From Paired Comparisons and Cycles to Arrow’s Theorem

Abstract

What makes paired comparisons so easy to accept is that they arise everywhere, and an appealing aspect of this approach is that it directly compares the merits of two opponents. However, paired comparisons can generate a wide array of difficulties that can lead to what appear to be paradoxes. Preference aggregation based solely on pairwise comparisons is at the heart of Arrow’s theorem. This chapter indicates that the Arrow impossibility result is a special case of a more generic type of problem involving parts and whole, and it offers an interpretation of it that shows that it does not have the implications for democratic theory that it is commonly assumed to have.