[EM] Alright, next try. Range voting fix, version 2.

[Rob LeGrand]

Rob Brown wrote:
> What I suggest is that, prior to tabulating, each Range ballot be
> processed into an Approval ballot.  But, it should be done taking
into
> account optimum strategy, with knowledge of how others are voting.
 You
> could call this a "Nash equilibrium seeking" system, as it keeps
> adjusting Approval ballots (that is, picking the cutoff point)
until a
> state is reached where no voter can improve his or her own
strategy
> given that all other people's strategy stays fixed.  (in reality
it is
> not the voter that is modifying their strategy, it is the formula
that
> converts the voter's range ballot into an approval ballot, which
can be
> considered to be operating as an "agent" of the voter)
. . .
> So the ballot is adjusted, giving only A a yes.  The formula would
> simply be that all candidate's that are preferred to the leader
are
> given a yes, and all that are less preferred are given a no. The
leader
> is given a yes if he is preferred to the second place candidate,
> otherwise a no.

You have rediscovered Lorrie Cranor's Declared-Strategy Voting in
batch
mode using Approval and my "strategy A".  Some of my current
doctoral
research is concerned with investigating DSV using different systems
(plurality, Approval, Borda, etc.) and strategies like the above. 
Please
see http://lorrie.cranor.org/dsv.html for Cranor's dissertation on
DSV.

Unfortunately, DSV in batch mode using Approval and strategy A won't
always find a Condorcet winner.  Consider the following votes:

      A   B   C   D
33: 100  70  30   0
16:  10 100  70   0
17:   0  70  30 100
34:  30   0  70 100

Reasonably assuming a 50 cutoff for each voter in the first round, B
will
lead in the first "poll".  After cutoffs are adjusted, A will lead,
then
C will lead next.  Then B will lead again and the cycle repeats.  D,
the
Condorcet winner, will never lead, even though the only potential
equilibrium (still assuming strategy A for all voters) results in a
D
win.

--
Rob LeGrand, psephologist
rob at approvalvoting.org
Citizens for Approval Voting
http://www.approvalvoting.org/

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