2008/03/10 by Masahiro Kumabe, H. Reiju Mihara · 1 citation
Computer Science · Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Artificial intelligence #Auction Theory and Applications #Computer science #Extensive-form game #Game Theory and Voting Systems #Game theory #Logic, Reasoning, and Knowledge #Mathematical economics #Mathematics #Monotonic function #Preference #Ranking (information retrieval) #Sequential game #Simple (philosophy) #Statistics #acm:68Q05 #acm:91A12 #acm:91A13 #acm:91B12 #acm:91B14 #cs.GT #cs.LO #msc:68Q05 #msc:91A12 #msc:91A13 #msc:91B12 #msc:91B14
paper · pdf · doi:10.1007/s00355-008-0300-5
published as Social Choice and Welfare (2008) 31:621-640 · 24+1 pages
openalex publication_date 2008/03/10 · arxiv created 2011/07/03 · arxiv updated 2011/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.