A note on strategic ambiguity and coalition structure in electoral competition

We revisit the two-candidate, three-alternative election campaign game with strategic ambiguity of Aragones & Postlewaite (2002), in which ambiguity arises in equilibrium when no pure alternative is majority-winning and voters exhibit sufficiently intense preferences. We show that the existence condition for winning strategies of the candidate associated with the Condorcet alternative is not sufficient for the existence of such a strategy. The original derivation evaluates the worst-case opponent strategy only at two extreme points of the feasible set, whereas the relevant bound is attained elsewhere. We provide a counterexample showing that the original condition can be satisfied even though no winning strategy exists, and derive a corrected characterization: winning strategies rely on voters who most prefer the remaining alternative, associated with neither candidate, rather than those who rank the Condorcet alternative second. This mirrors the coalition logic of the non-Condorcet candidate, yielding a structural symmetry between the two candidates' equilibrium strategies. As a consequence, association with a Condorcet alternative does not confer a systematic strategic advantage, and strategic ambiguity operates as a selective rather than aggregative electoral device.