Elect the candidate not beaten among all the strongest defeats that don’t contradict (form any cycles with) eachother. ————- In my recent Approval-post, I forgot to mention (but have mentioned elsewhere) that Approval’s Myerson-Weber equilibrium is at the voter-median. i.e. Approval homes-in on where the CW is. (A Myerson-Weber equilibrium is an outcome consistent with, confirming, the voters’ beliefs that led to that outcome.)

It seems to me that Meyerson & Weber said that Vote-For-1 Plurality can elect any two candidates forever at Myerson-Weber equilibrium. (Meyerson & Weber called their equilibrium “Voting-Equilibrium”. I think their paper was called “A Voting Equlibrium”. It was probably in Econometria.) On Thu, May 16, 2024 at 18:25 Michael Ossipoff <email9648742@gmail.com> wrote: > > Elect the candidate not beaten among all the strongest defeats that don’t > contradict (form any cycles with) eachother. > ————- > In my recent Approval-post, I forgot to mention (but have mentioned > elsewhere) that Approval’s Myerson-Weber equilibrium is at the voter-median. > > i.e. Approval homes-in on where the CW is. > > (A Myerson-Weber equilibrium is an outcome consistent with, confirming, > the voters’ beliefs that led to that outcome.) >

Mike, > Elect the candidate not beaten among all the strongest defeats that > don’t contradict (form any cycles with) each other. That definition is "brief" but isn't complete, i.e. it doesn't give enough information to know how to operate the method because it doesn't explain what "strongest" means (or exactly how we measure "strength"). As you know, more than one way has been suggested/advocated.   You like "Winning Votes"  (that used to be called on EM "Votes Against").  There used to be some people here who advocated for Margins. I like Approval Margins (explicit) which gives similar results to the Margins Sorted Approval method I now support.  And others are possible. Chris B. On 17/05/2024 10:55 am, Michael Ossipoff wrote: > > Elect the candidate not beaten among all the strongest defeats that > don’t contradict (form any cycles with) eachother. > ————- > In my recent Approval-post, I forgot to mention (but have mentioned > elsewhere) that Approval’s Myerson-Weber equilibrium is at the > voter-median. > > i.e. Approval homes-in on where the CW is. > > (A Myerson-Weber equilibrium is an outcome consistent with, > confirming, the voters’ beliefs that led to that outcome.) > > ---- > Election-Methods mailing list - see https://electorama.com/em for list info

Absolutely right !! As I said before, RP needs the same preliminary pairwise-count & defeat-strength definitions as the other entirely-pairwise-count Condorcet methods. I was just stating the specifically RP definition. On Sun, May 26, 2024 at 13:47 Chris Benham <cbenhamau@yahoo.com.au> wrote: > Mike, > > > Elect the candidate not beaten among all the strongest defeats that > > don’t contradict (form any cycles with) each other. > > That definition is "brief" but isn't complete, i.e. it doesn't give > enough information to know how to operate the method because it doesn't > explain what "strongest" means (or exactly how we measure "strength"). > > As you know, more than one way has been suggested/advocated. You like > "Winning Votes" (that used to be called on EM "Votes Against"). There > used to be some people here who advocated for Margins. > > I like Approval Margins (explicit) which gives similar results to the > Margins Sorted Approval method I now support. And others are possible. > > Chris B. > > On 17/05/2024 10:55 am, Michael Ossipoff wrote: > > > > Elect the candidate not beaten among all the strongest defeats that > > don’t contradict (form any cycles with) eachother. > > ————- > > In my recent Approval-post, I forgot to mention (but have mentioned > > elsewhere) that Approval’s Myerson-Weber equilibrium is at the > > voter-median. > > > > i.e. Approval homes-in on where the CW is. > > > > (A Myerson-Weber equilibrium is an outcome consistent with, > > confirming, the voters’ beliefs that led to that outcome.) > > > > ---- > > Election-Methods mailing list - see https://electorama.com/em for list > info >