[Election-Methods] [EM] Is "sincere" voting in Range suboptimal?

[Abd ul-Rahman Lomax]

Oops! I wrote:

>The results: expected utility for the "sincere" Range vote: 40. For 
>the Approval style vote: 39.

Those were the sums of the utility for each of 27 possible pre-vote 
patterns, so the expected utilities are 1.481 for the "sincere" vote 
and 1.444 for the Approval style vote.

To put this in better perspective, the voter gains a relative 
expected utility of 0.481 by voting sincerely (i.e., by accurately 
rating the midrange candidate according to true expected 
satisfaction) and 0.444 by exaggerating the midrange candidate to 
either extreme, over not voting at all, which should be considered a 
baseline. Thus the return for voting sincerely, over voting in an 
exaggerated way, is 0.037/0.444 or 8.3%.

One thing I had not considered yet. What would these utilities look 
like, with the same conditions, same utilities, but under Approval as 
a voting system? Does Approval *as a system* generate greater utility 
for the individual voter?

No. If I look only at the votes in the matrix that are 0 or multiples 
of 2, the expected return for the voter is  1.375. Range generates 
better return for the voter.

Improving Range resolution thus generates better expected utility for 
the individual voter, in the zero knowledge case, than lower 
resolution (at least the change from Range 1 to Range 2 shows this), 
in this case. I have some suspicion that it generates even better 
results for middle candidate utilities that are not in the exact 
midrange, but certainly have not shown that yet.

None of these results would have been expected from the claims being 
made about Range by some writers recently.