[EM] Range voting, zero-info strategy simulation

[Kevin Venzke]

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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