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Results n° 1 to 8 of 74 matches
| Title |
The measured power and the elector's capacity of influencing the voting outcome |
| Author |
DIFFO LAMBO Lawrence, TCHANTCHO Bertrand, MOULEN Joël |
| Keywords |
Influence relation, Performance relation, Power indices, Power relation, Simple game |
| Topics |
Game Theory, Orders and preorders, Social Choice, Voting |
| Abstract |
We study the power relation ≥ P. This binary relation on the set of voters was used in [Diffo Lambo, Moulen, 2000] to show that the Taylor's influence relation ≥ T appraises the voter's capacity of influencing the voting outcome when individual preference relations are linear orders, if the classical dominance stands for the social outcome and the Kendal's distance is the means of measuring a voter's dissatisfaction. In this paper, the definition of ≥P is extended in two directions: on the one hand, dissatisfaction is measured by any distance (apart from the Kendal's distance), and on the other hand, the domain of individual preference relations has no restriction (it may contain complete weak orders apart from complete linear orders). The above mentioned result on ≥ T now being at times wrong, we come out with a sufficient condition under which ≥ T actually appraises the voter's capacity of influencing the voting outcome. Moreover we succeed, thanks to this highly unifying condition, in generalizing all the other results of [Diffo Lambo, Moulen, 2000]. |
| Number |
166, Summer 2004 |
| Language |
 French | Read the article
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| Title |
From Condorcet to Arrow via Guilbaud, Nakamura and the "simple games" |
| Author |
MONJARDET Bernard |
| Keywords |
Aggregation of preferences, Arrow's theorem, Effet Condorcet, Guilbaud's theorem, Nakamura's theorem, Simple game, Ultrafilter |
| Topics |
History of Mathematics, Orders and preorders, Social Choice, Voting |
| Abstract |
The aim of this paper is to present Arrow's theorem and more generally the common framework of many results which can be called "Arrovian theorems". We begin by recalling the Condorcet majority rules and why they fail: the so called "effet Condorcet". These rules are examples of preference aggregation functions defined by a simple game, and then following Guilbaud's approach, we seek if in the class of all these functions we can find some functions avoiding this problem. The rather negative answer is given by the Guilbaud and Nakamura theorems. Taking then an axiomatic approach we show that some independent and Paretian preference aggregation functions avoiding the "effet Condorcet" are defined by a simple game. So the previous results allow to get several Arrovian theorems and finally Arrow's theorem. In the last section we give some historical and bibliographical comments on these results and on several developments showing essentially the robustness of Arrow's theorem. |
| Number |
163, Fall 2003, special issue: Social choice theory: golden jubilee |
| Language |
French | Read the article
| Title |
Preference aggregation, collective choice and generalized binary constitutions |
| Author |
ANDJIGA Nicolas-Gabriel, MOULEN Joël |
| Keywords |
Core, General binary constitution, Independence of irrelevant alternatives, Preference aggregation rule, Simple game |
| Topics |
Decision Theory, Orders and preorders, Social Choice |
| Abstract |
The aim of this paper is to study the notion of Generalized Binary Constitution (GBC), a distribution of power due to Ferejohn and Fishburn (1979), which generalizes some classical notions such as simple games and voting games. The GBC helps us to define a preference aggregation rule (PAR) and we characterize GBC's whose collective preferences are either complete, asymmetric, transitive or acyclic when individual preferences are weak orders or linear orders. Since the procedure of aggregation of preferences which satisfies IIA is equivalent to the preference aggregation rule of a GBC, we give relations between our results and some Arrovian results. We also characterize core-stable GBC's and therefore deduce classical results and in particular Nakamura's theorem for simple games. |
| Number |
163, Fall 2003, special issue: Social choice theory: golden jubilee |
| Language |
 English | Read the article
| Title |
The axiomatic characterizations of majority voting and scoring rules |
| Author |
MERLIN Vincent |
| Keywords |
Borda count, Majority voting, Scoring rules, Social choice, Vote uninominal |
| Topics |
Orders and preorders, Social Choice, Voting |
| Abstract |
The Arrovian framework of social choice theory is flexible enough to allow for a precise axiomatic study of the voting rules that are used in political elections, sport competitions or expert committees, etc. such as the majority rule or the scoring rules. The objective of this paper is to give an account of the results that have been obtained in this direction since 1951. We first present some basic conditions for a collective decision rule to be democratic. Next, we expound in detail two fundamental results: the characterization of the majority rule by May, and the axiomatization of the family of scoring rules by Young. Afterwards, using these results, some specific scoring rules, such as the plurality vote or the Borda count, have also been characterized. Some remarks on other directions of research and open issues conclude the paper. |
| Number |
163, Fall 2003, special issue: Social choice theory: golden jubilee |
| Language |
English | Read the article
Read the article
| Title |
Sufficient conditions of monotonicity for a ranking procedure |
| Author |
JURET Xavier |
| Keywords |
Decision making, Group decision, Iterative procedures, Monotonicity, Multicriteria ranking |
| Topics |
Decision Theory, Orders and preorders, Social Choice |
| Abstract |
In this paper, we present some sufficient conditions of monotonicity for an iterative ranking procedure. In the framework of the aggregation of individual preferences, after recalling the notion of monotonicity, we present some results using rationnality and stability conditions of choice procedures. After showing that not all monotonic iteratives ranking procedures are concerned by the previous results, we introduce new results using the notion of respect of a monotonic scoring function. Then, these results are applied to establish the monotonicity of several iteratives ranking procedures. |
| Number |
161, Spring 2003, special issue: Operations research and decision aid |
| Language |
French | Read the article
| Title |
Solving aggregation of preferences problems using doubly stochastic matrix approximation |
| Author |
TAKOUDA Pawoumodom-L. |
| Keywords |
Aggregation of preferences, Alternating projection, Doubly stochastic matrices, Permutation matrice |
| Topics |
Approximation, Linear Algebra, Numerical Analysis, Permutations, Social Choice |
| Abstract |
In this work, we consider the classical problem of aggregation of preferences. We extend a previous work by Blin [5]. Under some assumptions, he formulated this problem as that of finding the nearest permutation matrix to a doubly stochastic matrix (called normalized of the agreement matrix, which collects the information contained in the expressed individual preferences). We reduce these assumptions, and we introduce a two-phase scheme for solving the problem. The first phase consists in approximating the matrix that contains the individual preferences information (which looses here the doubly stochastic character) by a doubly stochastic matrix using an algorithm proposed by the author [20 in a previous work. We thereby reduce the more general problem to that considered by Blin, which can be solved by using linear programming or, more directly, as a weighted bipartite matching problem. |
| Number |
161, Spring 2003, special issue: Operations research and decision aid |
| Language |
French | Read the article
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