[EM] Copeland, Landau

[Kevin Venzke]

Hi Forest,

Le samedi 5 août 2023 à 20:32:28 UTC−5, Forest Simmons <forest.simmons21 at gmail.com> a écrit :
> Kevin,
> 
> Copeland is the simplest monotone Landau method.
> 
> Do we have a clone free version of Copeland that is for sure monotone?

This I don't know, but such a simple method as Copeland satisfying Landau is quite
interesting, and I suppose we have to somehow proceed from Copeland in searching for
additional methods.

> Here's another one that (unlike Copeland) is definitely clone free as well as monotonic
> (if my proof holds warer):
> 
> Initialize a candidate variable X as the highest approval candidate. Then while X is
> covered, update X to be the most approved candidate that covers the recent value of X that
> we are updating.

In a UD context relying on implicit approval, this doesn't work wrt monotonicity, because
a raised winner can obtain approval at the expense of another candidate.

For example say A is the approval winner and B covers A and wins. Then some ballots are
changed from ...A>B to ...B>A (these are the bottom of the ranking) so that A is losing
approval to B, and now some C is the approval winner, and B does not cover C.

> If I am not mistaken Agenda Based Chain Climbing is monotonic in the sense that if the winner
> moves "up" the agenda without disturbing the relative agenda order of the other candidates ...
> then the winner will still win.
> 
> If the agenda is based on approval scores, it seems to me that this requirement should be met.
> 
> Am I wrong?

With implicit approval I guess the issue appears.

Kevin
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