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

[rob brown]

On 12/8/05, Scott Ritchie <scott at open-vote.org> wrote:
>
>
> Then make it 5 A>B>C, 4 B>C>A, and 3 C>A>B, and watch the same thing
> happen.
>

I looked into this a bit, and see what's going on and think it is easily
fixable.

My approach would be to stick with the conceptual point of view that each
voter has one software "agent", that attempts to convert the range ballot to
the most strategic approval ballot, considering only that individual voters'
strategic interest.  In order for each agent to be effective, though, it has
to have the best information as to how all the other voters are likely to
vote.

The problem was that each agent was basing its strategy on the outcome of
the previous round, assuming that to be the most accurate predictor of the
outcome of the current round.  In a cyclic situation, this could be very
inaccurate, since it could bounce back and forth between different leading
candidates with each round.  If instead, the system averaged the scores of
past rounds, this would stabilize the data and therefore be a far more
accurate predictor of the current round's outcome.  (If we averaged ALL the
past rounds, this would work fine and be very stable, but might take a bit
longer to converge to the final results than if we just averaged a few
rounds' worth each time)

Of course in the end, we would not be using averaged totals, but current
totals.  Once we have reached an equilibrium (which will happen as soon as
the ordering of the totals doesn't change from one round to the next), we're
good and there is no need to base anything on totals from previous rounds.
We can easily determine all approval ballots are optimum, and produce the
final results from that Nash equilibrium ballot set.

Note that I had initially considerered making it the agent look at the
current vote counts, as opposed to the results of the last full round (or
rounds).  This has a stability -- and efficiency -- benefit, at the cost of
strict determinism, since the ordering of the ballots could (in theory) have
an effect on the outcome.

BTW, one other minor detail:  when dealing with very small numbers of
voters, such as the examples you provided with only 3 voters, technically
the agent should subtract its own previous vote from the previous round's
totals.  That may or may not have made a difference in your examples.

-rob
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