McKelvey–Schofield chaos theorem
The McKelvey–Schofield chaos theorem is a result in social choice theory. It states that if preferences are defined over a multidimensional policy space, then majority rule is in general unstable: there is no Condorcet winner. Furthermore, any point in the space can be reached from any other point by a sequence of majority votes.
The theorem can be thought of as showing that Arrow's impossibility theorem holds when preferences are restricted to be concave in . The median voter theorem shows that when preferences are restricted to be single-peaked on the real line, Arrow's theorem does not hold, and the median voter's ideal point is a Condorcet winner. The chaos theorem shows that this good news does not continue in multiple dimensions.
Richard McKelvey initially proved the theorem for Euclidean preferences.[1] Norman Schofield extended the theorem to the more general class of concave preferences.[2]
References
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