Abstract
This paper provides variants of Arrow’s impossibility theorem, which states that there exists no non-dictatorial aggregation rule satisfying weak Pareto, independence of irrelevant alternatives and collective rationality. In this paper, independence of irrelevant alternatives and collective rationality are simultaneously relaxed. Weak independence is imposed instead of independence of irrelevant alternatives. Social preferences are assumed to satisfy the semi-order properties of semi-transitivity and the interval-order property. We prove that there exists a vetoer when the number of alternatives is greater than or equal to six.
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I thank the anonymous referees of this journal for their helpful comments and for pointing out the errors in the original manuscript. This paper was financially supported by Grants in Aid for Young Scientists (B) from the Japan Society for the Promotion of Science and the Ministry of Education, Culture, Sports, Science and Technology.
