[EM] reply to venzke re utility, approval, range

[Warren Smith]

>Venzke:
THIS IS useful TO know, since it means that the range voter's greater
ability to express himself (relative to the approval voter) isn't part
of why WDS feels social utility IS a useful measure. That means there's
no reason to discuss only range, since approval should justify the use
of social utility to the same extent that range does.

--WDS: I agree: that is fully correct IF we have strategic voters only.
But if there are some honest voters, though, THEN range and approval will differ.

>Venzke:
I did simulations comparing sincere Schulze(wv) voting with various
scenarios for approval voting:
   http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2004-March/012292.html

The results tend TO be pretty Close. Approval was most impressive WHEN
all voters know which candidate maximizes utility, AND vote strategically
as though they believe THIS candidate will win with 90% probability:

5 candidates:
IN 25.38% of trials, approval winner had higher utility
IN 4.81%, Schulze winner had higher utility
IN 69.81%, same winner
+1.55 average difference IN utility of approval winner over Schulze
winner (scale being 0-100)

7 candidates:
IN 31.03% of trials, approval winner had higher utility
IN 4.49%, Schulze winner had higher utility
IN 64.48%, same winner
+2.07 average difference IN utility of approval winner over Schulze
winner (scale being 0-100)

I think THIS IS impressive IN some respects.


--WDS: Your sims were more extensive than mine in various ways, at least as far as
the schulze vs approval comparison is concerned.
However your sims are somewhat unfair in that your approval voters are
strategic in a number of possible ways, but meanwhile your Schulze voters are always
honest and thus never suffer from, e.g. DH3 pathology, which would have led to
heavy utility decreases for strategic Schulze which your sim could not detect.
That gave Schulze a large a priori advantage over approval in
many of your sims.  Nevertheless approval often did better than Schulze in your sims.

The particular sim you just talked about seems to involve fairly honest approval voters.
It looks like from two of your sims that if the approval voters have a pretty good idea
of (1) their own private utilities, and (2) of the names of some candidates
that society considers good (e.g. the true util maxer or the the Schulze winner),
then the threshold strategy is good enough to make approval voters using that strategy
produce better election results than Schulze (with honest voters) produces.  It would be more
reassuring if more sims of this ilk were run, using more thresholds.  For example, try
80% estimated prob for Schulze or MaxUtil winner.  Or try using the utility between
A's and B's which is 95% of the way toward B (assuming that voter prefers B>A)
as threshold.  That might lead to a more realistic sim.


>Venzke: I assume that you did test approval strategy.

--WDS: yes: I considered both honest approval voters, honest range voters,
and strategic approval = strategic range voters.  The honest range voters
did not do any downweighting: they voted 100 for the favorite
and 0 for the most hated, that was my definition of honesty for that purpose.
My strategic voters (one version) used something which presumably was essentially was the same as
in your "lesser of two evils A & B" sim.  However in that sim my Schulze voters
were also being strategic to try to make the comparison fair, and each voter's strategy involved
top rating and bottom rating A and B.  Other Schulze strategies have since been suggested to me,
but have not been tried.

wds