[EM] "non-cyclic" pairwise loss?

Kevin Venzke stepjak at yahoo.fr
Mon Apr 13 15:56:05 PDT 2015

```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 at adam.com.au>
À : "election-methods at lists.electorama.com" <election-methods at 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

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