Editing Two-round system (section)

==Compliance with voting method criteria==
{{More sources|section|date=July 2024}}

Most of the mathematical criteria by which voting methods are compared were formulated for voters with ordinal preferences. Some methods, like [[approval voting]], request information than cannot be unambiguously inferred from a single set of ordinal preferences. The two-round system is such a method, because the voters are not forced to vote according to a single ordinal preference in both rounds.

If the voters determine their preferences before the election and always vote directly consistent to them, they will emulate the [[contingent vote]] and get the same results as if they were to use that method. Therefore, in that model of voting behavior, the two-round system passes all criteria that the contingent vote passes, and fails all criteria the contingent vote fails.

Since the voters in the two-round system do not have to choose their second round votes while voting in the first round, they are able to adjust their votes as players in a [[Game theory|game]]. More complex models consider voter behavior when the voters reach a game-theoretical equilibrium from which they have no incentive, as defined by their internal preferences, to further change their behavior. However, because these equilibria are complex, only partial results are known. With respect to the voters' internal preferences, the two-round system passes the majority criterion in this model, as a majority can always coordinate to elect their preferred candidate. Also, in the case of three candidates or less and a robust political equilibrium,<ref>{{Cite web |last=Messner |display-authors=etal |date=2002-11-01 |title=Robust Political Equilibria under Plurality and Runoff Rule |url=http://politics.as.nyu.edu/docs/IO/4753/polborn.pdf |access-date=2011-06-04 |archive-url=https://web.archive.org/web/20100612051725/http://politics.as.nyu.edu/docs/IO/4753/polborn.pdf |archive-date=2010-06-12 |url-status=dead }}</ref> the two-round system will pick the Condorcet winner whenever there is one, which is not the case in the contingent vote model.

The equilibrium mentioned above is a perfect-information equilibrium and so only strictly holds in idealized conditions where every voter knows every other voter's preference. Thus it provides an upper bound on what can be achieved with rational (self-interested) coordination or knowledge of others' preferences. Since the voters almost surely will not have perfect information, it may not apply to real elections. In that matter, it is similar to the [[perfect competition]] model sometimes used in economics. To the extent that real elections approach this upper bound, large elections would do so less so than small ones, because it is less likely that a large electorate has information about all the other voters than that a small electorate has.