In single elections? In single elections, with more than 2 alternatives, a rational player tríes to infere the two outcomes with higher number of votes, and vote for the one she prefers. This leads to inevitable preference falsification (you probably prefer a different outcome from those two, but spending votes on it is “wasting” them).
With múltiple elections, it can be different, as the literature reviewed above shows.
“The typical framework for the analysis of multiperiod voting is the “independent identically distributed””
In the i.i.d framework, what happens in a period stays in that period. That is, you vote, the outcome happens, it influences your utility in the period, but the possible outcomes in (t+1) does not depend in the outcomes in the period t. Another way to say this, is that the only “memory variable” in any period is the votes endowment at the end of period. With “path dependence” (beyond vote endowments), dynamic voting theory is too dynamic...
Arrow is too complex to be discussed here, while the short explanation here (you cannot turn N ordinal preferences into a “social ordinal preference” for a group) is in my view captures the most important meassage. Any general mechanism to turn a group of ordinal preferences into a social preference is susceptible of creating paradoxical results. On the other hand, Dhillon & Mertens Relative Utilitarianism shows this is not the case for turning individual cardinal preferences into social ones[at least for a finite number of possible outcomes]. It is a little bit puzzling that this is not the standard intepretation, and that is why I wrote this.
Thank you for your interest!