[EM] another lottery for the record

[Forest Simmons]

To make this method clone proof we need to tweak the definition of covering
set: a covering set is a subset of the candidates such that any candidate
who is beaten pairwise is beaten by a member of the subset.

As with the old definition, a minimal covering will always be a subset of
Smith.

In the case of the new difinition, if Smith has three or fewer members,
then the minimal covering set will be the entire Smith set.

Forest



Date: Sat, 3 May 2014 17:52:52 -0700
> From: Forest Simmons <fsimmons at pcc.edu>
> To: EM <election-methods at lists.electorama.com>
> Subject: [EM] another lottery for the record
> Message-ID:
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> A subset K of candidates covers the set of candidates if every candidate
> that is not in K is beaten pairwise by some member of K.
>
> A covering set K is minimal if no set with fewer candidates covers the set
> of candidates.
>
> Here's our new method:
>
> Let K be the minimal covering set with the greatest total approval (sum of
> approval over candidates in K).
>
> Put the names of the members of K on otherwise identical slips of paper,
> and elect the candidate whose name is drawn at random.
>
> I believe this method is monotone and clone free, and relatively strategy
> free.  It certainly satisfies the Condorcet Criterion; whenever there is a
> ballot CW the only possible minimal covering set is the one whose only
> member is the CW.
>
> In almost all of our other examples it would be a tossup between the top
> two approval members of Smith.
>
> Forest
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