Twitching weak dictators
In Arrow's version of his impossibility theorem, collective rationality requires that social choices are determined by a transitive social preference. This attracted much criticism and there is now an extensive literature on weakening this condition. The result of this line of inquiry is that dictators disappear but Weak Dictators (vetoers) and Oligarchies appear. In achieving these results Arrow's condition of independence of irrelevant alternatives is invariably maintained. The purpose of this note is to show that the same effect may be obtained by maintaining Collective Rationality and weakening the Independence of Irrelevant Alternatives. In the particular weakening considered here, the social preference over a particular pair of alternatives is allowed to change a little, that is to twitch, while the independence of irrelevant alternatives would insist on no change at all. Weak dictators replace dictators as a result of this weakening. It is somewhat intriguing that weakening a condition that was confused with one aspect of collective rationality should have much the same effect as weakening collective rationality itself.
scientific article; zbMATH DE number 4022972