Structural effects are, indeed, super important. Deciding what the options are (or even just what order the options are presented in: imagine United States elections, but with the general election held first (voting only for party) and then the party with the most votes picks the officeholder afterwards—you get a very different set of incentives).
Also, knowing how others are going to vote: as detailed elsewhere, if there are two close options, the exact mechanics of the election and the knowledge available to strategic voters can allow either (or neither) of them to win, even with the same set of preferences in the population.
Structural effects are, indeed, super important. Deciding what the options are (or even just what order the options are presented in: imagine United States elections, but with the general election held first (voting only for party) and then the party with the most votes picks the officeholder afterwards—you get a very different set of incentives).
Also, knowing how others are going to vote: as detailed elsewhere, if there are two close options, the exact mechanics of the election and the knowledge available to strategic voters can allow either (or neither) of them to win, even with the same set of preferences in the population.