[EM] Situations where IIA failure may be natural

[Forest Simmons]

This line of thought reminds me of the kind of ballot used in Jobst's
MaxParC:

Next to each candidate's name you specify the total approval that candidate
would have to have from the other voters before you would get on board.

Why should other vogers' support affect your support?

That's also implicit in the Nash Lottery where the candidate probabilites
are adjusted to maximize the product of the (score) ballot expectations.

It turns out that this maximization rule requires that (1) each voter's
total contribution to the lottery probability be 1/n, where n is the number
of voters, and (2l that contribution be allocated to the respective
candidates' winning probabilities in joint proportion to the ballot ratings
and the (equilibrium) probabilities of the respective candidates.

Nash's "efficient" allocation of resources general rule requires the
allocations to be proportional to the respective (expected) payoff shares
... which is why we named this election method the "Nash Lottery".

Roughly speaking, the more popular something is, the more of your capital
(eg your vote) you should devote to it ... according to Nash's general rule
of efficient allocation.

This rule is different from, but related to, the rational strategy of
maximizing the likelihood of your vote being pivotal.

MaxParC's allocation is closer to optimal rational strategy than is Nash's
allocation. I can elaborate on this comment if there is serious interest.

fws





On Fri, Aug 25, 2023, 5:20 AM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> IIA failure is generally considered to be a bad thing. But perhaps
> sometimes "all things equal" is not so!
>
> Consider the restaurant joke: Sidney is offered a choice of apple pie
> and blueberry, and says "I'll have apple". Then the waitress says "Oh,
> we also have cherry". "Well, in that case, I'll take blueberry". This
> seems completely unreasonable.
>
> But here's a variant. Suppose I'm a fan of desserts that are difficult
> to make, like (just picking something here) baked Alaska and meringue
> pie. But I know that they're easy to get wrong and so I'll settle with
> apple pie as a good dessert that's easy to make.
>
> I'm visiting a restaurant with generally good reviews and I ask what
> desserts they have. They say "there's meringue pie and apple pie". I'm
> not willing to risk, despite their good reviews, that they can pull off
> the meringue properly, so I say "okay, I'll have apple pie". Then the
> waiter says "Oh, hang on, we also have baked Alaska".
>
> Now I may reason: given the good reviews, and that they have multiple
> difficult desserts, more people may have tried the difficult ones; so if
> they weren't any good, it wouldn't have been reviewed so well. So I say
> "well, in that case, I'll take the meringue".
>
> In a political context, the closest thing would be something like: I've
> moved to a new town, and there are local elections with some left and
> right parties. The parties' candidates seem sensible at first glance,
> but they could just be tailoring their message to the audience. Now if
> I'm a left-wing voter (say), and there are multiple left-wing parties,
> this may indicate that there's a demand for left-of-center policies, and
> thus that the left-wing candidates are more likely to mean what they're
> saying, thus making it less risky to support one of them.
>
> It's kind of tenuous, but still I thought it's an interesting example :-)
>
> If it's at least somewhat realistic, it could bring more subtle dynamics
> into elections, no matter whether they pass IIA or not. For instance, if
> voters are likely to consider a particular political position more
> sincere if there are multiple parties based on it, then that's an
> obvious (theoretical) clone failure. On the other hand, maybe not so
> much: the inference works precisely because it's hard to set up proxy
> parties that seem legitimate. If that becomes easy, then there's little
> value in the observation, and the voters would stop judging the number
> of parties as an indication of the strength of the position.
>
> -km
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
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