We study the incentives of candidates to strategically affect the outcome of a voting procedure. We show that the outcomes of evety nondictatorial voting procedure that satisfies unanimity will be affected by the incentives of noncontending candidates (i.e ., who cannot win the election) to influence the outcome by entering or exiting the election.
KEYWORDS: Strategic candidacy, voting procedures, candidates, voting rules.

THE DECISIONO F A CANDIDATEto enter an election can affect its outcome even in situations where the candidate is not the winner of the election. For instance, consider a scenario in which three national parties A, B, and C can contest an election in which the winner is decided by plurality rule. Although party A may have the highest number of first-preference votes, it may still fail to win the election if, for instance, B drops out of the race in order to let C win.2 If the voting process is viewed as a mapping from preferences to outcomes, then strategic behavior in the first stage can be just as important as strategic voting in the second stage. As we shall show, this phenomenon is important to all voting procedures, and thus spans applications ranging from political elections to committee decisions.
To be precise, we consider a framework in which there is a finite set of voters and potential candidates. We allow for the possibility that some or all of the candidates may also be voters, and consider situations where each individual (including candidates) has preferences over the set of all candidates. We examine a two-stage procedure where in a first stage candidates decide on whether or not they will enter the election, and then in a second stage a voting procedure is implemented to select from the candidates who enter. Before outlining our analysis, let us describe in more detail the way in which we model voting procedures. We model a voting procedure as specifying the winning candidate as a function of the set of entering candidates and voters' preferences over the entering candidates. The only restriction that we place on such a voting procedure is that it satisfy unanimity. Unanimity requires that if all voters find the same candidate most preferred out of the entering candidates, then that candidate is selected. We focus on the following issue. Which voting procedures are not influenced by candidates' incentives to exit an election? More precisely, for which voting procedures is it always a Nash equilibrium for all candidates to enter the election? We call this condition "candidate stability." We show that if the sets of voters and candidates are distinct, then the only voting procedures satisfying candidate stability are dictatorial procedures. When the set of candidates and voters overlap, then there exist nondictatorial voting procedures that satisfy candidate stability and unanimity. However, we show that none of these voting procedures satisfy an appealing "almost"-unanimity condition together with a very weak monotonicity condition that is satisfied by most standard voting procedures (e.g., tree implementable procedures, Condorcet consistent procedures, scoring rules, etc.). This implies that most standard voting procedures fail to satisfy candidate stability regardless of the overlap between candidates and voters. We should mention that these results are not simple extensions of an Arrow-type impossibility theorem, even though we invoke Arrow's theorem at one point in the proof of the first theorem. The bulk of the proof develops the joint implications of candidate stability and unanimity. We discuss this in more detail in what follows. Why should we care whether a voting procedure is candidate stable? Regardless of how one feels about candidate stability as a normative property, the results here must be taken seriously if we are at all interested in evaluating and comparing voting procedures. Much of what we know about voting rules is based on comparisons of the properties of different voting procedures when the set of candidates is taken as given.3 The results here show that the outcome of all nondictatorial and unanimous voting procedures will be influenced by the entry decisions of candidates. This implies that it is not valid to treat the set of candidates as fixed for any nondictatorial voting procedure. As most of what we know about voting rules treats the set of candidates as fixed, our results suggest that these need to be revisited accounting for strategic candidacy. For instance, example 5 below shows that the Pareto property of voting by successive elimination is upset when one allows for strategic candidacy. So, the results here show...........