[EM] Does High Resolution Range offer a solution to the ABE?

[Jameson Quinn]

2011/11/26 <fsimmons at pcc.edu>

> While working with MinMaxCardinalRatingsPairwiseOpposition (MMcrwPO) I got
> an
> idea that high resolution Range might have an acceptable solutin to the
> defection problem that we have been considering:
>
> Sincere ballots
>
> 49 C
> x: A>B
> y: B>A
>
> where x appears to be slightly larger than y in the polls.
>
> The A and B factions can agree to enough support such that if they both
> follow
> through the one with the larger support will win, but if one defects, C X
> will win.
>
> In this case that level of support is about 96%.  If the A voters and the B
> voters both give 96% to their second choice, then A or B will win,
> depending on
> whether or not x is greater than y.  If anybody defects from this, then C
> sill win.
>
> This offers an equilibrium which is "stable" in the sense that if everyone
knows everyone else's ballot then nobody has the incentive to defect. But
it's drastically unstable and failure-prone if you dont have pre-election
polls that measure down to the last ballot.

That's one of the main advantages of a system like SODA. Because delegated
ballots are assigned after the election, by the time that happens everyone
does know the size of each faction down to the last ballot, and so
solutions of this nature are in principal feasible. (For instance, this
exact solution would work in "SODR", that is to say SODA with Range instead
of Approval.)

Jameson
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