The irrationality of transitivity in social choice

Examples are presented that illustrate the untenability of the transitivity condition as a general desideratum for social choice (or group decision) functions. The first two examples assume that each individual has a weak order preference-indifference relation on the set of alternatives. The second two examples assume only that individual preference is transitive and permit individual indifference to be intransitive, thus adding a degree of reality to the analysis. The latter two examples show that acceptance of a typical unanimity principle requires the rejection of social transitivity. The first example (which has no indifference) shows that if, in any election between two candidates with a number of voters, any candidate that receives all or all but one of the votes is to win, then social transitivity cannot hold.

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