On Thu, 4 Sep 2003, [iso-8859-1] Kevin Venzke wrote: > > Out of curiosity, do you think sixteen is not too many levels? I think > even four is too many. There would be three ways to win: Majority favorite, > greatest approval, and something in-between that we have difficulty > describing ("median at second-highest level"). >
I think three levels are just right for single winner MCA. More levels should be used when there are many winners. Here's my suggestion for a many winner method based on CR style ballots: Let's say that there are eight levels of CR and five vacancies to be filled. After the ballots are collected we start with the approval cutoff just below the highest level. Let's say that there is exactly one candidate who has approval from more than one sixth of the voters (at this level). This candidate is moved into the winners' circle. Then the approval cutoff is lowered a notch at a time until there is at least one other candidate that has one sixth approval in a partition of approval that gives everybody in the winners' circle so far this minimum quota of approval at this level. If there is more than one way to do this, then conditional PAV (conditioned on the previously decided winners) is used to choose the new winners. [Sequential PAV is conditional PAV in the case where the number to be added to the winners' circle is just one.] This is continued until the winners circle has the required number of winners or until the next to bottom level is reached, in which case conditional PAV is used to complete the winners circle, even if there is no partition of approval at this level that gives five candidates the minimum quota of one sixth each. Forest ---- Election-methods mailing list - see http://electorama.com/em for list info