Irrational individuals and collective intransitivity


  • Alan Roff

    1. University of Kent at Canterbury
    Search for more papers by this author
    • The author wishes to thank Mr. John Craven for his advice and the referee for drawing my attention to the work of Amos Tversky.


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.