Abstract. Arrow's Impossibility Theorem provided a turning point for political science. It suggests that all preference aggregation rules (PARs) must violate a set of fairness conditions. However, the theorem does not address which PARs are more likely to violate those conditions across preference profiles. We fill this gap by comparing the probabilities that seven PARs (plurality, anti-plurality, Hare, Nanson, Borda, Copeland, and pairwise majority) violate Arrow's conditions individually and jointly. We prove that Borda and Copeland are more likely to adhere to Arrow's conditions than the first four PARs and are less likely to violate his independence condition. We then calculate more precise probabilities for three alternatives using simulations and find the differences in performance to be quite large. Among the PARs studied, pairwise majority is the most likely to adhere to Arrow's conditions jointly.

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