Relaxing IIA and the effect on individual power (Q370962)

This paper studies how relaxations in the condition of independence of irrelevant alternatives are related to weakening dictatorship in Arrow's theorem. Information gathering costs are measured and associated with the presence of individuals whose preference is decisive in some instances. It is evaluated how much the scope of particular individual's power increases in step with a reduction in the amount of information on other alternatives that has to be gathered to socially order two alternatives. The concepts of sufficient and relevant sets of alternatives play a basic role in the analysis. A concept of conditional dictators is also proposed. The framework established allows for developing the analysis in terms of social choice functions as well as in terms of social welfare functions.