Convergence Results for Unanimous Voting

We develop a unidimensional spatial model of two party competition in which parties are better informed than voters about the bliss point of voters. The announced positions of the two parties serve as signals to the voters concerning the parties' private information. Surprisingly, in all separating equilibria the policies implemented by the left-wing party, when it attains power, are to the right of the policies implemented by the right-wing party when it attains power in turn. The driving force behind this result is that, in the event of a shock making right-wing policies more attractive, the incentives pushing the left party to the right are strong, since by winning the election it can avoid the right party implementing extreme policies, while the right-wing party can stay put in a radical stance with the prospect of seeing relatively attractive policies implemented by the rival party.

Beyond Condorcet: Optimal Aggregation Rules Using Voting Records

In certain judgmental situations where a “correct” decision is presumed to exist, optimal decision making requires evaluation of the decision-maker's capabilities and the selection of the appropriate aggregation rule. The major and so far unresolved difficulty is the former necessity. This paper presents the optimal aggregation rule that simultaneously satisfies these two interdependent necessary requirements. In our setting, some record of the voters' past decisions is available, but the correct decisions are not known. We observe that any arbitrary evaluation of the decision-maker's capabilities as probabilities yields some optimal aggregation rule that, in turn, yields a maximum-likelihood estimation of decisional skills. Thus, a skill-evaluation equilibrium can be defined as an evaluation of decisional skills that yields itself as a maximum-likelihood estimation of decisional skills. We show that such equilibrium exists and offer a procedure for finding one. The obtained equilibrium is locally optimal and is shown empirically to generally be globally optimal in terms of the correctness of the resulting collective decisions. Interestingly, under minimally competent (almost symmetric) skill distributions that allow unskilled decision makers, the optimal rule considerably outperforms the common simple majority rule (SMR). Furthermore, a sufficient record of past decisions ensures that the collective probability of making a correct decision converges to 1, as opposed to accuracy of about 0.7 under SMR. Our proposed optimal voting procedure relaxes the fundamental (and sometimes unrealistic) assumptions in Condorcet celebrated theorem and its extensions, such as sufficiently high decision-making quality, skill homogeneity or existence of a sufficiently large group of decision makers.

Beyond Condorcet: Optimal Aggregation Rules Using Voting Records

The difficulty of optimal decision making in uncertain dichotomous choice settings is that it requires information on the expertise of the decision makers (voters). This paper presents a method of optimally weighting voters even without testing them against questions with known right answers. The method is based on the realization that if we can see how voters vote on a variety of questions, it is possible to gauge their respective degrees of expertise by comparing their votes in a suitable fashion, even without knowing the right answers.

Sequential Deliberation for Social Choice

In large scale collective decision making, social choice is a normative study of how one ought to design a protocol for reaching consensus. However, in instances where the underlying decision space is too large or complex for ordinal voting, standard voting methods of social choice may be impractical. How then can we design a mechanism - preferably decentralized, simple, scalable, and not requiring any special knowledge of the decision space - to reach consensus? We propose sequential deliberation as a natural solution to this problem. In this iterative method, successive pairs of agents bargain over the decision space using the previous decision as a disagreement alternative. We describe the general method and analyze the quality of its outcome when the space of preferences define a median graph. We show that sequential deliberation finds a 1.208- approximation to the optimal social cost on such graphs, coming very close to this value with only a small constant number of agents sampled from the population. We also show lower bounds on simpler classes of mechanisms to justify our design choices. We further show that sequential deliberation is ex-post Pareto efficient and has truthful reporting as an equilibrium of the induced extensive form game. We finally show that for general metric spaces, the second moment of of the distribution of social cost of the outcomes produced by sequential deliberation is also bounded

Making Consensus Tractable

We study a model of consensus decision making, in which a finite group of Bayesian agents has to choose between one of two courses of action. Each member of the group has a private and independent signal at his or her disposal, giving some indication as to which action is optimal. To come to a common decision, the participants perform repeated rounds of voting. In each round, each agent casts a vote in favor of one of the two courses of action, reflecting his or her current belief, and observes the votes of the rest. We provide an efficient algorithm for the calculation the agents have to perform, and show that consensus is always reached and that the probability of reaching a wrong decision decays exponentially with the number of agents.Comment: 18 pages. To appear in Transactions on Economics and Computatio

A model of influence with a continuum of actions

In the paper, we generalize a two-action (yes-no) model of influence to a framework in which every player has a continuum of actions and he has to choose one of them. We assume the set of actions to be an interval. Each player has an inclination to choose one of the actions. Due to influence among players, the final decision of a player, i.e., his choice of one action, may be different from his original inclination. In particular, a coalition of players with the same inclination may influence another player with different inclination, and as a result of this influence, the decision of the player is closer to the inclination of the influencing coalition than his inclination was. We introduce and study a measure of such a positive influence of a coalition on a player. Several unanimous influence functions in this generalized framework are considered. Moreover, we investigate other tools for analyzing influence, like the concept of a follower of a given coalition, its particular case - a perfect follower, and the kernel of an influence function. We study properties of these concepts. Also the set of fixed points under a given influence function is analyzed. Furthermore, we study linear influence functions. We also introduce a measure of a negative influence of a coalition on a player.action, decision ; influence index ; unanimous influence function ; follower of a coalition ; kernel ; fixed point ; linear influence function

Power in the Design of Constitutional Rules

This paper examines different ways of measuring power and the use of these measures in the context of the European Union. The paper deals with classical power indices of co-operative games and more recent non-cooperative a priori measures. Special emphasis of the paper is in inter-institutional balance of power, Nice reforms and eastern enlargement.

The Decisions and Ideal Points of British Law Lords

Policy-sensitive models of judicial behaviour, whether attitudinal or strategic, have largely passed Britain by. This article argues that this neglect has been benign, because explanations of judicial decisions in terms of the positions of individual judges fare poorly in the British case. To support this argument, the non-unanimous opinions of British Law Lords between 1969 and 2009 are analysed. A hierarchical item-response model of individual judges’ votes is estimated in order to identify judges’ locations along a one-dimensional policy space. Such a model is found to be no better than a null model that predicts that every judge will vote with the majority with the same probability. Locations generated by the model do not represent judges’ political attitudes, only their propensity to dissent. Consequently, judges’ individual votes should not be used to describe them in political terms