On the probability of observing Borda’s paradox

Previous studies have shown that, when voters’ preferences become more internally consistent or mutually coherent, the probability of observing Condorcet’s Paradox of cyclic majorities is reduced and tends to zero, in accordance with intuition. The current study shows that the impact of an increasing degree of mutual coherence among voters’ preferences on the likelihood of observing Borda’s Paradox is much more subtle and more difficult to analyze. The degree of the impact in this case depends both on the measure of mutual coherence that is considered and on the voting rule that is used. In some circumstances, the probability that Borda’s Paradox will occur actually increases when voters’ preferences become more internally consistent.

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