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We consider the possibility of designing an election method that eliminatesthe incentives for a voter to rank any other candidate equal to or ahead of hisor her sincere favorite. We refer to these methods as satisfying the ``StrongFavorite Betrayal Criterion" (SFBC). Methods satisfying our strategic criteriacan be classified into four categories, according to their geometricalproperties. We prove that two categories of methods are highly restricted andclosely related to positional methods (point systems) that give equal points toa voter's first and second choices. The third category is tightly restricted,but if criteria are relaxed slightly a variety of interesting methods can beidentified. Finally, we show that methods in the fourth category are largelyirrelevant to public elections. Interestingly, most of these methods forsatisfying the SFBC do so only ``weakly," in that these methods make nomeaningful distinction between the first and second place on the ballot.However, when we relax our conditions and allow (but do not require) equalrankings for first place, a wider range of voting methods are possible, andthese methods do indeed make meaningful distinctions between first and secondplace.

Geometric construction of voting methods that protect voters' first choices