[EM] Remember Toby

[Rob LeGrand]

Kathy wrote:
> Let all the voters vote for one or two candidates.

Considering this Approval-like method on its own, without any proxy
aspects, I see problems.  Capping the number of candidates that each
voter is allowed to approve at 2 destroys some of Approval's desirable
properties.  First, no longer is your best strategic vote necessarily
even weakly sincere; in other words, it will often be to your advantage
to approve B and not A even when you prefer A to B.  Second, even when
all voters have strict preferences over all candidates, there may be an
equilibrium that doesn't elect a sincere Condorcet winner.  As an overly
dramatic example, if the sincere preferences are

49:A>B>C>D>E>F
 3:D>C>F>E>B>A
48:F>E>C>D>B>A

One equilibrium, I claim, would be

49:A,B
 3:D
48:F,D

which elects D even though 97 of the 100 voters prefer C to D.  Just
going by intermediate results, as from polls, it might be very difficult
for C to emerge as a contender.

--
Rob LeGrand
rob at approvalvoting.org