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