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

[Kristofer Munsterhjelm]

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