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Irrational individuals and collective intransitivity
Author(s) -
Roff Alan
Publication year - 1977
Publication title -
behavioral science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 45
eISSN - 1099-1743
pISSN - 0005-7940
DOI - 10.1002/bs.3830220207
Subject(s) - irrational number , arrow , impossibility , arrow's impossibility theorem , mathematical economics , set (abstract data type) , social choice theory , preference , positive economics , economics , microeconomics , mathematics , computer science , political science , law , geometry , programming language
In considering a model for individual decision making we adapt Arrow's general impossibility theorem for collective choice situations to the individual's situation. Thereby, we build up a set of minimal conditions under which any individual will run the risk of arriving at a cyclic ordering of alternatives no matter how he aggregates his preference over decision‐influencing criteria. There is always a distinct possibility of such irrational individuals in any society. We inspect the influence such persons have to induce cycles for society. We use the method of majority decisions, which can give cycles with all individuals having noncyclic orderings, by calculating some probabilities of occurrences under the assumption of impartial culture. We conclude that the presence of individual intransitivity significantly increases the probability of social intransitivity.