[EM] von Neumann-Morgenstern utility criterion

[Kristofer Munsterhjelm]

Here's a possible interesting criterion for rated methods:

Suppose the ratings are on a continuum (discrete versions automatically
fail). Then the winner should not change if any voter's rating vector is
subjected to some arbitrary nonnegative affine scaling, as long as the
resulting values do not go outside the scale.

The idea is that lottery utilities (which I understand are called von
Neumann-Morgenstern utilities) are only defined up to two constants per
voter, which we may call constants of incommensurability or affine
scaling constants. And if the method is serious about being utilitarian,
it shouldn't make any assumptions about what these scaling constants are.

Obviously, ranked methods pass this criterion since affine scalings are
monotone. But some rated methods might also do so. Range clearly doesn't.

I would suspect that methods that pass this criterion will fail IIA. But
in a sense, that's more honest than technically passing IIA but still
having the election outcome depend on losers (like Range does when the
voters do the normalization themselves).

-km