[EM] Maximal lotteries (was :Re: The critical importance of Precinct Summability.)

[Closed Limelike Curves]

I think votingtheory.org has saved all the conversations from that forum:
https://votingtheory.org/archive/posts?where=%7B%22topic_id%22%3A566%7D

On Sun, Aug 11, 2024 at 8:22 AM Kristofer Munsterhjelm <
km-elmet at munsterhjelm.no> wrote:

> On 2024-08-08 17:53, Closed Limelike Curves wrote:
> > I suspect the uncovered set might be slightly better because it's a
> > close approximation of the bipartisan set that isn't too hard to
> > explain. Maximal lotteries also have some very nice strategy-resistance
> > properties.
>
> You've referred to the maximal lottery and strategic voting before. I'd
> like to know in more detail what you're referring to by your statements.
>
> In the Monroe post, you said:
>
> > If group strategy was a reasonable model of voters, it wouldn't
> > matter which electoral system we picked, because the outcome would
> > always be maximal lottery.
> What do you mean? Do you mean that:
>
> - Every (non-strategyproof) method has a unique Nash equilibrium per
> election under group strategy, whose expected outcome is that election's
> maximal lottery,
>
> - Every method has the maximal lottery as one of its Nash equilibria,
>
> - The relation between group strategy and the maximal lottery only holds
> for some methods, and these methods have the ML as their unique Nash
> equilibrium,
>
> - As above, but "as one of its Nash equilibria".
>
> or something else entirely?
>
> > On this topic and the lack of focus on proportional representation
> > mentioned elsewhere, I think it would be super useful to have some kind
> > of strongly-summable PR algorithm. ElectoWiki claims Ebert's method is
> > summable
> > <
> https://electowiki.org/wiki/Summability_criterion#Multi-winner_generalizations_and_results>,
> but the link is broken and Ebert has some big issues (e.g. negative
> response and Pareto inefficiency).
>
> I tried to look at the forum through IA and I couldn't find any mention
> of strong summability; it must have been in a later post on that thread,
> which IA hasn't archived. So at best that needs a {{cn}}.
>
> To my knowledge, whether Droop proportionality is compatible with strong
> summability is still open. I have a very broad idea of how one might
> resolve summability questions like this, but I would need some
> mathematical primitives that I'm not sure how to construct.
>
> -km
>
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