I suspect that SODA would be Condorcet compliant (over ballots) if the first player was, not the DSC winner, but the DAC winner (re-ordering between each delegated assignment).
I'll see if I can work up a proof on this. JQ 2011/7/30 <[email protected]> > One of the features of SODA is a step where the candidates decide what > their approval cutoffs will be.on > behalf of themselves and the voters for whom they are acting as proxies. > One of the many novel features > is that instead of making these decisions simultaneously, the candidates > make them sequentially with > full knowledge of the decisions of the candidates preceding them in the > sequence. > > I wonder if anybody has ever tried a DSV (designated strategy voting) > method based on these ideas. > > Here's one way it could go: > > Voters submit range ballots. > > Factions are amalgamated via weighted averages, so that each candidate ends > up with one faction that > counts according to its total weight. For large electorates, these faction > scores will almost surely yield > complete rankings of the candidates. > > From this point on, only these rankings will be used. The ratings were > only needed for the purpose of > amalgamating the factions. If we had started with rankings, we could have > converted them to ratings via > the method of my recent post under the subject "Borda Done Right." In > either case, once we have the > rankings from the amalgamated factions we proceed as follows: > > Based on these rankings the DSC (descending solid coalitions) winner D is > found. The D faction ranking > determines the sequential order of play. When it is candidate X's turn in > the order of play, X's approval > cutoff decision is made automatically as follows: > > For each of the possible cutoffs, the winner is determined recursively (by > running through the rest of the > DSV tentatively). The cutoff that yields the best (i.e. highest ranked) > candidate according to X's faction's > ranking, is the cutoff that is applied to X's faction. > > After all of the cutoffs have been applied, the approval winner (based on > those cutoffs) is elected. > > It would be too good to be true if this method turned out to be monotone. > For that to be true moving up > one position in the sequence of play could not hurt the winner. Although I > think that this is probably > usually true, I don't think that it is always true. Anybody know any > different? > ---- > Election-Methods mailing list - see http://electorama.com/em for list info >
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