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

[Rob LeGrand]

Rob Brown wrote:
> 1) start with a much lower cutoff. Say 10 or 20.  Or, if the
ballots
> are simply ranked, start by giving a "yes" to all but the
bottom-most
> candidates.

No, the same B->A->C->B cycle obtains given the 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

> 2) use an average of all previous totals to determine strategy
> each round.

You have rediscovered Forest Simmons's cumulative batch mode for
DSV:
Instead of compiling a fresh poll for each round, the current votes
are
added to a cumulative poll.  For the above example, D does in fact
break
the cycle and emerge as the leader and eventual winner, but it takes
more
than 170 rounds.  Unfortunately, even Approval DSV in cumulative
batch
mode using strategy A will cycle forever when there is a strong top
cycle.

> I'm still thinking the results will converge, if not on a true
> equilibrium.

What do you mean by "a true equilibrium"?  A strong Nash
equilibrium?

> Unfortunately this stuff is too tedious to work out by hand, so
I'd
> have to write something to test it.

I've written my own software to simulate DSV with all of these
tweaks.
Let me know if there's another test election you'd like me to try.

> However, looking at the case you gave, I almost want to say that D
> shouldn't win, even though he's the condorcet winner (since he is
> clearly a very polarizing candidate, with half loving him and half
> hating him).

I agree that D seems to be a polarizing candidate, but no other
candidate
can be elected at an equilibrium.  Any voting system that doesn't
elect D
will be prone to manipulation.  For example, say a voting system
elects C
for the above example.  Then the factions of 17 and 34 voters would
be
motivated to bullet-vote for D.  It's a strange voting system that
wouldn't then elect D.

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

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