We investigate the possibility of designing a voting rule that both meets the Condorcet criterion and has a low vulnerability to coalitional manipulation. For this purpose, we examine the Condorcification of a voting rule, where the original rule is altered to elect the Condorcet winner when one exists, and we study its impact on coalitional manipulability. A recent result states that for a large class of voting rules based on strict total orders, their Condorcification is at most as coalitionally manipulable as the original rule. We show that for most of them, the improvement is strict. We extend these results to a broader framework that includes weak orders and cardinal voting rules. These results support the main message of this paper: when searching for a "reasonable" voting rule with minimal coalitional manipulability, investigations can be restricted to Condorcet rules. In other words, in a class of "reasonnable" voting rules, it is possible to have both the Condorcet criterion and a minimal vulnerability to coalitional manipulation.
['François Durand', 'Fabien Mathieu', 'Ludovic Noirie']
Can a Condorcet Rule Have a Low Coalitional Manipulability