scholarly journals A REPRESENTATION THEOREM FOR VOTING WITH LOGICAL CONSEQUENCES

2006 ◽  
Vol 22 (2) ◽  
pp. 181-190 ◽  
Author(s):  
PETER GÄRDENFORS
Keyword(s):  
Social Choice ◽  
Representation Theorem ◽  
Impossibility Theorem ◽  
Choice Functions ◽  
Natural Conditions ◽  
Independence Of Irrelevant Alternatives ◽  
The Social ◽  
Social Choice Functions ◽  
Central Result ◽  
Choice Set

This paper concerns voting with logical consequences, which means that anybody voting for an alternative x should vote for the logical consequences of x as well. Similarly, the social choice set is also supposed to be closed under logical consequences. The central result of the paper is that, given a set of fairly natural conditions, the only social choice functions that satisfy social logical closure are oligarchic (where a subset of the voters are decisive for the social choice). The set of conditions needed for the proof include a version of Independence of Irrelevant Alternatives that also plays a central role in Arrow's impossibility theorem.

Full Implementation under Ambiguity

2021 ◽  
Vol 13 (1) ◽  
pp. 148-178
Author(s):  
Huiyi Guo ◽  
Nicholas C. Yannelis
Keyword(s):  
Social Choice ◽  
Expected Utility ◽  
Sufficient Conditions ◽  
Choice Functions ◽  
Maxmin Expected Utility ◽  
Special Cases ◽  
Social Choice Functions ◽  
Bayesian Implementation ◽  
Pareto Efficient ◽  
Choice Set

This paper introduces the maxmin expected utility framework into the problem of fully implementing a social choice set as ambiguous equilibria. Our model incorporates the Bayesian framework and the Wald-type maxmin preferences as special cases and provides insights beyond the Bayesian implementation literature. We establish necessary and almost sufficient conditions for a social choice set to be fully implementable. Under the Wald-type maxmin preferences, we provide easy-to-check sufficient conditions for implementation. As applications, we implement the set of ambiguous Pareto-efficient and individually rational social choice functions, the maxmin core, the maxmin weak core, and the maxmin value. (JEL D71, D81, D82)

scholarly journals SOCIAL CHOICE AND JUST INSTITUTIONS: NEW PERSPECTIVES

2007 ◽  
Vol 23 (1) ◽  
pp. 15-43 ◽  
Author(s):  
MARC FLEURBAEY
Keyword(s):  
Social Choice ◽  
Social Preferences ◽  
Well Being ◽  
Impossibility Theorem ◽  
Choice Functions ◽  
New Approach ◽  
Second Best ◽  
Interpersonal Comparisons ◽  
Theories Of Justice ◽  
Social Choice Functions

It has become accepted that social choice is impossible in the absence of interpersonal comparisons of well-being. This view is challenged here. Arrow obtained an impossibility theorem only by making unreasonable demands on social choice functions. With reasonable requirements, one can get very attractive possibilities and derive social preferences on the basis of non-comparable individual preferences. This new approach makes it possible to design optimal second-best institutions inspired by principles of fairness, while traditionally the analysis of optimal second-best institutions was thought to require interpersonal comparisons of well-being. In particular, this approach turns out to be especially suitable for the application of recent philosophical theories of justice formulated in terms of fairness, such as equality of resources.

scholarly journals On the manipulability of a class of social choice functions: plurality kth rules

2021 ◽  
Author(s):  
Dezső Bednay ◽  
Attila Tasnádi ◽  
Sonal Yadav
Keyword(s):  
Social Choice ◽  
Vote Rule ◽  
Plurality Rule ◽  
Social Ranking ◽  
Choice Functions ◽  
The Social ◽  
Social Choice Functions ◽  
The Individual ◽  
Group Member ◽  
Special Case

AbstractIn this paper we introduce the plurality kth social choice function selecting an alternative, which is ranked kth in the social ranking following the number of top positions of alternatives in the individual ranking of voters. As special case the plurality 1st is the same as the well-known plurality rule. Concerning individual manipulability, we show that the larger k the more preference profiles are individually manipulable. We also provide maximal non-manipulable domains for the plurality kth rules. These results imply analogous statements on the single non-transferable vote rule. We propose a decomposition of social choice functions based on plurality kth rules, which we apply for determining non-manipulable subdomains for arbitrary social choice functions. We further show that with the exception of the plurality rule all other plurality kth rules are group manipulable, i.e. coordinated misrepresentation of individual rankings are beneficial for each group member, with an appropriately selected tie-breaking rule on the set of all profiles.

A Comment on Arrow’s Impossibility Theorem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Alec Sandroni ◽  
Alvaro Sandroni
Keyword(s):  
Social Choice ◽  
Choice Function ◽  
Social Preference ◽  
Social Choice Function ◽  
Individual Preference ◽  
Impossibility Theorem ◽  
Preference Order ◽  
Individual Choice ◽  
Choice Functions ◽  
Preference Orders

AbstractArrow (1950) famously showed the impossibility of aggregating individual preference orders into a social preference order (together with basic desiderata). This paper shows that it is possible to aggregate individual choice functions, that satisfy almost any condition weaker than WARP, into a social choice function that satisfy the same condition (and also Arrow’s desiderata).

scholarly journals Self-selective social choice functions

2007 ◽  
Vol 31 (1) ◽  
pp. 129-149 ◽  
Author(s):  
Semih Koray ◽  
Arkadii Slinko
Keyword(s):  
Social Choice ◽  
Choice Functions ◽  
Social Choice Functions
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