2002/01/29 by Jobst Heitzig, Heitzig, Jobst · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #Combinatorics (math.CO) #Decision-Making and Behavioral Economics #Economic theories and models #Experimental Behavioral Economics Studies #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.math/0201285
The presented algorithms can be tested at http://welcome.to/groucho
arxiv created 2002/01/29 · openalex publication_date 2002/01/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Actual individual preferences are neither complete (=total) nor antisymmetric in general, so that at least every quasi-order must be an admissible input to a satisfactory choice rule. It is argued that the traditional notion of ``indifference'' in individual preferences is misleading and should be replaced by `equivalence' and `undecidedness'. In this context, ten types of majority and minority arguments of different strength are studied which lead to social choice rules that accept profiles of arbitrary reflexive relations. These rules are discussed by means of many familiar, and some new conditions, including `immunity from binary arguments'. Moreover, it is proved that every choice function satisfying two weak Condorcet-type conditions can be made both composition-consistent and idempotent, and that all the proposed rules have polynomial time complexity.