Legitimacy

Legitimacy is the measure of how much voters accept something, usually an election outcome, based on several perceived factors.

There is not always agreement over what gives legitimacy to an election winner, but it is agreed that generating legitimacy is very important to prevent voters who "lost" from opposing the democratic process. Generally speaking, the more popular the winner, the more legitimate. In addition, the greater the voter turnout, the more likely the outcome will be seen as democratic.

Arguments
Cardinal method advocates often argue that the utilitarian winner is most legitimate, because they best satisfy the electorate and may tend to leave less voters unhappy with the outcome.

Advocates of IRV and Condorcet often contend that legitimacy is offered by looking at the strategic resistance of a voting method i.e. how many voters could have gotten a better outcome for themselves by voting differently. They tend to further contend that majority rule offers more legitimacy, in part for strategy resistance, but also because it is seen as giving more power to voters.