At 05:23 PM 5/3/02 -0700, you wrote: >The Gibbard-Satterthwaite result doesn't rule out Alex's SVM (Small Voting >Machine) when you take into account that the voting machine is supposed to >apply the OPTIMAL strategy, which is sometimes a probabilistic mixture of >pure strategies requiring coin tosses, die throwing, or needle spinning.
I'm still very skeptical that the SVM could work in theory. The problem is that, in essence, this is nothing but a voting system. Probabilistic or not, all this is is a system that takes in a set of preference ballots and produces a result. As such, I find it extremely difficult to believe that some voter might not be able to achieve a better result by falsifying their input to the SVM. The G-W theorem only works when every voter knows every other voter's sincere preferences. It doesn't necessarily follow that you can't spoof the SVM by falsifying your preferences; if everyone else thinks you are less likely to support the true Condorcet winner, then that can affect their optimal strategies. The beauty of a method like CRAB is that it relies on the nature of equilibria to eventually steer the result toward a Condorcet winner. It won't always work, but it usually does. A SVM couldn't really simulate this, since it only has one set of preferences to work with. If voters are insincere in what they enter, then they never have a chance to budge from this insincere position. >The beauty of Cumulative Repeated Approval Balloting is that the >randomness required for non-manipulability is approximated by the pseudo >randomness inherent in the chaos of the cyclic patterns. So the method is >absolutely deterministic, but random enough to thwart insincere voting. It's not absolutely deterministic, although I admit it is close. Alex came up with this example where Approval voting can settle in a rut: 25 A>B>C 49 B>A>C 26 C>A>B Now suppose the initial approval votes are 25 AB 49 B 26 C So B wins, 25-74-26, even though A is the Condorcet winner. No voter has a clear incentive to change their vote; the vote combination is a Nash equilibrium, when factions are considered players. Now this rut is very tenuous, and one could certainly imagine the voters breaking out of it. But they will not certainly break out of it. Don't get me wrong; I think CRAB is a fabulous procedure for committees and other settings that can support repeated balloting. I just don't believe that it is completely deterministic. Has anyone tried to simulate a repeated approval balloting election where some voters use insincere strategy - that is, they approve a candidate who they like less than a candidate they do not approve? Obviously, there is no incentive to do so in a normal approval vote, but in a repeated approval vote, such disinfestation may help you by convincing other voters to approve your favorite as a compromise. -Adam ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
