Electing versus Ranking in the Traditional Model

Author(s):  
Michel Balinski ◽  
Rida Laraki

This chapter discusses the pros and cons of electing and ranking methods of the traditional model of social choice, and depicts the situation for large classes of methods as more chaotic than is depicted in Arrow’s impossibility theorem. Candidate-scoring methods, including Borda and Condorcet-ranking methods, are discussed, along with their contrasting ideologies. Suggestions are presented for discarding both Borda and Condorcet approaches on the grounds that the former is depicted as the sole winner while the latter is used for ranking designation. Incompatibility between rankings and winners under the traditional model is explored, following the difference between problem of choice and the problem of ranking.

2016 ◽  
Vol 32 (2) ◽  
pp. 323-352 ◽  
Author(s):  
Michael Morreau

Abstract:Juries, committees and experts panels commonly appraise things of one kind or another on the basis of grades awarded by several people. When everybody's grading thresholds are known to be the same, the results sometimes can be counted on to reflect the graders’ opinion. Otherwise, they often cannot. Under certain conditions, Arrow's ‘impossibility’ theorem entails that judgements reached by aggregating grades do not reliably track any collective sense of better and worse at all. These claims are made by adapting the Arrow–Sen framework for social choice to study grading in groups.


2013 ◽  
Vol 09 (01) ◽  
pp. 97-123 ◽  
Author(s):  
GILBERT NJANPONG NANA ◽  
LOUIS AIME FONO

Fono et al.11 characterized, for an intuitionistic fuzzy t-norm [Formula: see text], two properties of a given regular intuitionistic fuzzy strict component of a (T,S)-transitive intuitionistic fuzzy preference. In this paper, we examine these characterizations in the particular case where [Formula: see text]. We then use these (general and particular) results to obtain some intuitionistic fuzzy versions of Arrow's impossibility theorem. Therefore, by weakening a requirement to social preferences, we deduce a positive result, that is, we display an example of a non-dictatorial Intuitionistic Fuzzy Agregation Rule (IFAR) and, we establish an intuitionistic fuzzy version of Gibbard's oligarchy theorem.


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