The main part of Duverger’s Law states that “a majority vote on one ballot is conducive to a two-party system” (Duverger 1972). By this, he meant plurality elections in single-seat districts (e.g., most Congressional elections) or multi-seat districts in which all seats go to a single winner (e.g., in the Electoral College).
What “conducive” means is up for grabs, but many tend to add the following logic: voters are irrational when they vote for other than one of two front-runners. And: there needs to be some other system for hopeless candidates to stand a chance (e.g., PR, runoffs, whatever).
It is well-known that strategic-voting logic does not bind voter behavior, at least not in a deterministic way, and certainly not at the system-wide level. Canada, India, the United Kingdom, and so on. See Shugart’s blog for a running tally of “non-Duvergerian” outcomes.
And when we say you can’t vote for X without a new electoral system, we forget to ask an important question. How did countries move away from plurality voting in the first place? More on that here, here, here, here, here, and here.
So, why do we keep insisting on the power of Duverger’s Law? What follows are some potentially helpful excerpts.
Cox (1997, p. 98): “I think strategic voting survives, both in theory and in practice, because one of the things outcome-oriented elites can do in close races to reallocate resources from trailing to front-running candidates is to flood the mass media with ‘wasted vote’ arguments (including therein both the relevant evidence on candidate standings and the basic logic motivating a strategic vote).”
Riker (1982, p. 765): “So the answer to the question of failure is that third parties are rejected in the rational calculus of expected utility especially by leaders, though also in the calculus by many simple voters. Any adequate theory to subsume Duverger’s law must, I believe, begin there, which is a task for scholars in the next decade.”
And Duverger (1964, p. 205) himself: “the two-party system favors the adoption of the simple-majority single-ballot form…”