Re: [EM] Question about Schulze beatpath method
Hallo, I rewrote section 5 (Tie-Breaking) of my paper, so that it is now more in accordance with the other parts of my paper: http://m-schulze.webhop.net/schulze1.pdf Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Question about Schulze beatpath method
Hallo, in example 3 of my paper, the weakest link of the strongest path from candidate A to candidate C is the same link as the weakest link in the strongest path from candidate C to candidate A: http://m-schulze.webhop.net/schulze1.pdf Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Question about Schulze beatpath method
On 2/20/12 1:15 PM, Markus Schulze wrote: Hallo, in example 3 of my paper, the weakest link of the strongest path from candidate A to candidate C is the same link as the weakest link in the strongest path from candidate C to candidate A: http://m-schulze.webhop.net/schulze1.pdf the thing that had been confusing me (until Kevin replied) is that the *direction* through that link is the same whether your defeat path is from A to C or the reverse. that seems sorta counter-intuitive. -- r b-j r...@audioimagination.com Imagination is more important than knowledge. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Question about Schulze beatpath method
On 2/17/12 1:27 PM, Markus Schulze wrote: it can happen that the weakest link in the strongest path from candidate A to candidate B and the weakest link in the strongest path from candidate B to candidate A is the same link, say CD. how can that be? since a path is a *defeat* path. you only traverse a beatpath from a candidate who beats the next candidate in the path. is it that candidates C and D are exactly tied? other than that, i cannot understand how the weakest link from A to B can be the same as *any* link from B to A. -- r b-j r...@audioimagination.com Imagination is more important than knowledge. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Question about Schulze beatpath method
Hi Robert, Suppose there are four candidates ABCD. B beats A with strength of 10. C beats D with strength of 20. With strength of 30, A beats C, B beats C, D beats A, and D beats B. Then every candidate has a path to every other candidate, and the best path from A to B or from B to A involves traversing the CD win (which is the weakest link in those paths). Kevin De : robert bristow-johnson r...@audioimagination.com À : election-methods@lists.electorama.com Envoyé le : Vendredi 17 février 2012 12h56 Objet : Re: [EM] Question about Schulze beatpath method On 2/17/12 1:27 PM, Markus Schulze wrote: it can happen that the weakest link in the strongest path from candidate A to candidate B and the weakest link in the strongest path from candidate B to candidate A is the same link, say CD. how can that be? since a path is a *defeat* path. you only traverse a beatpath from a candidate who beats the next candidate in the path. is it that candidates C and D are exactly tied? other than that, i cannot understand how the weakest link from A to B can be the same as *any* link from B to A. -- r b-j r...@audioimagination.com Imagination is more important than knowledge. Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Question about Schulze beatpath method
If one removed all pairwise defeats that contradict the Schulze beathpath order and then constructed a new beatpath order from the reduced set of defeats, would the new beatpath order always be consistent with (although not necessarily the same as) the previous beatpath order? Could this method, repeatedly applied, be used to construct a monotonic and clone proof strict linear ordering if the original beatpath order produced a partial linear ordering? Example: If the defeat order is AB, AC BD, CD DA BC ED AE BE CE The beatpath ordering is: EA(B,C)D. This is a partial order since the order of B and C is not completely specified by beatpath. Removing all defeats that are not consistent with the partial beatpath order produces: AB, AC BD, CD BC ED The beatpath order derived from these defeats is: ((ABC),E)D The two partial orderings EA(B,C)D and ((ABC),E)D are consistent and together produce the linear ordering EABCD. Election-Methods mailing list - see http://electorama.com/em for list info
