On Some Incompatible Properties of Voting Schemes

In this paper, we study the problem of simultaneously achieving several security properties, for voting schemes, without non-standard assumptions. More specifically, we focus on the universal veriability of the computation of the tally, on the unconditional privacy/anonymity of the votes, and on the receipt-freeness properties, for the most classical election processes. Under usual assumptions and efficiency requirements, we show that a voting system that wants to publish the final list of the voters who actually voted, and to compute the number of times each candidate has been chosen, we cannot achieve: - universal verifiability of the tally (UV) and unconditional privacy of the votes (UP) simultaneously, unless all the registered voters actually vote; - universal verifiability of the tally (UV) and receipt- freeness (RF), unless private channels are available between the voters and/or the voting authorities

Robust mechanism design and dominant strategy voting rules

We develop an analysis of voting rules that is robust in the sense that we do not make any assumption regarding voters’ knowledge about each other. In dominant strategy voting rules, voters’ behavior can be predicted uniquely without making any such assumption. However, on full domains, the only dominant strategy voting rules are random dictatorships. We show that the designer of a voting rule can achieve Pareto improvements over random dictatorship by choosing rules in which voters’ behavior can depend on their beliefs. The Pareto improvement is achieved for all possible beliefs. The mechanism that we use to demonstrate this result is simple and intuitive, and the Pareto improvement result extends to all equilibria of the mechanism that satisfy a mild refinement. We also show that the result only holds for voters’ interim expected utilities, not for their ex post expected utilities.robust mechanism design; dominant strategies; voting; Gibbard-Satterthwaite theorem

Set-Monotonicity Implies Kelly-Strategyproofness

This paper studies the strategic manipulation of set-valued social choice functions according to Kelly's preference extension, which prescribes that one set of alternatives is preferred to another if and only if all elements of the former are preferred to all elements of the latter. It is shown that set-monotonicity---a new variant of Maskin-monotonicity---implies Kelly-strategyproofness in comprehensive subdomains of the linear domain. Interestingly, there are a handful of appealing Condorcet extensions---such as the top cycle, the minimal covering set, and the bipartisan set---that satisfy set-monotonicity even in the unrestricted linear domain, thereby answering questions raised independently by Barber\`a (1977) and Kelly (1977).Comment: 14 page

Computability of simple games: A complete investigation of the sixty-four possibilities

Classify simple games into sixteen "types" in terms of the four conventional axioms: monotonicity, properness, strongness, and nonweakness. Further classify them into sixty-four classes in terms of finiteness (existence of a finite carrier) and algorithmic computability. For each such class, we either show that it is empty or give an example of a game belonging to it. We observe that if a type contains an infinite game, then it contains both computable ones and noncomputable ones. This strongly suggests that computability is logically, as well as conceptually, unrelated to the conventional axioms.Comment: 25 page

Paradoxes of Fair Division

Two or more players are required to divide up a set of indivisible items that they can rank from best to worst. They may, as well, be able to indicate preferences over subsets, or packages, of items. The main criteria used to assess the fairness of a division are efficiency (Pareto-optimality) and envy-freeness. Other criteria are also suggested, including a Rawlsian criterion that the worst-off player be made as well off as possible and a scoring procedure, based on the Borda count, that helps to render allocations as equal as possible. Eight paradoxes, all of which involve unexpected conflicts among the criteria, are described and classified into three categories, reflecting (1) incompatibilities between efficiency and envy-freeness, (2) the failure of a unique efficient and envy-free division to satisfy other criteria, and (3) the desirability, on occasion, of dividing up items unequally. While troublesome, the paradoxes also indicate opportunities for achieving fair division, which will depend on the fairness criteria one deems important and the trade-offs one considers acceptable.FAIR DIVISION; ALLOCATION OF INDIVISIBLE ITEMS; ENVY-FREENESS; PARETO- OPTIMALITY; RAWLSIAN JUSTICE; BORDA COUNT.

Collective Choice under Dichotomous Preferences

Agents partition deterministic outcomes into good or bad. A direct revelation mechanism selects a lottery over outcomes - also interpreted as time-shares. Under such dichotomous preferences, the probability that the lottery outcome be a good one is a canonical utility representation. The utilitarian mechanism averages over all deterministic outcomes "approved" by the largest number of agents. It is efficient, strategy-proof and treats equally agents and outcomes. We reach the impossibility frontier if we also place the lower bound 1/n on each agent's utility, where n is the number of agents; or if this lower bound is the fraction of good outcomes to feasible outcomes. We conjecture that no ex-ante efficient and strategy-proof mechanism guarantees a strictly positive utility to all agents at all profiles, and prove a weaker version of this conjecture.