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@t-online.de> Fecha: 28/7/21 1:13 p. m. (GMT-08:00) A: Susan Simmons <suzerainsimmons@outlook.com>, election-methods@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