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

[rob brown]

Fascinating, thanks!

So do you think it still won't find a condorcet winner if it is modified as
I suggested:

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

I guess it won't, because lots of the voters gave that candidate a 0.  I'm
still thinking the results will converge, if not on a true equilibrium.
Unfortunately this stuff is too tedious to work out by hand, so I'd have to
write something to test it.  But maybe you have a better idea than my own
"gut feel".

Just a thought, what if you do this:  first time, first round, approve all
but the lowest rated candidates on each ballot.  If no equilibrium is found,
run it again, approving only the highest ranked candidates on the first
round.  Obviously that is sloppy, but I'm just curious if it might work.  I
think in the real world, the chance of that "failsafe" having to kick in
would be remote.

I can certainly accept that you could contrive a case where it might never
find the equilibrium.  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).

-rob

On 12/9/05, Rob LeGrand <honky1998 at yahoo.com> wrote:
>
> 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.
>
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