On Sat, 19 Mar 2005, Jobst Heitzig wrote:
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However, one could make a minor modification which would only seldom be used: Determine P, and as long as all of P is beaten by a candidate outside P, add the most approved such candidate to P. I will try to prove its monotonicity...
That would be nice if it works out.
Here's how we might change it:
Use a random approval ballot order in place of the approval order.
Also a good idea, but it requires to let go of the nice interpretation of strong defeat...
Right. The randomly confirmed defeat is not as good as the strong defeat, so if we go this way, we should finish up the way Ted likes ... pick the pairwise winner among those whose defeats were not confirmed by the random ballot order.
This method would be Smith efficient, so if we want a Smith efficient lottery, this would be a possibility.
We choose from P either by (ordinary) random ballot or by (another) set of random approval ballots, how ever many it takes to determine a winner.
I think that it is better to use ordinary random ballot since then all three major kinds of preference information (approval, pairwise preferences, direct support) are used to determine the winner, and that is a very good marketing argument!
Great point!
By the way, here's a simple "procedural" version of the method, to be used in meetings: First, options may be suggested, and for every option it is asked who approves of it. They are written onto blackboard in order of approval. Then some member of the group is picked at random. S/he proposes some of the options, and then this option is subjected to pairwise contests with the more approved ones, beginning with the most approved one. If none of them wins with majority strength, the proposed option wins. Otherwise, the next person is chosen at random and proposes an option, until the proposed option survives all pairwise contests with more approved ones. This will hopefully lead to people proposing very good compromises, since otherwise they will experience to have their proposal defeated by a more approved option, which would make their proposal look somewhat ridiculous.
I'd like to ask you to test this procedure with your favourite group!
This procedure is very appealing to me.
It would be a good way to sell the method in a group setting.
One could use it to pick a restaurant for the group to adjourn to after the meeting if they didn't want to test it on a more important decision.
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