[EM] D2MAC can be much more efficient than Range Voting (corrected)
Jobst Heitzig
heitzig-j at web.de
Wed Mar 7 12:20:49 PST 2007
Dear Warren,
I wrote:
> Recall that in D2MAC you specify a favourite and as many "also approved"
> options as you want. Then two ballots are drawn and the winner is the
> most approved option amoung those that are approved on both ballots
> (if such an option exists), or else the favourite option of the first
> ballot.
>
> If voters are sincere, the result will be this:
> 55%: favourite A, also approved C
> 45%: favourite B, also approved C
> Winner: C
And you answered:
> --WDS correction: actually, it appears to me that the winner is
> A with probability 30.25%
> B with probability 20.25%
> C with probability 49.50%
> with social average utility = 7.03
That's definitely wrong: No matter what two ballots are drawn, both approve of C and C is the most approved option. Hence C is elected with certainty.
Then I wrote:
> The only way the A-voters could have to strategically improve the result
> is to switch to something like this:
> 55-x%: favourite A, none also approved
> x%: favourite A, also approved C
And you replied:
> --WDS correction of Jobst wrong probabilities: in that case, winner is
> A with probability 55 - 0.45*x %
> B with probability 45 - 0.45*x %
> C with probability 0.9*x %
Are you sure you understand D2MAC correctly? How do you get these numbers?
Yours, Jobst
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