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1 Introduction Mostapha Diss and Vincent Merlin -- Part IThe Condorcet Efficiency of Voting Rules and Related Paradoxes -- 2 Analyzing the Probability of Election Outcomes with Abstentions William V. Gehrlein and Dominique Lepelley -- 3 Condorcet Efficiency of General Weighted Scoring Rules under IAC: Indifference and Abstention Mostapha Diss, Eric Kamwa, Issofa Moyouwou, and Hatem Smaoui -- 4 The Effect of Closeness on the Election of a Pairwise Majority Rule Winner Mostapha Diss, Patrizia Pérez-Asurmendi, and Abdelmonaim Tlidi -- 5 Analyzing the Practical Relevance of Voting Paradoxes via Ehrhart Theory, Computer Simulations, and Empirical Data Felix Brandt, Christian Geist, and Martin Strobel -- Part II Other Voting Paradoxes -- 6 On the Probability of the Ostrogorski's Paradox William V. Gehrlein and Vincent Merlin -- 7 Violations of Reversal Symmetry under Simple and Runoff Scoring Rules. Raouia Belayadi and Boniface Mbih -- Part III Binary Voting in Federations -- 8 Majority Efficient Representation of the Citizens in a Federal Union Marc Feix, Dominique Lepelley, Vincent Merlin, Jean Louis Rouet, and Laurent Vidu -- 9 "One Man, One Vote" Part 1: Electoral Justice in the U.S. Electoral College: Banzhaf and Shapley/Shubik versus May Olivier de Mouzon, Thibault Laurent, Michel Le Breton, and Issofa Moyouwou -- Part IV Resistance to Manipulations -- 10 Further Results on the Manipulability of Social Choice Rules: A Comparison of Standard and Favardin-Lepelley types of Individual Manipulations Fuad Aleskerov, Daniel Karabekyan, Alexander Ivanov, and Vyacheslav Yakuba -- 11 Exploring the No-Show Paradox for Condorcet Extensions Using Ehrhart Theory and Computer Simulations Felix Brandt, Johannes Hofbauer, and Martin Strobel -- 12 Susceptibility to Manipulation by Sincere Truncation: Scoring Rules and Scoring Run-off Systems. Eric Kamwa and Issofa Moyouwou -- Part V Game Theory 13 Dummy Players and the Quota in Weighted Voting Games: Some Further Results Fabrice Barthelemy and Mathieu Martin -- 14 Who Wins and Loses under Approval Voting? An Analysis in Large Elections Sébastien Courtin and Matias Nuñez -- Part VI Techniques for Probability Computations -- 15 Combinatorics of Voting Rules under Anonymity and Neutrality Alexander Karpov -- 16 From Gehrlein-Fishburn Frequency Representation to a Direct Proof of the Ehrhart Extended Conjecture Nicolas-Gabriel Andjiga, Boniface Mbih, and Issofa Moyouwou -- 17 IAC-Probability Calculations in Voting Theory: Progress Report Abdelhalim El Ouafdi, Issofa Moyouwou, and Hatem Smaoui. .

International audience ; The notion of the existence of a Strict Ostrogorski Paradox presents an interesting phenomenon that could lead to some very unsettling outcomes in group decision-making situations. This phenomenon cannot be observed in two-issue situations, and when three-issue situations are considered, the probability that such an outcome will be observed never reaches a likelihood of as much as two percent for large electorates, regardless of the propensity of voters to align their preferences on issues with the standards of political parties. The probability of observing a Strict Ostrogorski Paradox in four-issue situations is nearly zero when using an assumption that exaggerates the likelihood that such a paradoxical outcome will be observed. We conclude that it is very unlikely that a Strict Ostrogorski Paradox would ever be observed in any real voting situation with a large electorate

International audience ; The notion of the existence of a Strict Ostrogorski Paradox presents an interesting phenomenon that could lead to some very unsettling outcomes in group decision-making situations. This phenomenon cannot be observed in two-issue situations, and when three-issue situations are considered, the probability that such an outcome will be observed never reaches a likelihood of as much as two percent for large electorates, regardless of the propensity of voters to align their preferences on issues with the standards of political parties. The probability of observing a Strict Ostrogorski Paradox in four-issue situations is nearly zero when using an assumption that exaggerates the likelihood that such a paradoxical outcome will be observed. We conclude that it is very unlikely that a Strict Ostrogorski Paradox would ever be observed in any real voting situation with a large electorate

International audience ; In most of the social choice literature dealing with the computation of the exact probability of voting events under the impartial culture assumption, authors deal with no more than four constraints to describe voting events. With more than four constraints, most of the authors rely on Monte-Carlo simulations. It is usually more tricky to estimate the probability of events described by five constraints. Gehrlein and Fishburn (1980) have tried, but their conclusions are based on conjectures. In this paper, we circumvent this conjecture by having recourse to the technique suggested by Saari and Tataru (1999) in order to compute the limit probability of the consistency of collective rankings when there are four competing alternatives given that the decision rule is a scoring rule. We provide a general formula for the limit probability of the consistency and we determine the optimal decision rules among the scoring rules that provide the best guarantee of consistency. Given the collective ranking on a set A, we have consistency if the collective ranking on B a proper subset of A is not altered after some alternatives are removed from A.

International audience ; In most of the social choice literature dealing with the computation of the exact probability of voting events under the impartial culture assumption, authors deal with no more than four constraints to describe voting events. With more than four constraints, most of the authors rely on Monte-Carlo simulations. It is usually more tricky to estimate the probability of events described by five constraints. Gehrlein and Fishburn (1980) have tried, but their conclusions are based on conjectures. In this paper, we circumvent this conjecture by having recourse to the technique suggested by Saari and Tataru (1999) in order to compute the limit probability of the consistency of collective rankings when there are four competing alternatives given that the decision rule is a scoring rule. We provide a general formula for the limit probability of the consistency and we determine the optimal decision rules among the scoring rules that provide the best guarantee of consistency. Given the collective ranking on a set A, we have consistency if the collective ranking on B a proper subset of A is not altered after some alternatives are removed from A.

International audience ; In most of the social choice literature dealing with the computation of the exact probability of voting events under the impartial culture assumption, authors deal with no more than four constraints to describe voting events. With more than four constraints, most of the authors rely on Monte-Carlo simulations. It is usually more tricky to estimate the probability of events described by five constraints. Gehrlein and Fishburn (1980) have tried, but their conclusions are based on conjectures. In this paper, we circumvent this conjecture by having recourse to the technique suggested by Saari and Tataru (1999) in order to compute the limit probability of the consistency of collective rankings when there are four competing alternatives given that the decision rule is a scoring rule. We provide a general formula for the limit probability of the consistency and we determine the optimal decision rules among the scoring rules that provide the best guarantee of consistency. Given the collective ranking on a set A, we have consistency if the collective ranking on B a proper subset of A is not altered after some alternatives are removed from A.

International audience ; In most of the social choice literature dealing with the computation of the exact probability of voting events under the impartial culture assumption, authors deal with no more than four constraints to describe voting events. With more than four constraints, most of the authors rely on Monte-Carlo simulations. It is usually more tricky to estimate the probability of events described by five constraints. Gehrlein and Fishburn (1980) have tried, but their conclusions are based on conjectures. In this paper, we circumvent this conjecture by having recourse to the technique suggested by Saari and Tataru (1999) in order to compute the limit probability of the consistency of collective rankings when there are four competing alternatives given that the decision rule is a scoring rule. We provide a general formula for the limit probability of the consistency and we determine the optimal decision rules among the scoring rules that provide the best guarantee of consistency. Given the collective ranking on a set A, we have consistency if the collective ranking on B a proper subset of A is not altered after some alternatives are removed from A.

International audience ; When choosing a voting rule to make subsequent decisions, the members of a committee may wish this rule to be self-selected when it is the object of a choice among a menu of different possible voting rules. Such concepts have recently been explored in Social Choice theory, and a menu of voting rule is said to be stable if it contains at least one self-selective voting rule at each profile of preferences on voting rules. We consider in this article the menu constituted by the three well-known scoring rules {Borda, Plurality, and Antiplurality}. Under the Impartial Culture assumption, which proposes an a priori model to estimate the likelihood of the profiles, we will derive a probability for the stability of this triplet of voting rules.

International audience ; When choosing a voting rule to make subsequent decisions, the members of a committee may wish this rule to be self-selected when it is the object of a choice among a menu of different possible voting rules. Such concepts have recently been explored in Social Choice theory, and a menu of voting rule is said to be stable if it contains at least one self-selective voting rule at each profile of preferences on voting rules. We consider in this article the menu constituted by the three well-known scoring rules {Borda, Plurality, and Antiplurality}. Under the Impartial Culture assumption, which proposes an a priori model to estimate the likelihood of the profiles, we will derive a probability for the stability of this triplet of voting rules.

International audience ; When choosing a voting rule to make subsequent decisions, the members of a committee may wish this rule to be self-selected when it is the object of a choice among a menu of different possible voting rules. Such concepts have recently been explored in Social Choice theory, and a menu of voting rule is said to be stable if it contains at least one self-selective voting rule at each profile of preferences on voting rules. We consider in this article the menu constituted by the three well-known scoring rules {Borda, Plurality, and Antiplurality}. Under the Impartial Culture assumption, which proposes an a priori model to estimate the likelihood of the profiles, we will derive a probability for the stability of this triplet of voting rules.

This paper is devoted to the analysis of all constitutions equipped with electoral systems involving two step procedures. First, one candidate is elected in every jurisdiction by the electors in that jurisdiction, according to some aggregation procedure. Second, another aggregation procedure collects the names of the jurisdictional winners in order to designate the final winner. It appears that whenever individuals are allowed to change jurisdiction when casting their ballot, they are able to manipulate the result of the election except in very few cases. When imposing a paretian condition on every jurisdiction?s voting rule, it is shown that, in the case of any finite number of candidates, any two steps voting rule that is not manipulable by movement of the electors necessarily gives to every voter the power of overruling the unanimity on its own. A characterization of the set of these rules is next provided in the case of two candidates.