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| Volume 3, Number 1, January 2007, pp. 11-25 | |||||||||
| Kazutoshi Ando,Masafumi Tsurutani, Masashi Umezawa and Yoshitsugu Yamamoto | |||||||||
| Key words: | |||||||||
| social choice function, impossibility theorem, mutual evaluation, strong positive association, strategy-proofness, dictatorship, independence of irrelevant alternatives, Pareto principle | |||||||||
| Mathematices Subject Classification: 91B14, 91B08, 91B12 | |||||||||
| References | |||||||||
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| Abstract: | |||
| Given a set of individuals and a set of alternatives, an ordinary social choice function is a rule to choose one alternative aggregating preference orders on the alternativesreported by the individuals. We generalize this notion of social choice function where some individual's preference order may be incomplete: each individual reports his preference on his alternative set that is a subset of the whole set of alternatives. Axioms like strategy-proofness and dictatorship are suitably redefined and we show that these two notions are incompatible. In addition, we weaken the definition of strategy-proofness as well as dictatorship, and show the existence of a social choice function with desirable properties | |||
| Impossibility and possibility theorems for social choice functions on incomplete preference profiles | ||