Thanks for the suggestions. I'm open to new ideas for measuring candidate viability at the various stages, but I am wary of methods that use probabilities to compute expectations, because it is very tricky to pin down the precise probabilities that some candidate will eventually win.
That's the main reason I adopted the "wait and see" creative procrastination strategy. If the viabilities roughly correspond in order (though not necessarily strictly proportional in magnitude) to the probabilities of winning, then one can safely choose one merger on each ballot, procrastinating the remaining mergers until the viabilities are known more precisely. I'm confident that the new rule for using the viabilities would be precisely right if we knew the exact order of the probabilities, without knowing the probabilities themselves. For example, it doesn't matter if the probability lineup on a ballot is 20%, 65%, 15% or 35%, 40%, 25% . The viabilities could be 2,3,1 or 5,6,2 or 4,9,2. The mergers are the same, the second and third slots merge. This robustness is appealing to me for the following reason: If the voters can estimate the viabilities of the candidates on the basis of imperfect polls, then they can order the n candidates on a three slot ballot well enough for the robustness to give the right result, making up for the deficiencies of the polls. And we know that we have the right rule for the three slot ballot! So in the case of the Three Slot Max Power Cardinal Rating method, we could justly claim the name MVP, the "Max Voting Power" method. Note how this corresponds with the technical definition of voting power, the probability of your vote being pivotal. Forest On Fri, 1 Aug 2003, [iso-8859-1] Kevin Venzke wrote: > I have a decent idea for a refinement, which might permit CR to boil down > to Approval ballots filled out per the Better-Than-Expectation strategy. > You could also do the Maximum Power strategy. > > Suppose there are two factions that vote roughly as follows: > 50%: A 10, others 0 > 50%: B 10, C 10, others 0 > > If you use the normal viability definition (Borda score, or CR sum), it looks > like the candidates have an equal chance of winning. But intuitively this is > not so. A has a 50% chance of winning, and B and C each have about a 25% > chance. The math to produce these odds is pretty simple: > > Instead of giving a candidate the score it was given from a certain ballot, give > it the score AS A PERCENTAGE of the total points awarded from that ballot. (That > means total points awarded from a ballot equal 1.0, regardless of how many slots > were on that ballot.) > > Now that the score is measured with more sophistication, we can actually guess > at each candidates' odds of winning. No need to worry about front-runners. > > Let me attempt an example. > > 50: A 10, E 3 > 50: B 10, C 10, D 10, E 6 > > A gets (10/13)*50 or 38.46% odds > B C and D each get (10/36)*50 or 13.88% odds > E gets (3/13)*50 plus (6/36)*50 or 19.87% odds > > Odds total 100% (or should). > > First faction's expectation: > 10*38.46% + 3*19.87% = 3.846 + .5961 = 4.4421 > Second faction's expectation: > 3(10*13.88%) + 6*19.87% = 4.164 + 1.1922 = 6.086 > > Resulting approval ballots: > 50: A > 50: BCD > > I do find it slightly bizarre that E gets "more odds" from the first faction > than the second. > > > For the Maximum Power strategy: > Instead of calculating expectation, you try to approve candidates with a total > of 50% odds. > > First faction: > A alone is 38.46 (11.54 from 50), A and E is 58.33 (8.33 away). > Second faction: > BCD sum to 41.64 (8.36 off); adding in E gives 61.51 (11.51 off). > > So the result is the same, except that the first faction also approves E. > > Any thoughts? > > > Kevin Venzke > [EMAIL PROTECTED] > > > ___________________________________________________________ > Do You Yahoo!? -- Une adresse @yahoo.fr gratuite et en fran�ais ! > Yahoo! Mail : http://fr.mail.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
