  We consider the possibility of designing an election method that eliminates
the incentives for a voter to rank any other candidate equal to or ahead of his
or her sincere favorite. We refer to these methods as satisfying the ``Strong
Favorite Betrayal Criterion" (SFBC). Methods satisfying our strategic criteria
can be classified into four categories, according to their geometrical
properties. We prove that two categories of methods are highly restricted and
closely related to positional methods (point systems) that give equal points to
a voter's first and second choices. The third category is tightly restricted,
but if criteria are relaxed slightly a variety of interesting methods can be
identified. Finally, we show that methods in the fourth category are largely
irrelevant to public elections. Interestingly, most of these methods for
satisfying the SFBC do so only ``weakly," in that these methods make no
meaningful distinction between the first and second place on the ballot.
However, when we relax our conditions and allow (but do not require) equal
rankings for first place, a wider range of voting methods are possible, and
these methods do indeed make meaningful distinctions between first and second
place.
