We introduce the randomized Condorcet voting system. Our main contribution is to present it as a natural extension of Condorcet’s ideas, hence giving it solid philosophical grounds. Namely, the randomized Condorcet voting system elects the essentially unique Condorcet winner of lotteries of candidates. Moreover, we prove three major results regarding Condorcet compatibility, that is, the fact that a voting system elects Condorcet winners when they exist and is incentive-compatible. First, we show that there is no strongly Condorcet-compatible voting system. Second, we show that the randomized Condorcet voting system is the unique dominant-strategy Condorcet-compatible voting system, in a large class of voting systems. Third, we prove that, as opposed to other known methods, the randomized Condorcet voting system is strongly incentive-compatible when alternatives range on a left-right axis. Eventually, these fundamental properties of the randomized Condorcet voting system lead us to strongly recommend its use in practice, especially when deterministic Condorcet winners are likely to exist.
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