[EM] Condorcet methods and Hare versus Median Ratings methods like Majority Judgement and Bucklin

[Closed Limelike Curves]

>
> Finally, I'm not sure if Approval converges to anything useful in the
> presence of a sincere cycle. I would imagine that the strategic voters
> would chase each other through the cycle.

In real life, or in models? The answer to "what will approval actually do"
depends on which (if any) of those models is correct.

I'd conjecture every well-designed voting system converges, under plausible
models of strategic voting, to something that looks basically like a
maximal lottery. The perfect-group-strategy model predicts a maximal
lottery. I'm not sure what other models predict, but I'm guessing they'll
say approval (or score, or most Condorcet methods) will produce very
similar results.

But if nothing else, every strategic model of voters is clearly incomplete,
because some voters are honest. My main reason for supporting score is that
if we add in some honest voters, it can give us better results than
Condorcet.

round and round and round it goes. Where it stops, nobody knows!

Funnily enough, that's also how a maximal lottery behaves. ;) Choosing
candidates at random from a sincere cycle probably wouldn't be that bad a
system. (Hell, it's arguably better than breaking the ties
deterministically—less bias, so it'll tend to cancel out across election
cycles or within a legislature!)


> If I'm wrong, it would be interesting to take a leaf out of the
> revelation principle book and create a ranked method that does directly
> what Approval would do through strategy, and see what its
> characteristics are. E.g. is it monotone?
>
Unfortunately, maximal lotteries aren't monotone. :(

On the plus side, they somehow satisfy participation, which I count as a
miracle.

On Fri, Apr 12, 2024 at 3:59 PM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> On 2024-04-12 19:41, Closed Limelike Curves wrote:
> > This is probably true under much weaker conditions. It feels like every
> > good (FBC, monotone?) method converges to approval with strategic
> > voters. (And approval converges to Smith//Approval.)
>
> I seem to recall someone saying that MMPO is a method that passes FBC
> and monotonicity yet doesn't behave like Approval. (Then again, its
> Plurality criterion failure is really a bummer.)
>
> There might also be methods that converge directly to something that
> passes Smith without going through Approval first. It's difficult to say
> since so few methods' equilibria are known.
>
> Finally, I'm not sure if Approval converges to anything useful in the
> presence of a sincere cycle. I would imagine that the strategic voters
> would chase each other through the cycle.
>
> For Condorcet, everybody who prefers the Condorcet winner W to the
> current Approval winner A could (theoretically, given continuously
> updating polls) place their cutoff between W and A, which would then
> stabilize the result there. But if they do that when there's a cycle,
> they would just end up chasing each other through it.
>
> E.g. with
>
> 36: A>B>C
> 34: B>C>A
> 32: C>A>B
>
> then suppose we start with everybody approving the first two. Then the
> winner is B. So the A>B voters compensate:
>
> 36: A>|B>C
> 34: B>C>|A
> 32: C>A|>B
>
> Then the winner is A. So the C>A voters compensate:
>
> 36: A>|B>C
> 34: B>C>|A
> 32: C>|A>B
>
> Then the winner is C. So the B>C voters compensate:
>
> 36: A>B|>C
> 34: B>|C>A
> 32: C>|A>B
>
> round and round and round it goes. Where it stops, nobody knows!
>
> The actual outcome would be heavily influenced by polling access and
> timing. So it doesn't seem like the "induced" Smith//Approval method
> would mean much.
>
>
> If I'm wrong, it would be interesting to take a leaf out of the
> revelation principle book and create a ranked method that does directly
> what Approval would do through strategy, and see what its
> characteristics are. E.g. is it monotone?
>
> It's only fair, if the purpose of Approval is to enact a higher order
> distributed algorithm that uses the polls as state data, to analyze this
> algorithm, whatever it is. That's why I keep coming back to the "manual
> DSV" objection.
>
> -km
>
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