[EM] D2MAC can be much more efficient than Range Voting (corrected)

[Jobst Heitzig]

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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