Results 1  10
of
48
2000): ”A bargaining model of Collective Choice
 American Political Science Review
"... We analyze sequential bargaining in general political and economic environments, where proposers are recognized according to a random recognition rule and a proposal is implemented if it passes under an arbitrary voting rule. We prove existence of stationary equilibria, upper hemicontinuity of equil ..."
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Cited by 44 (3 self)
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We analyze sequential bargaining in general political and economic environments, where proposers are recognized according to a random recognition rule and a proposal is implemented if it passes under an arbitrary voting rule. We prove existence of stationary equilibria, upper hemicontinuity of equilibrium proposals in structural and preference parameters, and core equivalence One of the central findings in the spatial model of social choice is that in two or more dimensions the majority rule core, consisting of those alternatives unbeaten in pairwise majority comparisons, is empty for “most ” profiles of individual preferences. 1 This result extends beyond majority rule to include
Winner determination in sequential majority voting
 In Proceedings of the ECAI2006 Multidisciplinary Workshop on Advances in Preference Handling
, 2007
"... Preferences can be aggregated using a voting rule. Each agent gives their preference orderings over a set of candidates, and a voting rule is used to compute the winner. We consider voting rules which perform a sequence of pairwise comparisons between two candidates, where the result of each is comp ..."
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Cited by 38 (12 self)
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Preferences can be aggregated using a voting rule. Each agent gives their preference orderings over a set of candidates, and a voting rule is used to compute the winner. We consider voting rules which perform a sequence of pairwise comparisons between two candidates, where the result of each is computed by a majority vote. The winner thus depends on the chosen sequence of comparisons, which can be represented by a binary tree. There are candidates that will win in some trees (called possible winners) or in all trees (called Condorcet winners). While it is easy to find the possible and Condorcet winners, we prove that it is difficult if we insist that the tree is balanced. This restriction is therefore enough to make voting difficult for the chair to manipulate. We also consider the situation where we lack complete informations about preferences, and determine the computational complexity of computing possible and Condorcet winners in this extended case. 1
A ThreePlayer Dynamic Majoritarian Bargaining Game
 Journal of Economic Theory
, 2004
"... for comments. All errors are mine. ..."
Optimizing group judgmental accuracy in the presence of interdependencies
 Public Choice
, 1984
"... Consider a group of people confronted with a dichotomous choice (for example, a yes or no decision). Assume that we can characterize each person by a probability, pi, of making the 'better ' of the two choices open to the group, such that we define 'better ' in terms of some linear ordering of the a ..."
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Cited by 20 (0 self)
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Consider a group of people confronted with a dichotomous choice (for example, a yes or no decision). Assume that we can characterize each person by a probability, pi, of making the 'better ' of the two choices open to the group, such that we define 'better ' in terms of some linear ordering of the alternatives. If individual choices are independent, and if the a priori likelihood that either of the two choices is correct is one half, we show that the group decision procedure that maximizes the likelihood that the group will make the better of the two choices open to it is a weighted voting rule that assigns weights, wi, such that Pi wi ~ log 1ffi " We then examine the implications for optimal group choice of interdependencies among individual choices.
A Model of Farsighted Voting
, 2008
"... I present a new method of interpreting voter preferences in settings where policy remains in effect until replaced by new legislation. In such settings voters consider not only the utility they receive from a given policy today, but also the utility they will receive from policies likely to replace ..."
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Cited by 15 (0 self)
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I present a new method of interpreting voter preferences in settings where policy remains in effect until replaced by new legislation. In such settings voters consider not only the utility they receive from a given policy today, but also the utility they will receive from policies likely to replace that policy in the future. The model can be used to both characterize longterm preferences and distributions over policy outcomes in situations where policy is ongoing and voters are farsighted.
Computing the minimal covering set
 In Proceedings of the 11th Conference on Theoretical Aspects of Rationality and Knowledge
, 2007
"... We present the first polynomialtime algorithm for computing the minimal covering set of a (weak) tournament. The algorithm draws upon a linear programming formulation of a subset of the minimal covering set known as the essential set. On the other hand, we show that no efficient algorithm exists fo ..."
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Cited by 14 (11 self)
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We present the first polynomialtime algorithm for computing the minimal covering set of a (weak) tournament. The algorithm draws upon a linear programming formulation of a subset of the minimal covering set known as the essential set. On the other hand, we show that no efficient algorithm exists for two variants of the minimal covering set, the minimal upward covering set and the minimal downward covering set, unless P equals NP. Finally, we observe a strong relationship between von NeumannMorgenstern stable sets and upward covering on the one hand, and the Banks set and downward covering on the other.
Minimal Stable Sets in Tournaments
, 2009
"... We propose a systematic methodology for defining tournament solutions as extensions of maximality. The central concepts of this methodology are maximal qualified subsets and minimal stable sets. We thus obtain an infinite hierarchy of tournament solutions, which encompasses the top cycle, the uncove ..."
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Cited by 9 (8 self)
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We propose a systematic methodology for defining tournament solutions as extensions of maximality. The central concepts of this methodology are maximal qualified subsets and minimal stable sets. We thus obtain an infinite hierarchy of tournament solutions, which encompasses the top cycle, the uncovered set, the Banks set, the minimal covering set, the tournament equilibrium set, the Copeland set, and the bipartisan set. Moreover, the hierarchy includes a new tournament solution, the minimal extending set, which is conjectured to refine both the minimal covering set and the Banks set. 1
A New Perspective on Implementation by Voting Trees
"... Voting trees describe an iterative procedure for selecting a single vertex from a tournament. They provide a very general abstract model of decisionmaking among a group of individuals, and it has therefore been studied which voting rules have a tree that implements them, i.e., chooses according to ..."
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Cited by 9 (1 self)
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Voting trees describe an iterative procedure for selecting a single vertex from a tournament. They provide a very general abstract model of decisionmaking among a group of individuals, and it has therefore been studied which voting rules have a tree that implements them, i.e., chooses according to the rule for every tournament. While partial results concerning implementable rules and necessary conditions for implementability have been obtained over the past forty years, a complete characterization of voting rules implementable by trees has proven surprisingly hard to find. A prominent rule that cannot be implemented by trees is the Copeland rule, which singles out vertices with maximum degree. In this paper, we suggest a new angle of attack and reexamine the implementability of the Copeland solution using paradigms and techniques that are at the core of theoretical computer science. We study the extent to which voting trees can approximate the maximum degree in a tournament, and give upper and lower bounds on the worstcase ratio between the degree of the vertex chosen by a tree and the maximum degree, both for the deterministic model concerned with a single fixed tree, and for randomizations over arbitrary sets of trees. Our main positive result is a randomization over surjective trees of polynomial size that provides an approximation ratio of at least 1/2. The proof is based on a connection between a randomization over caterpillar trees and a rapidly mixing Markov chain.
Computational Aspects of Covering in Dominance Graphs
, 2008
"... Various problems in AI and multiagent systems can be tackled by finding the “most desirable” elements of a set given some binary relation. Examples can be found in areas as diverse as voting theory, game theory, and argumentation theory. Some particularly attractive solution sets are defined in term ..."
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Cited by 7 (4 self)
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Various problems in AI and multiagent systems can be tackled by finding the “most desirable” elements of a set given some binary relation. Examples can be found in areas as diverse as voting theory, game theory, and argumentation theory. Some particularly attractive solution sets are defined in terms of a covering relation—a transitive subrelation of the original relation. We consider three different types of covering (upward, downward, and bidirectional) and the corresponding solution concepts known as the uncovered set and the minimal covering set. We present the first polynomialtime algorithm for finding the minimal bidirectional covering set (an acknowledged open problem) and prove that deciding whether an alternative is in a minimal upward or downward covering set is NPhard. Furthermore, we obtain various settheoretical inclusions, which reveal a strong connection between von NeumannMorgenstern stable sets and upward covering on the one hand, and the Banks set and downward covering on the other hand. In particular, we show that every stable set is also a minimal upward covering set.
Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections
, 1998
"... We prove that the support of mixed strategy equilibria of twoplayer, symmetric, zerosum games lies in the uncovered set, a concept originating in the theory of tournaments and the spatial theory of politics. We allow for uncountably infinite strategy spaces, and, as a special case, we obtain a lon ..."
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Cited by 7 (2 self)
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We prove that the support of mixed strategy equilibria of twoplayer, symmetric, zerosum games lies in the uncovered set, a concept originating in the theory of tournaments and the spatial theory of politics. We allow for uncountably infinite strategy spaces, and, as a special case, we obtain a longstanding claim to the same eect, due to McKelvey (1986), in the political science literature. Further, we prove the nonemptiness of the uncovered set under quite general assumptions, and we establish, under various assumptions, the measurability and coanalyticity of this set. In the concluding section, we indicate how the inclusion result may be extended to multiplayer, nonzerosum games.