Characterization of the Pareto social choice correspondence

Abstract We consider choice correspondences that assign a subset to every choice set of alternatives, where the total set of alternatives is an arbitrary finite or infinite set. We focus on the relations between several extensions of the condition of independence of irrelevant alternatives on one hand, and conditions on the revealed preference relation on sets, notably the weak axiom of revealed preference, on the other hand. We also establish the connection between the condition of independence of irrelevant alternatives and so-called strong sets; the latter characterize a social choice correspondence satisfying independence of irrelevant alternatives.

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Characterising scoring rules by their solution in iteratively undominated strategies

Economic Theory ◽

10.1007/s00199-021-01353-w ◽

2021 ◽

Author(s):

Christian Basteck

Keyword(s):

Monotonicity Property ◽

Scoring Rules ◽

The Other ◽

Approval Voting ◽

Property A ◽

Borda Rule ◽

Scoring Rule ◽

Direct Mechanism ◽

Social Choice Correspondence ◽

Choice Correspondence

AbstractWe characterize voting procedures according to the social choice correspondence they implement when voters cast ballots strategically, applying iteratively undominated strategies. In elections with three candidates, the Borda Rule is the unique positional scoring rule that satisfies unanimity (U) (i.e., elects a candidate whenever it is unanimously preferred) and is majoritarian after eliminating a worst candidate (MEW)(i.e., if there is a unanimously disliked candidate, the majority-preferred among the other two is elected). In a larger class of rules, Approval Voting is characterized by a single axiom that implies both U and MEW but is weaker than Condorcet-consistency (CON)—it is the only direct mechanism scoring rule that is majoritarian after eliminating a Pareto-dominated candidate (MEPD)(i.e., if there is a Pareto-dominated candidate, the majority-preferred among the other two is elected); among all finite scoring rules that satisfy MEPD, Approval Voting is the most decisive. However, it fails a desirable monotonicity property: a candidate that is elected for some preference profile, may lose the election once she gains further in popularity. In contrast, the Borda Rule is the unique direct mechanism scoring rule that satisfies U, MEW and monotonicity (MON). There exists no direct mechanism scoring rule that satisfies both MEPD and MON and no finite scoring rule satisfying CON.

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A characterization of fuzzy strategy-proof social choice functions

2013 5th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO) ◽

10.1109/icmsao.2013.6552715 ◽

2013 ◽

Cited By ~ 1

Author(s):

Olfa Meddeb ◽

Fouad Ben Abdelaziz ◽

Jos Rui Figueira

Keyword(s):

Social Choice ◽

Choice Functions ◽

Social Choice Functions ◽

Strategy Proof

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Bargaining in Legislatures

American Political Science Review ◽

10.2307/1961664 ◽

1989 ◽

Vol 83 (4) ◽

pp. 1181-1206 ◽

Cited By ~ 943

Author(s):

David P. Baron ◽

John A. Ferejohn

Keyword(s):

Social Choice ◽

Choice Theory ◽

Social Choice Theory ◽

Institutional Structure ◽

The Social ◽

Free Model ◽

Sequential Nature ◽

Choice Literature ◽

Formal Rules

Bargaining in legislatures is conducted according to formal rules specifying who may make proposals and how they will be decided. Legislative outcomes depend on those rules and on the structure of the legislature. Although the social choice literature provides theories about voting equilibria, it does not endogenize the formation of the agenda on which the voting is based and rarely takes into account the institutional structure found in legislatures. In our theory members of the legislature act noncooperatively in choosing strategies to serve their own districts, explicitly taking into account the strategies members adopt in response to the sequential nature of proposal making and voting. The model permits the characterization of a legislative equilibrium reflecting the structure of the legislature and also allows consideration of the choice of elements of that structure in a context in which the standard, institution-free model of social choice theory yields no equilibrium.

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