On 20 Jul 2005 at 18:51 UTC-0700, Abd ulRahman Lomax wrote: >At 03:47 PM 7/20/2005, Dan Bishop wrote: >>[...]I think a good solution would be for elections to have two rounds: >> >> 1. A qualifying primary, done entirely with write-in ballots, and >> counted using Approval. Candidates with a sufficient number of >> votes would advance to... >> >>2. A runoff election, using ranked ballots. > T. S. continued with comments and other suggestions, including the use of Jobst "direct support and also approved" style ballots in the primary, posing the question of how to make the best use of Jobst's ballots. I like this idea, and It seems to me that ranked ballots would not be necessary in the second round (the "runoff election") if the information from the first round (the primary) were used to form a reasonable lottery L as a standard of comparison. Here's an example of how those ballots could be used: 1. After the primary (using Jobst style ballots) list the candidates in approval order. 2. Go down the list to the highest approval level at which a majority of ballots express approval for some candidate at or above that level. Eliminate the candidates below that level. 3. Form a lottery L in which the remaining candidates' probabilities are proportional to their direct supports. 4. The second round is pure approval. If no candidate receives more than 50% approval, then lottery L is used to choose the winner. Otherwise, the candidate with the greatest approval in the second round is the winner. Note that in the second round, approval has a definite meaning: you approve candidate X iff you like X better than the lottery L. If there are N remaining candidates, it takes only N comparisons (of the form X?L) to fill out this approval ballot, whereas an ordinal ballot would take at least N*lg(N) comparisons ( of the form X?Y), where lg(N) is the integer part of the base two log of N. Note, also, that if L supports just one candidate X, then the only way that the lottery L can be the winner is if candidate X is a Condorcet Winner. In general (even when L gives probability to more than one candidate), the only time the lottery L will be used to pick the winner is when L beats every flesh and blood candidate by a majority of votes, i.e. when L is the Condorcet Winner, which means that a majority of the electorate prefers to take their chances with L over any individual candidate. It seems to me that this would be rare, but if it did happen, it would be lottery by popular acclaim, not by imposition of a lottery method per se. The method could be nick-named AvTF for "Approve or Tempt Fate," or perhaps AvD for "Approve or Dare." Comments? Better ideas for the lottery L? Better name for the method? Forest
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