The Nakamura numbers for computable simple games

被引：0
作者：
Masahiro Kumabe
H. Reiju Mihara
机构：
[1] The University of the Air,Kanagawa Study Center
[2] Kagawa University,Graduate School of Management
来源：
Social Choice and Welfare | 2008年 / 31卷
关键词：
Social Choice; Initial Segment; Recursive Function; Game Form; Simple Game;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The Nakamura number of a simple game plays a critical role in preference aggregation (or multi-criterion ranking): the number of alternatives that the players can always deal with rationally is less than this number. We comprehensively study the restrictions that various properties for a simple game impose on its Nakamura number. We find that a computable game has a finite Nakamura number greater than three only if it is proper, nonstrong, and nonweak, regardless of whether it is monotonic or whether it has a finite carrier. The lack of strongness often results in alternatives that cannot be strictly ranked.
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页码：621 / 640
页数：19
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