[EM] Range voting, zero-info strategy simulation

[Dave Ketchum]

Quoting from below:
 >
 > These results suggest to me that in the zero-info case, if there are
 > thought to be more than about 2 other voters, Range should be voted
 > as in Approval.
 >
 > D. Zero-info Approval strategy. The voter gives a 10 to every candidate
 > at least as good as the average value of all candidates, and gives a
 > 0 to the others.
 >
Interpreting, I see, as a common case, a couple tolerable candidates, more 
lemons, at least a few dozen voters - and thus every voter who is playing 
this strategy approving both tolerable candidates without indicating which 
of them is preferred as best.

I see such strategy as a lemon, and this research as a lemon if it 
promotes such strategy as it seems to.

DWK

On Mon, 30 Oct 2006 22:42:09 +0100 (CET) Kevin Venzke wrote:
> Hello,
> 
> I wrote a simulation to measure the utility of zero-info Approval
> strategy in zero-info Range elections.
> 
> In each of 100,000 elections one specific voter has sincere ratings 
> from 0-10 for each of five candidates. Four methods of voting are
> implemented:
> 
> A. Sincere. This voter rates the candidates sincerely even if this means
> he doesn't use the top or bottom ratings.
> B. Maximized sincere. This is the same as A, except that the best and
> worst candidates are moved to the 10 and 0 positions, in order to
> maximize the weight between these two candidates.
> C. "Acceptables" strategy. The voter gives a 10 to every candidate worth
> 5 or more, and a 0 to the others. This can mean that the voter gives a
> 10 to every candidate, or a 0 to every candidate.
> D. Zero-info Approval strategy. The voter gives a 10 to every candidate
> at least as good as the average value of all candidates, and gives a
> 0 to the others.
> 
> Every candidate randomly has a score from 0 to S, prior to this voter
> casting his vote. S can be changed; S of 0 would mean there are no
> other voters in the election at all. S of 10 means there is probably
> one other voter, and at least one other voter. S of 50 would mean at
> least five other voters, etc.
> 
> Ties are broken according to an index that doesn't change between the
> before and after, so that when the voter fails to break a tie between
> two candidates, the same one of these candidates "wins" as before.
> 
> 100,000 trials each. For each strategy, I list the average improvement
> that this voter achieved (from his own perspective) due to his vote. This
> is of course measured in points, so that a result of 1 means that on
> average, this voter's ballot caused the election of a candidate considered
> 1 point better than the candidate who won before this voter was counted.
> 
> with S = 0 (no other voters at all)
> A: 3.638
> B: 3.625
> C: 2.397
> D: 2.518
> 
> with S = 5
> A: 3.222
> B: 3.393
> C: 2.389
> D: 2.525
> 
> with S = 10 (probably one other voter)
> A: 2.630
> B: 2.924
> C: 2.382
> D: 2.503
> 
> with S = 20
> A: 1.755
> B: 2.028
> C: 1.955
> D: 2.105
> 
> with S = 30
> A: 1.310
> B: 1.528
> C: 1.537
> D: 1.710
> 
> with S = 100
> A: 0.465
> B: 0.555
> C: 0.615
> D: 0.656
> 
> with S = 10000
> A: 0.00494
> B: 0.00612
> C: 0.00748
> D: 0.00761
> 
> with S = 500000 (1000000 trials here)
> A: 0.000075
> B: 0.000088
> C: 0.000131
> D: 0.000174
> 
> (I increased the trials at the end because as the number of other
> voters increases, the likelihood that our single voter can change
> the result decreases, making the result less accurate.)
> 
> These results suggest to me that in the zero-info case, if there are
> thought to be more than about 2 other voters, Range should be voted 
> as in Approval.
> 
> (I did run some simulations with different numbers of candidates,
> but the results didn't seem very different.)
> 
> Any thoughts are welcome.
> 
> Kevin Venzke
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  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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