferences that permit the construction of Arrow social welfare functions and nonmanipulable voting procedures in which each of n voters has some power are characterized. In this context a domain is the Cartesian product of n sets of strict preference orderings. Variants of this result are obtained under the additional requirement of neutrality and in the case when alternatives are vectors whose ith components affect only the ith voter. Kalai and Muller's analogous result (J. Econ. Theory16 (1977), 457–469) concerning nondictatorial procedures is discussed and proved as a corollary to the main theorem.     

Computing revealed preferences and limits to the validity of quadratic objective functions for policy optimization

Planning problems with m targets, n instruments and quadratic objective functions have often been used to study the revealed preferences of governments' stabilization policies. Problems with the homogeneity of the objective function and related issues of approximation theory are explored.     

Demand of direct democracy

The growing demand for referendum challenges the traditional model of representative democracy. In this paper we study under which conditions voters prefer a system of representative democracy to direct democracy. In direct democracies voters choose a policy among two alternatives, under uncertainty about which policy better fits the realized state of the world; in representative democracies voters select a candidate who, once elected, chooses a policy having observed which is the realized state of the world. Voters and politicians' payoffs depend on a common component which is positive only if the policy fits the state of the world, and on a private ideological bias towards one of the policies. In direct democracies voters are uncertain about the future state of the world, while in representative democracies they are uncertain about the degree of ideological bias of the candidates, even if they know towards which policy each candidate is biased. We show that representative democracy is preferred if (i) the majority of voters are pragmatic (the common component prevails), and (ii) society is ideologically polarized, meaning that the majority of voters are ideological (the private component prevails), but the median voter is pragmatic. Direct democracy is the preferred instrument for collective choices in societies in which the majority of voters and the median voter are ideological, implying that the majority of voters have the same ideological bias, as, for instance, it occurs when the populist rhetoric of people against the elite succeeds.     

Arrow's Possibility Theorem for one-dimensional single-peaked preferences

In one-dimensional environments with single-peaked preferences we consider social welfare functions satisfying Arrow's requirements, i.e. weak Pareto and independence of irrelevant alternatives. When the policy space is a one-dimensional continuum such a welfare function is determined by a collection of 2^N strictly quasi-concave preferences and a tie-breaking rule. As a corollary we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voter's preference is strictly quasi-concave.     

Experts against adverse selection: A note on the existence of equilibrium with costly appropriable information

The existence of competitive equilibrium in Laffont's (J. Econ. Theory10 (1975)) model of adverse selection with costly information is studied. The existence of an equilibrium with finite prices is demonstrated without unusual restrictions on preferences or the technology of information production. This is made possible by changing the way in which the behaviour of information producing agents is modelled, and allowing for some public information.     

A choice experiment on fuel taxation and earmarking in Norway

Pigouvian taxes are efficient — but unpopular among voters — and hence often politically infeasible. Earmarking of revenues has been widely reported to increase public support for taxes, but earmarking is generally not the most efficient use of the revenues. This trade-off between efficiency and political feasibility is the motivation for our primary research objective: to quantify the effect of earmarking on support for fuel tax rises. Our secondary research objective is to investigate why earmarking increases support. Using data from a representative sample of the Norwegian voter population (N = 1147), we estimate models of voter preferences for fuel taxes using logistic regression models. Our results show that, in the absence of earmarking, the majority of voters would like to reduce fuel taxes, but earmarking the revenues for environmental measures has a substantial effect on voter support for fuel tax increases, garnering a majority for increases of up to 15% above present levels. Further analysis indicates that a prime reason why earmarking for environmental measures is popular is that it increases the perceived environmental effectiveness of the tax, and hence its legitimacy as an environmental rather than a fiscal policy instrument.     

Strategy-Proof Probabilistic Decision Schemes for One-Dimensional Single-Peaked Preferences

Collective decision problems are considered with a finite number of agents who have single-peaked preferences on the real line. A probabilistic decision scheme assigns a probability distribution over the real line to every profile of reported preferences. The main result of the paper is a characterization of the class of unanimous and strategy-proof probabilistic schemes with the aid of fixed probability distributions that play a role similar to that of the phantom voters in H. Moulin (Public Choice35 (1980), 437-455). Thereby, the work of Moulin (1980) is extended to the probabilistic framework. Journal of Economic Literature Classification Numbers: D71, D81.