Dear Chris! You wrote:
> I like this table. Thanks. > Doesn't AM look like the most "natural" and "balanced"? Yes, but that's only an aesthetical judgement... > I was wondering if it is possible in AM for a > candidate who is both the sincere CW and sincere AW to > successfully Buried, and I've come up with an example > that shows that unfortunately it is, but AWP and DMC > likewise fail in the same example. But not DFC (Democratic Fair Choice aka Random Ballot from Forest's P), as I will show below! > Sincere preferences: > 48: A>B>>C > 01: A>>C>B > 03: B>>A>C > 48: C>>B>A > B is the CW and AW. Also DFC elects B here. > Then 45 of the 48 A>B voters Bury B "strongly", i.e. > with both rankings and approval, while the other 3 of > the 48 only Bury with their rankings (not approving > C). [...] > All three methods elect the Burier's candidate, A. But DFC elects A only with 52% probability, and C with 48% probability. This means the Buriers would get their least prefered candidate with a large probability, which should deter them from strategizing. > When there are three candidates in the top cycle, AM > has the property that the candidate with the lowest > voted approval score can't win. But that's also true for DMC and DFC since that candidate is always strongly defeated. > Jobst wrote: > "Here you state the obvious problem when looking at > both approval and defeat information. Forest's > ingenious argument was that we should at least not > elect a candidate where both kinds of information > agree that the candidate is defeated, leaving us with > his set P of candidates which are not strongly > defeated. > > But when we take both kinds of information serious, it > does not seem appropriate to me to always elect a > candidate from the two extremes of P like Approval and > DMC do. Still, DMC has the obvious advantage of > extreme simplicity. > > I would find it much more natural if the winner was > somewhere in the "middle" of P!" > > Doesn't Approval Margins fill the bill? Welcome to > the AM fan club! I don't know... Which cycle resolution technique does AM use? The claim that the winner belongs to P seems to hold at least when you use an immune cycle resolution technique like that of Beatpath, RP, or River... Yours, Jobst ---- Election-methods mailing list - see http://electorama.com/em for list info