Abstract
Various properties of preferential election rules are described, including nine forms of monotonicity. It is shown that Condorcet's principle is incompatible with many of them. Some progress is made towards the task of determining all maximal mutually compatible subsets of these properties. To that end, a survey is given of the monotonicity properties of many known single-seat preferential election rules, and four new rules are described, including one that is offered as a more monotonic practical alternative to the Alternative Vote.
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