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

[Michael Ossipoff]

On Fri, Apr 12, 2024 at 20:27 Closed Limelike Curves <
closed.limelike.curves at gmail.com> wrote:

Finally, I'm not sure if Approval converges to anything useful in the
>> presence of a sincere cycle.
>
>
Just the  candidate or alternative liked by the most people.


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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