Majority winner criterion

The Condorcet criterion gives a stronger and more intuitive notion of majoritarianism (and as such is sometimes referred to as majority rule).

A Condorcet winner C only has to defeat every other candidate "one-on-one"—in other words, when comparing C to any specific alternative.

In systems with absolute rating categories such as score and highest median methods, it is not clear how the majority criterion should be defined.

There are three notable definitions of for a candidate A: The first criterion is not satisfied by any common cardinal voting method.

Thus in cardinal voting systems a sufficiently-motivated minority can sometimes outweigh the voices of a majority, if they would be strongly harmed by a policy or candidate.

Instant-runoff voting satisfies majority--if a candidate is rated first by 50% of the electorate, they will win in the first round.

If "A is preferred" means that the voter gives a better grade to A than to every other candidate, majority judgment can fail catastrophically.