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We consider voting rules on a multidimensional policy space for a continuum of voters with elliptic preferences. Assuming continuity, gamma-strategy-proofness-meaning that coalitions of size smaller or equal to a small number gamma cannot manipulate-and unanimity, we show that such rules are decomposable into one-dimensional rules. Requiring, additionally, anonymity leads to an impossibility result. The paper can be seen as an extension of the model of Border and Jordan (1983) to a continuum of voters. Contrary, however, to their finite case where single voters are atoms, in our model with nonatomic voters even a small amount of strategy-proofness leads to an impossibility.

In this paper we address several issues related to collective dichotomous decision-making by means of quaternary voting rules, i.e., when voters may choose between four actions: voting yes, voting no, abstaining and not turning up - which are aggregated by a voting rule into a dichotomous decision: acceptance or rejection of a proposal. In particular we study the links between the actions and preferences of the actors. We show that quaternary rules (unlike binary rules, where only two actions -yes or no- are possible) leave room for manipulability (i.e., strategic behaviour). Thus a preference profile does not in general determine an action profile. We also deal with the notions of success and decisiveness and their ex ante assessment for quaternary voting rules, and discuss the role of information and coordination in this context.

International audience; no abstract

I discuss instances where a committee wants to deviate from the simple majority rule by adopting an alternative voting scheme for two consecutive binary ballots. The alternative voting rule, called Minority Voting as an Exception (MVE), works as follows: In the first ballot a b-majority rule is used, where b < 1/2 is equal to the minority fraction that favors some project, say project 1. This allows the minority to induce the adoption of project 1. After the first ballot all voting winners, i.e. the minority of project winners, lose their voting rights for the upcoming second ballot, where the simple majority rule is used. Hence, MVE may benefit both project losers and winners and may thus be unanimously accepted. The analysis of this short-term deviation is presented with a potential application in the sphere of communal politics.

In this paper we propose minority voting as a scheme that can partially protect individuals from the risk of repeated exploitation. We consider a committee that meets twice to decide about projects where the first-period project may have a long-lasting impact. In the first period a simple open majority voting scheme takes place. Voting splits the committee into three groups: voting winners, voting losers, and absentees. Under minority voting only voting losers keep the voting right in the second period. We show that as soon as absolute risk aversion exceeds a threshold value minority voting is superior to repeated application of the simple majority rule.

The likely extension of the euro area has triggered a debate on the organization of the ECB, in particular on the apparent mismatch between relative economic size and voting rights in the Council. We present a simple model of optimal representation in a federal central bank addressing this question. Optimal voting weights re ect two opposing forces: the wish to insulate common monetary policy from changing preferences at the national level, and the attempt to avoid an overly active or passive reaction to idiosyncratic national economic shocks. A perfect match between economic size and voting rights is rarely optimal, and neither is the one country, one vote princi- ple . Empirically, there are indications that the pattern of over- and under-representation of member countries in the ECB Council might be extreme by the standards of the US Fed and German Bundesbank and not always optimal.

Consider a voting procedure where countries, states, or districts comprising a union each elect representatives who then participate in later votes at the union level on their behalf. The countries, provinces, and states may vary in their populations and composition. If we wish to maximize the total expected utility of all agents in the union, how to weight the votes of the representatives of the different countries, states or districts at the union level? We provide a simple characterization of the efficient voting rule in terms of the weights assigned to different districts and the voting threshold (how large a qualified majority is needed to induce change versus the status quo). Next, in the context of a model of the correlation structure of agents preferences, we analyze how voting weights relate to the population size of a country. We then analyze the voting weights in Council of the European Union under the Nice Treaty and the recently proposed constitution, and contrast them under different versions of our model, and compare them to the weights derived from poll data.

We investigate the implications for the setting of interest rateswhen monetary policy decisions are taken by a committee, in whicha subset of members may meet prior to the voting in the committeeand therefore has the possibility to reach consensus ex ante to voteunanimously ex post. We allow for different committee sizes, variousvoting rules and differences in skills among committee members. Wefind that the size of the committee is much less important in deter-mining the degree of interest rate inertia than the skills of committeemembers. Moreover, prior interaction of a subgroup only has a minoreffect on the setting of interest rates by the committee, provided thatmembers on average are equally skilled and voting takes place using asimple majority rule. If either of those assumptions are relaxed, priorinteraction has substantial effects on the setting of interest rates. Inaddition, prior interaction increases the optimal size of the Committee,ceteris paribus.

This paper studies studies two-party electoral competition in a setting where no policy is unbeatable. It is shown that if parties take turns in choosing platforms and observe each other's choises, altering one's platform so as to win is pointless since the other party never accepts an outcome where it is sure to loose. If there is any cost to changing platform, the prediction is that the game ends in the first period with the parties converging on whatever platform the incumbent chooses. If, however, there is a slight chance of a small mistake, the incumbent does best in choosing a local equilibrium platform. This suggest that local equilibrium policies can be the predicted outcome even if the voting process is not myopic in any way.

This note studies the choice of tax structure in a majority voting model with tax competition. Regions may tax mobile capital or immobile labor. Individuals differ with respect to their relative endowments of labor and capital. Even though a lump sum tax is available, the equilibrium capital tax in a jurisdiction may be positive. In a symmetric equilibrium, this will be true if the median capital endowment is smaller than average.

Collective decision procedures should balance the incentives they provide toacquire information and their capacity to aggregate private information. In a decisionproblem in which a project can be accepted or rejected once information about its qualityhas been acquired or not, we compare the performance of a delegation structure with that oftwo voting procedures. Delegation makes one's acceptance decision pivotal by definition.The decisiveness of one's vote in a voting procedure depends on the other agent's vote.This in turn determines the decision to acquire information. In the debate about a rationalchoice foundation of Condorcet's Jury Theorem, the distribution of information was leftexogenous. Mixed (acceptance) strategies were required to validate the Theorem.Endogenizing information acquisition as we do reveals mixed (acceptance) strategies to bedetrimental for welfare as they lead to indifference between buying and not buyinginformation.

We study a problem of individual manipulation in an impartial culture (IC) framework using computer modeling. We estimate the degree of manipulability of ten positional voting rules in the case of multiple choice for 3 and 4 alternatives.

The average voting procedure reflects the weighted average of expressed opinions in [0,1]. Participants typically behave strategically. We evaluate the discrepancy between the average taste and the average vote. If the population is sufficiently large, it is possible to construct approximations of both the average vote and the average taste which may be readily compared. We construct upper and lower bounds for the limit average vote that depend on the limit average taste. If the average taste is central enough, the range of possible values for the average voting outcome is narrower than the corresponding range for majority voting. For instance, if the average taste is at 1/2, the limit equilibrium outcome is this value plus or minus roughly .2, whereas the weighted median maybe anywhere in the [0,1] interval.