[EM] Approval ballots. Two to elect. Best method?

[Andy Jennings]

SPAV?
1. Candidate with most approvals wins.
2. That candidate's voters have their voting weight halved (or multiplied
by 1/3).
3. Remaining candidate with most points wins.

STV-like?
1. Choose quota Q = one-third (or one half) of voters.
2. Candidate with most approvals wins.  (T = # of approvals)
3. That candidate's voters have their voting weight multiplied by
max(1-(Q/T), 0)
4. Remaining candidate with most points wins.

Monroe-like?
1. For each pair of candidates, find the voter-assignment which maximizes
the number of voters assigned to a candidate they approved, such that no
more than half the voters are assigned to one candidate.
2. Elect the pair which satisfies the most voters.

Others?  Toby, what are your favorite PR methods at the moment?  Can you
give a short explanation of how Phragmen/Ebert would work with only two to
elect?



Specifically, I'm worried that in practically every approval-ballot PR
method, if there is a candidate you really like, but are sure that she can
get elected without your vote, you gain an advantage by not approving
them.  Is there any method that minimizes that incentive?

~ Andy
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