The Electowiki page on Heitzig's River method includes: > River can be interpreted as a Minmax > <http://wiki.electorama.com/wiki/Minmax> method, Minmax(non-cyclic > pairwise loss) or MMNCPL. It is similar to Minmax(winning votes) > except that River elects the candidate whose greatest /non-cyclic/ > pairwise loss to another candidate is least. As in Ranked Pairs > <http://wiki.electorama.com/wiki/Ranked_Pairs>, the greatest pairwise > loss (GPL) of each candidate is considered in order from largest > (among all candidates) to smallest and locked. If a candidate's GPL is > cyclic, it is discarded, and the next-greatest pairwise loss of that > candidate is added to the list. When the non-cyclic greatest pairwise > losses of (N-1) candidates have been locked, the remaining candidate > is the winner. http://wiki.electorama.com/wiki/River What is the clear and simple definition of a "cyclic" pairwise loss? If all the candidates are in the Smith set, aren't *all* the pairwise losses (at least in some sense) "cyclic"? Chris Benham

Hi Chris, "Non-cyclic pairwise loss" just means a loss that wouldn't create a cycle of locked wins (at the time in the process that you consider the loss). RP has this concept just like River does. What makes River seem similar to a Minmax method is that only one loss (the strongest non-cyclic one) will get counted for any particular candidate. Once you lock a win against somebody, you won't lock any more against them. I can't say I had thought of it that way before, though. Kevin De : C.Benham <cbenham@adam.com.au> À : "election-methods@lists.electorama.com" <election-methods@lists.electorama.com> Envoyé le : Lundi 13 avril 2015 13h10 Objet : "non-cyclic" pairwise loss? The Electowiki  page on Heitzig's  River method includes: River can be interpreted as a Minmax method, Minmax(non-cyclic pairwise loss) or MMNCPL. It is similar to Minmax(winning votes) except that River elects the candidate whose greatest non-cyclic pairwise loss to another candidate is least. As in Ranked Pairs, the greatest pairwise loss (GPL) of each candidate is considered in order from largest (among all candidates) to smallest and locked. If a candidate's GPL is cyclic, it is discarded, and the next-greatest pairwise loss of that candidate is added to the list. When the non-cyclic greatest pairwise losses of (N-1) candidates have been locked, the remaining candidate is the winner. http://wiki.electorama.com/wiki/River What is the clear and simple definition of a  "cyclic" pairwise loss?   If all the candidates are in the Smith set, aren't  *all* the pairwise losses (at least in some sense)  "cyclic"? Chris Benham

On 4/13/15 6:56 PM, Kevin Venzke wrote: > > "Non-cyclic pairwise loss" just means a loss that wouldn't create a > cycle of locked wins (at the time in the process that you consider the > loss). RP has this concept just like River does. What makes River seem > similar to a Minmax method is that only one loss (the strongest > non-cyclic one) will get counted for any particular candidate. Once > you lock a win against somebody, you won't lock any more against them. > quick question: if A beats B and A beats C and both B and C beat D, does River open that loop? it ain't a cycle. A has two beat-paths against D. does River prevent one of them? just trying to grok the basic. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."

Hi Robert, Yes. Only one of B>D or C>D (you don't mention whether perhaps A>D is also the case) can be locked against D. If B>D is stronger than C>D, then when we encounter C>D, we'll throw it out, even if it wouldn't cause a cycle. (D has already lost the election.) Kevin De : robert bristow-johnson <rbj@audioimagination.com> À : election-methods@lists.electorama.com Envoyé le : Lundi 13 avril 2015 18h49 Objet : Re: [EM] "non-cyclic" pairwise loss? On 4/13/15 6:56 PM, Kevin Venzke wrote: > > "Non-cyclic pairwise loss" just means a loss that wouldn't create a > cycle of locked wins (at the time in the process that you consider the > loss). RP has this concept just like River does. What makes River seem > similar to a Minmax method is that only one loss (the strongest > non-cyclic one) will get counted for any particular candidate. Once > you lock a win against somebody, you won't lock any more against them. > quick question: if A beats B and A beats C and both B and C beat D, does River open that loop?  it ain't a cycle.  A has two beat-paths against D.  does River prevent one of them? just trying to grok the basic. -- r b-j                  rbj@audioimagination.com "Imagination is more important than knowledge." ---- Election-Methods mailing list - see http://electorama.com/em for list info