[EM] declared strategy voting / Sarvo-range voting

[Warren Smith]

In a paper by me which does not yet exist (unfinished), I proposed the "SARVO"
transformation to a voting system.

SARVO = Strategy Advisor based on Randomized Voter Order.

Specifically, it works as follows.  

1. The voters input their votes,
plus they optionally can (as they do so) also push an "honesty button."

2. The voters are scrambled into random order.

3. We go thru the votes in that order one by one.
At the kth step (kth voter) the vote, before being incorporated into the election,
is pre-transformed as follows:
   A. If the vote had "honesty button" pushed, no transformation is done.  Otherwise:
   B. The vote is transformed to be maximally strategic based on that vote and based on
      the random sample of the other votes consisting of all previous-votes in the order,
      i.e. the "election results so far."
      (Incidentally, if optimal strategy is not known, a pre-announced perhaps-nonoptimal
      usually-good strategy could be used.)

4. The election results are output.

5. Go back to step 2 and do it again and again with different random orders each time,
a zillion times.

6. The AVERAGE of all the final election results announced in step 4 is announced
as the "final" election results.

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In preliminary computer-sim experiments, it appeared that Sarvo-Range Voting
was superior (in terms of Bayesian regret) to ordinary range voting,
which in turn was as good or superior to every other voting system I had tried
(about 30).  Sarvo-range was better than range because it handled strategic voters
better.  For honest voters, sarvo-range and range behave identically thanks to the
honesty button.
It looked like with any nonzero fraction of strategic voters, SR was better than R.

The idea is basically that strategic voters will want to input honest votes because the
strategy-transformation provided will do a better job of strategizing than that voter
would have by himself.  (This claim is only approximately correct, though.)
Then the Sarvo-ization has a less damaging effect than
non-averaged strategizing.   

However, I doubt that sarvo-range-voting would be acceptable in practice despite its
superior performance on paper.  It requires a lot of computer power and randomization,
and it is not simple to describe.

-------------------------------------

Forrest Simmons just described his own interesting DSV idea on EM, which
could also be regarded as a way to marry range voting and DSV.  I will rephrase and
alter and extend it thus:

1. Voters input honest range votes.
Plus they optionally can (as they do so) also push an "honesty button."

2. The winner W of the range election is announced.

3. Votes are transformed (unless honesty button pushed, in which
case original votes are used) so all candidates rated above W are
maxed and all rated below are minned within the allowed score range.
Candidates rated equal to W are maxxed or minned according to whether
W is rated above or below midpoint.

4. Back to step 2 trying a zillion elections.

If this process converges to a fixedpoint then the final winner W is the election winner.
But more generally if it settles into a cycle where W1 wins then W2 then W3... then W1 again, 
then the election winner is a random cycle member. 
(Examples of such cyclic behavior exist and have recently been posted on 
RangeVoting at yahoogroups.com
by me.)

Alternate (probably better) idea: a final election is done using as the threshhold on each vote,
the average honest-range vote for the cycle members.  Its winner is the final winner.

I have no idea how well this will work.  It is not the same as Simmons' idea
but it is close to it.  This method is superior to Sarvo-range voting in the
sense that it can be done algorithmically quickly (polytime), whereas sarvo-range voting can
be very slow for deciding close ones.

Warren D. Smith