[EM] von Neumann-Morgenstern utility criterion

[Forest Simmons]

El sáb., 29 de ene. de 2022 2:54 p. m., Kristofer Munsterhjelm <
km_elmet at t-online.de> escribió:

> 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.
>

I think invariance under affine transformation is too strong a condition.
Invariance under scaling by a positive constant should be enough.

Also, as in symmetrical MJ there should be an understood zero, a transition
between goods and bads.

However, negative ratings may not work in a political context.


> 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
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