Kevin, Interesting. What (if any) harm would be done by applying this to the three candidates remaining after the rest have been IRV-style eliminated?
Is there any actual criterion that this method meets but IRV doesn't? Chris Benham Kevin Venzke wrote: >Hi, > >Here's an attempt at a method that behaves well in the three-candidate >scenario with preferences based on distance on a one-dimensional spectrum. >I would call it "strongest pair with single transfer" or "SPST". It >satisfies LNHarm and Plurality, and doesn't suffer from the worst kind >of burial incentive. It also satisfies Clone-Loser I believe, though not >monotonicity. > >My idea was to come up with a method that, in the three-candidate case >with distance-based preferences on a one-dimensional spectrum, could >elect the inner candidate in the absence of a majority favorite. I also >wanted to avoid truncation strategy (Approval, Condorcet), gross Plurality >failures (as under MMPO), and the sort of burial strategy where you give >a lower preference to a candidate whose supporters are not ranking your >candidate. > >Definition: >1. The voter may vote for one first preference and one second preference. >2. The "strength" of a candidate, or pair of candidates, is defined as >the number of voters giving such candidates the top position(s) on >their ballots in some order. (This is as under DSC.) >3. A pair of candidates has no strength, if it includes any candidate >who is not among the top three on first preferences. (I don't like this >rule, but it's needed for LNHarm.) >4. If the strongest candidate is in the strongest pair, or stronger than >the strongest pair, then this candidate wins. >5. Eliminate the strongest candidate. The second preferences of his >supporters may be transferred to the individual candidate strengths of >the two members of the strongest pair of candidates. >6. Now, the strongest candidate in the strongest pair is elected. > >examples: >40 A>B >25 B>C >35 C>B > >Strongest pair is BC; strongest candidate is A. BC is stronger than A, >so A is eliminated and 40 preferences are transferred to B's strength. >B wins. > >35 A>B >25 B>C >40 C>B > >Here BC is again the strongest pair, but C is the strongest candidate and >wins immediately unfortunately. > >This method is a lot like DSC, but never requires more than N^2 numbers >to be counted, whereas DSC requires 2^N if you keep track of every set. >The elimination doesn't create IRV's counting issues, since with only >two preferences taken we can just count them all. > >The burial strategy works like this: Say it's A, B, and C, with B as the >middle candidate. A is expected to be the strongest candidate. Then >voters with the preference order B>A have incentive to instead vote >B>C. This is because if BC is the strongest pair, A will be eliminated >and hopefully transfer preferences to B. But if AB is the strongest >pair, A wins outright. As a result of this strategy, it is possible that >(despite the LNHarm guarantee) A voters would decline to give a second >preference to B, so that B>A voters can't count on the A voters to >give a second preference to B. > >It is only possible to eliminate the first preference winner, due to >LNHarm. It's only safe to eliminate a candidate who was going to win. >Otherwise it could happen that voters have incentive to weaken a pair >involving their favorite candidate, in order to prevent an elimination >that causes the favorite candidate to lose to the second preference. > >Limiting pairs to the top three FPP candidates is necessary for LNHarm >when there are more than three candidates. Otherwise it could happen, >say, that BC is stronger than BD is stronger than A, A is eliminated, >and then C wins. Whereas if BC were weakened and BD were strongest, A's >elimination might result in B winning. > >Monotonicity can be failed when the winner is not the FPP winner, he >gets more preferences, changing which pair is strongest, and causing >the other candidate in the pair to win. > >I ran some simulations to try to measure this method against others. When >the only ballot types are A>B, B>A, B>C, and C>B, this method is identical >to DSC. When all 9 ballot types are allowed, this method seems to be >strictly more Condorcet-efficient than DSC, although not by much. > >I found that IRV is more Condorcet-efficient than either, except in >the scenario where only the four ballot types are permitted, and the >proportions of the B>A and B>C ballots are divided by 5. There IRV is >worse because it wants to eliminate B. > >(With the four ballot types, IRV can elect B as long as B doesn't have >the fewest first preferences. That particular scenario is important to >me, though. DSC can elect B unless, say, the A>B faction outnumbers the >B>A B>C factions, and also the B>C C>B factions.) > >That's it for now. > >Kevin Venzke > > > > > > >___________________________________________________________________________ >Découvrez une nouvelle façon d'obtenir des réponses à toutes vos questions ! >Profitez des connaissances, des opinions et des expériences des internautes >sur Yahoo! Questions/Réponses >http://fr.answers.yahoo.com >---- >election-methods mailing list - see http://electorama.com/em for list info > > > > ---- election-methods mailing list - see http://electorama.com/em for list info