[EM] Copeland, Landau

[Forest Simmons]

Kevin is absolutely right ... all the more reason to heed Toby Pereira's
advice of using high definition ratings or else rankings with approval
cutoffs for Condorcet methods.

If you have a monotone one at a time elimination method, you can make it
Landau efficient by "covering takedown:"

Every time you eliminate a candidate take down with it every candidate that
is covers.

Although this disturbs the one-by-one property, the transitivity of
covering ensures that the order of take down of those candidates covered by
X does not matter: if X covers Y so Y is eliminated with X, and Y covers Z,
so Z is eliminated with Y, then Z is also covered by X, so Z is already
taken down by X without waiting for Y to be eliminated.

On Sun, Aug 6, 2023, 2:38 PM Kevin Venzke <stepjak at yahoo.fr> wrote:

> 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
> votingmethods.net
>
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