[EM] Hay voting bust, busted

[raphfrk at netscape.net]

  From: wds at math.temple.edu
 >
 > Sorry, I appear to have been an idiot. Peter de Blanc
 > answered my complaints at
 > http://www.spaceandgames.com/?p=8
 >
 > and it looks to me like I NOW have to agree with Forest Simmons that
 > this IS a great new contribution to voting theory.
 > Also, I showed there in my comment how to generalize their scheme
 > by adding a parameter P. It looks liek the best P is P=0.99 or
 > so, not P=0.5 (their value) or P=0+ (my value from before).
 
 I wonder if it might be worth having the voter write their honest
 utilities on the ballot. The 'backend' would then convert that
 vote into an optimised ballot for inclusion.
 
 If it truely is the optimal strategy to be honest, then there would
 be no incentive to lie. However, it would mean that very low
 probability of winning candidates would not get lost in the noise.
 
 For example, they could just have people write their truthful utilities.
 The backend would then just get the square-root of all their utilities
 and then renormalise so that it sums to unity. This would give the
 probabilities for each candidate.
 
 What about something like the following for a non-random method.
 
 Prior to the election:
 
 Determine the probability of each candidate having a total vote
 within a% of the highest other candidate.
 
 If a is low, then this should be proportional to the probability
 of the candidate ending up in a tie. It seems reasonable, but
 is that true ? Anyway, call this probability Pc for the cth
 candidate.
 
 Each voter votes a number of votes for each candidate and the
 candidate with the highest total wins.
 
 The benefit of giving a vote for a candidate is the probability
 of the candidate being in a tie times the utility of the candidate.
 
 Each vote cast by the voter should be weighted by:
 
 1/sum( Pc*(votes cast for candidate c)^N )
 
 This means that votes for an candidate who is unlikely to win
 cost almost nothing (as Pc is tiny), thus eliminating the spoiler effect.
 
 Using a different power than square/square root would mean that
 the probability of the highest utility candidate winning could
 be increased/decreased. However, setting the power to high,
 would introduce alot of noise to the system.
 
 The probabilities could be determined by the betting markets. The
 problem would be a candidate with say, a 1 in 1000 chance of winning
 would give a noisy Pc. Making 'a' larger helps here but may reduce
 accuracy.
 
 It also means that voting for a sure winner is costless.
    Raphfrk
 --------------------
 Interesting site
 "what if anyone could modify the laws"
 
 www.wikocracy.com  
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