The "Majority criterion" and Range Voting

If a majority of voters have candidate X as their common favorite, that does not force X to win the election. For example,

This illustrates the failure of the "majority criterion" by range voting. However, in such a situation we would argue that it is good that Y won and it is good that range voting found a way to evade the "tyranny of the majority." Indeed this is an advantage of range voting that all other common voting method proposals cannot match.

A good example of why intensity-blind "majority rule" is not always the best thing, is Lomax's "pizza example":

A group of people, let's say there are three of them to make it very simple, want to buy a pizza and split it. The pizza parlor, amazingly enough, will only allow them to choose one kind of pizza. Two of the three prefer pepperoni, but the third is a Jew who cannot eat pepperoni, but, we'll say, would have no problem with cheese or any vegetarian pizza. Now, if, for some reason, the two pepperoni fans must have their pepperoni, they certainly can get it. They might have some problems, though. The Jew might balk at paying for it. Suppose that the pepperoni fans, though, can agree that mushroom would be just fine, almost as good as pepperoni. And that just happens to be the favorite of the Jew.
Please give a cogent argument why the first preference of the majority should win.

Fans of majoritarianism need not despair, however;

1. Range voting obeys a variant form of the majority criterion (which I happen to prefer to the usual form), namely:

   If a majority with a common favorite exist, they can force his election.

   Specifically, they can do so by voting 99 for the common favorite and 0 for every opponent. Then no matter how the other voters vote, that favorite will win the election. Any majority acting this way, though, had better be sure they are a majority. Otherwise, somebody else could be elected, and they by their action would then have voluntarily prevented themselves from having input into who that will be. To avoid that risk, they are motivated not to vote in that manner – which as far as we are concerned is a good thing, since it motivates voters to provide more, and more honest, information.
2. With strategic voters, range voting under reasonable assumptions actually yields the "Condorcet winner" whenever one exists, and indeed experimentally can yield it more often than "Condorcet methods"(!).

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