[EM] majority winner and range & condorcet methods

[Warren Smith]

>robla:
Incidentally, Range voting wouldn't have prevented slavery.  Black
suffrage was a pretty important prerequisite which didn't exist back
then.  Also, I don't think that a bunch of people who were willing to
secede from the union and fight a war on their own soil would express a
mild preference for slavery in a Range vote.

--I did not say it would have.  In fact I pointed out the same 
problems.   However, let me make the following points.
  0. The exact same phenomenon comes up all the time in situations having nothing
      to do with slavery.  For example, some decision removes $100 from the pockets
      of all voters of (minority) type X, and awards $10 to all voters of majority type.
      Or say, women who want an abortion are a minority but who care a lot about it,
      whereas Christian anti-abortionist moralists debating on the exact beginning point of
      the "soul" may care comparatively less about it, but are more numerous.   
      This same mathematical structure happens all the time.  In such a situation, it is 
      not necessarily a "glaring defect" for the vote to be capable of saying "no" when enough
      voters are honest about the situation.
  1.  In 1860 only some southerners wanted to secede and war, not all.
  2.  My polls indicate that some range voters are strategic, some are
      honest, and some are somewhere in between.
  3.  Considering 1&2, it seems entirely plausible that a US-wide range vote could
      have abolished slavery.  Despite Robla & my own objections to that hypothesis.
      But I will not harp on the point (and neither should robla) because what is
      more important is point 0.  In the situation in point 0, both robla's
      voting methods and range voting - if voters strategic - will cause the problem.
      But range voting if voters honest, can avoid the problem.  Also if
      some voters are altruistic rather than totally greed-driven, the problem
      can be avoided, but it is more likely to be avoided with range voting
      because of the previous sentence.

Now concerning the "majority criterion" (Anderson 1994), let me say a few words.

I. Once again, this criterion has ignored the fact that votes are often strategic
rather than honest.  (I have made the same remark in criticizing the "condorcet criterion"
- it is not necessarily a good thing for a "condorcet winner" to win, if the rankings
that produced that winner were dishonest ones.)  Now in methods such as Condorcet
which disobey FBC, it is entirely possible that the "top rank" votes for A, are
in fact dishonest artifacts of voter strategy.  In that case, it is not necessarily
desirable for the A as "majority winner" to win.   In contrast, in range voting
(obeying FBC) every top-rank vote for A, is (assuming voters have brains) GENUINE.
So, we have a conflict here:
  range voting:                                          condorcet systems:
Majority winner (if exists) can fail to            Majority winner (if exists) wins.
win, but any votes top-ranking somebody,         But many of the votes that top-ranked him
are presumably genuinely honest.                    might have been dishonest.

   prob(failure in 1st sentence) = low.           prob(dishonesty) = high.

So, as you can see, it is not clear which voting method wins this conflict.  Robla
may have thought it was clear.  But if so he was wrong.   The decision is
difficult.  That is where Bayesian Regret simulation studies come in.  They
enable us to MEASURE and thus MAKE those hard decisions, as opposed to fruitless
unending speculation without measurement.

II. Robla failed to mention that range voting *does* obey a weakened form of
the majority-winner criterion (call it "WMW").  Specifically:
    "If a strict majority of the voters regard X as their unique favorite, then
   they, acting alone without regard to what the other voters do, can force his election."
I don't know about you, but I personally regard WMW as a more-desirable critrion for
a voting system to obey, than Anderson 1994's MW criterion. 

wds