[EM] Anyone got a good analysis on limitations of approval and range voting

[Warren Smith]

OK, this is an attempt to reply to Robert Bristow-Johnson.

>WDS: For Condorcet systems with ranking-equalities
> allowed,
> they might behave better with strategic voters, though.  I've posted
> on that topic before.
>RBJ: ... so [range is] *not* always "better than every rank-order system for ...
>strategic voters".

--1. I meant Condorcet with equalities permitted might behave better
for strat voters than Condorcet without equalities permitted.
Everybody seems to think that but no full understanding is available.
2. By "rank order system" I meant, equalities not permitted.  A>B>C>D
is a rank ordering. A>B=C>D is not.
3. For a partial understanding of Condorcet with equalities permitted
and strategic voting, see puzzle #113 here:
http://rangevoting.org/PuzzlePage.html

>RBJ:
now the relationship that citizens of a community or nation have with
each other is not the same kind of trusting and sometimes blind
relationships we have with members of our families and other partners
(like business partners) that we end up trusting by default,
essentially in our own enlightened self-interest.  in general, we
have contracts and laws essentially intended in the best
circumstances to "keep honest people honest".  we have locked doors,...

--Range voting in no way "assumes" that everybody is trustworthy and
nonstrategic.
It is designed to behave comparatively well with strategists present.

>RBJ:
so Warren, you're gonna sell your system on the hope that in this
place of absolute privacy, we'll all be sincere. [Tons of other blather too.]

--huh?

>RBJ:
i want a system that offers nothing for the voter's political
interest for voting insincerely.

--It is known that no deterministic voting system using rank-order ballots, or
rank-order-with-equalities-permitted,
can satisfy this desire.  See http://rangevoting.org/GibbSat.html

Range and approval voting, however, are not of the above types.
They partially-evade this impossibility theorem.
I have a theorem (discussed at that web page) extending this
impossibility theorem
to wider class of voting systems.   In short you here are asking for
the impossible.

>RBJ:
but, save for the case of a
Condorcet cycle, i don't see how voting insincerely in a Condorcet-
decided race ever serves the political interest of the voter.

--That is merely because your vision is poor.  E.g. see
http://www.rangevoting.org/CondStratProb.html

> WDS: 3. The main perceived flaw in range voting is for strategic+honest
> voter MIXTURES
> and under the worrying assumption that who decides to be strategic, is
> CORRELATED with the politics of that voter.  Thus for example,
> strategic Bush voters could beat unstrategic Gore voters.  Problem
> isn't really much of a problem if the Bush strategy-fraction is the
> same as the Gore strategy fraction (a claim backed up by computer
> sims).
> RBJ: just like the issue of drawing random ballots in multi-winner PR STV
and counting on that as "representative", i wonder why counting on
computer simulation to support this balance of tactical voters would
be as trustworthy.

--you are confused.  The simulation did not "support this balance of
tactical voters."
It simply asked: if there is some fixed fraction F of strategic
voters, rest honest, then
how well does range perform (measured by Bayesian regret) and how well do other
systems perform?   It turns out range outperforms every rank-order system,
with 3-10 candidates, for example, for EVERY value of F.


> RBJ:
in other words, if in some election, one side has more politically
savvy strategists, advocates, and voters?  isn't that often how one
side wins and the other side loses?  one side has a Karl Rove and the
other side has John Kerry and one of his 3 serial campaign managers.
don't count on it not differing.

--You are correct in principle.   If one side has more-strategic
voters than another, it could win even though with equal strategy it
would lose. This can happen with range voting.  It also can happen
with lots of other systems.  Including Condorcet.
Including Condorcet in an election which (with honest voters) has no cycles.

However, we have to ask what happens in reality.  Is it actually true that
Karl Rove, by advising voters, will somehow come upon some amazing
insight that will cause Bush to win, while the other side's voters
will fail to reach that insight?
Is this realistic?    In range voting, unlike Condorcet and IRV,
strategy is pretty simple.
Even you (RBJ) ought to be able to comprehend the basics of it.  Even
without any aid from Karl Rove.   And if Rove and Party Talking Heads
are busily telling everybody how to vote (which they will be) then
even if you did not have that level of intelligence, you'd
probably still get the idea.   Of course, somebody with IQ<50 might
still be unable to get it.  But I guess we have to ask: is it really
really important that people with IQ<50
must have equal voting influence?

Anyhow, unlike RBJ, I have actually enquired into the state of
reality, by performing poll studies of this very question.  So far, no
evidence has arisen that Rove could thus have any effect.

> WDS:    However, there is evidence that
> Nader voters are less strategic and more honest.  (Not surprisingly
> since voting Nader
> in the USA *was* unstrategic.)
>RBJ: sure, idealists throwing away their vote.  we want to be able to be
idealist without having to throw away our vote.  and we want to be
able to vote effectively without sacrificing or compromising our ideals.

--then I suggest you use range voting.  In particular, an "idealist"
giving Nader a score of 99 (for 0-99 range voting) would not be
"throwing away" her vote one iota.
However, with (say) Condorcet, a Nader supporter by ranking Nader top,
would in some
electoral situations cause the election winner to worsen in her view.
This worsening is
impossible with range voting under any circumstances.


>RBJ: Warren, i know you've worked so much more in this whole area than i
have, your experience is greater than mine, but i just cannot buy
into your premises.

--you have a wrong idea of what my "premises" are.

>RBJ:  I want a system that does not *assume* or count on our sincere
intentions, but *enables* or *supports* our sincere intentions by not
penalizing our acting according to our sincere intent..

--as I said, this "want" is known to be asking for the impossible.
Range voting however satisfies some weakened forms of this desire.
For example, voting your sincere favorite top, is never strategically
suboptimal with range voting.   That theorem however is false for
Condorcet and IRV.   For another example, range voting in computer
simulations with strategic voters (and honest+strat mixtures) actually
causes more honest-vote-Condorcet winners to be elected, than
Condorcet systems!   Finally, the proof is in the pudding.   You do
the computer sims.  You find out how well systems work with strategic
or honest voters.  Intuition only takes you so far; experiment reveals
the truth.

Re real human uses (not computer sims):
Range voting was used in Ancient Sparta and Renaissance Venice both
for over 500 years.  Those countries lasted longer than any
contemporary democracy (unless you
count Britain as a "500-year-old democracy" which I do not) despite
considerably greater odds against them.

Finally.   Your original question -- what are criticisms of range voting? --
is addressed on the CRV "range voting criticisms" page
http://rangevoting.org/RVcrit.html


-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
"endorse" as 1st step)
and
math.temple.edu/~wds/homepage/works.html