An important caveat to keep in mind when considering strategic behavior is that complementary strategic actions being rational requires shared beliefs on the state of the world.

(The assumption that the strategically optimal vote does not change with the addition of another vote is also generally not true for the entire space of results - just usually true if their is one salient boundary or the information available is indistinguishable.)

This is a standard game-theoretic assumption, but not always true in real life, especially in the realm of politics and propaganda.

E.g., one explanation for observed collapse of approval votes into plurality is that voters may have overestimate the degree to which their preferences are typical, and hence be overly optimistic about the prospects of their favorite candidate as opposed to, say, their second-favorite candidate.