[EM] Fwd: agenda landau winner

[Susan Simmons]

Kristofer,

Your comment below* has inspired an improved version of Agenda Based Landau:

Elect the most promising uncovered agenda item that covers each more promising item.

Proof of monotonicity coming in next message....

Sent from my MetroPCS 4G LTE Android Device

-------- Mensaje original --------
De: Kristofer Munsterhjelm <km_elmet at t-online.de>
Fecha: 28/7/21 1:13 p. m. (GMT-08:00)
A: Susan Simmons <suzerainsimmons at outlook.com>, election-methods at lists.electorama.com
Asunto: Re: [EM] Fwd: agenda landau winner

On 28.07.2021 21:28, Susan Simmons wrote:
>
> We work from an agenda of alternatives listed in order of “promise.” The
> agenda is “monotone” if increasing ballot support for an alternative
> moves it towards the promising end of the agenda without altering the
> relative order of the other candidates in the list.

Of note here is that this monotone agenda criterion (strong mono-raise?)
is much stronger than ordinary mono-raise. For instance, Plurality fails
it but passes ordinary mono-raise.

Also: I don't think the relation above is iff; there are looser criteria
that, if met, guarantee monotonicity of the agenda method. For instance,
if the winner W is raised, then the property only has to hold for
candidates ranked below the winner on the agenda, because (by assumption
that W was the original winner),
* W covers everybody ranked higher.

When the agenda method is Smith rather than Landau, I think an even
looser criterion can be phrased in the term of beatpaths, or in that
raising A should not swap the position of any pair of candidates B and C
ranked below A where B beats A pairwise and C is beaten pairwise by A.

These looser criteria are much harder to reason about, though.

And finding a burial immune strong mono-raise compliant method would be
very nice :-)

-km
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