Radial Symmetry Does Not Preclude Condorcet Cycles If Different Voters Weight the Issues Differently

Richard F. Potthoff
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Richard F. Potthoff: Department of Political Science and Social Science Research Institute, Duke University, Box 90420, Durham, NC 27708, USA

Economies, 2022, vol. 10, issue 7, 1-17

Abstract: Radial symmetry, by our definition, is a precise condition on continuous ideal-point distributions, rarely if ever found exactly in practice, that is similar to the classical 1967 symmetry condition of Plott but pertains to an infinite electorate; the bivariate normal distribution provides an example. A Condorcet cycle exists if the electorate prefers alternative X to Y , Y to Z , and Z to X . An alternative K is a Condorcet winner if there is no alternative that the electorate prefers to K . Lack of a Condorcet winner may engender turmoil. The nonexistence of a Condorcet winner implies that a Condorcet cycle exists. Radial symmetry precludes the existence of Condorcet cycles and thus guarantees a Condorcet winner; but this result assumes that all voters weight the dimensions alike. Our counterexamples show that a Condorcet cycle can arise, even under radial symmetry, if the weighting of issues varies across voters. This finding may be of more than theoretical value: It may suggest that in an empirical setting (without radial symmetry), a Condorcet cycle may be more frequent if voters differ as to how they weight the dimensions. We examine, for illustration based on two dimensions (left–right, linguistic), a Condorcet preference cycle in Finland’s 1931 presidential election.

Keywords: Condorcet cycle; Condorcet winner; Condorcet paradox; multidimensional issue space; radial symmetry; spatial modeling (search for similar items in EconPapers)
JEL-codes: E F I J O Q (search for similar items in EconPapers)
Date: 2022
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