Stable voting procedures for committees in economic environments (original) (raw)

Bargaining in committees of representatives: the optimal voting rule

Committees are often made up of representatives of different-sized groups of individuals, and make decisions by means of a voting rule which specifies what vote configurations can pass a decision. This raises the question of the choice of the optimal voting rule, given the different sizes of the groups that members represent. In this paper we take a new departure to address this problem, assuming that the committee is a bargaining scenario in which negotiations take place 'in the shadow of the voting rule' in search of unanimous consensus. That is, a general agreement is looked for, but any winning coalition can enforce an agreement.

An undominated Nash equilibrium for voting by committees with exit

Mathematical Social Sciences, 2007

We consider the problem of a society whose members choose, with a voting by committees, a subset of new members from a given set of candidates. After knowing the elected candidates, former members may decide to either stay or exit the society. We analyze the voting behavior of members who take into account the e¤ect of their votes not only on the elected candidates, but also on the …nal composition of the society. For additive and monotonic preferences with dichotomous bads we construct a strategy pro…le that is an undominated pure strategy Nash equilibrium of the induced voting game.

Bargaining Sets of Majority Voting Games

Mathematics of Operations Research, 2007

Let A be a finite set of m alternatives, let N be a finite set of n players, and let R N be a profile of linear orders on A of the players. Let u N be a profile of utility functions for R N . We define the nontransferable utility (NTU) game V u N that corresponds to simple majority voting, and investigate its Aumann-Davis-Maschler and Mas-Colell bargaining sets. The first bargaining set is nonempty for m ≤ 3, and it may be empty for m ≥ 4. However, in a simple probabilistic model, for fixed m, the probability that the Aumann-Davis-Maschler bargaining set is nonempty tends to one if n tends to infinity. The Mas-Colell bargaining set is nonempty for m ≤ 5, and it may be empty for m ≥ 6. Furthermore, it may be empty even if we insist that n be odd, provided that m is sufficiently large. Nevertheless, we show that the Mas-Colell bargaining set of any simple majority voting game derived from the k-fold replication of R N is nonempty, provided that k ≥ n + 2.

Stability and voting by committees with exit

Social Choice and Welfare, 2004

We study the problem of a society choosing a subset of new members from a finite set of candidates (as in Barberà et al. 1991). However, we explicitly consider the possibility that initial members of the society (founders) may want to leave it if they do not like the resulting new society. We show that, if founders have separable (or additive) preferences, the unique strategy-proof and stable social choice function satisfying founder’s sovereignty (on the set of candidates) is the one where candidates are chosen unanimously and no founder leaves the society.

Bargaining Sets of Voting Games

2004

Let A be a finite set of m <FONT FACE="Symbol">³</FONT> 3 alternatives, let N be a finite set of n <FONT FACE="Symbol">³</FONT> 3 players and let R<SUP>n</SUP> be a profile of linear preference orderings on A of the players. Throughout most of the paper the considered voting system is the majority rule. Let u<SUP>N</SUP> be a profile of utility functions

The stability set of voting games: Classification and genericity results

International Journal of Game Theory, 1990

In 1980 Rubinstein introduced a new solution concept for voting games called the stability set which incorporates the idea that before entering into a possibly winning coalition with respect to some pair of alternatives, a voter will consider what might happen in the future. He showed that if the voters' preferences are given by linear orders the stability set is non-empty for alarge class of voting games with finite sets of alternatives. We consider the case where indifference is allowed (preferences are then complete preorders) and show that the picture is then quite different. First, in the finite case, we obtain classification results for the non-emptiness of the stability set which are based on Nakamura's number. When preferences are continuous, we prove a general non-emptiness theorem and show that the set of profiles for which the stability set is non-empty is dense in the set of profiles. 1 We are most grateful to the French Commissariat G6n6ral du Plan for financial support and to

Optimal Committee Design and Political Participation

Building on a Condorcetian common-values framework, this paper tackles the question of optimal committee formation within a community of finite size. Solving for the Bayesian information aggregation game yields some interesting normative results that emphasize the presence of informational externalities as root causes of suboptimally low voluntary participation levels in communal decision-making and the potentially Pareto-enhancing nature of drafting vis-à-vis decentralized mechanisms of self-selection. I firstly derive the optimal size of a committee based on the assumption of informative voting and, then, I show that it is globally optimal amongst all voting equilibrium strategies. I subsequently compare it to the various symmetric equilibria that may arise in a complete information setting or a Bayesian environment with heterogeneous private costs. I finally sketch out an optimal transfer scheme that can ex ante implement the socially efficient committee size.