[EM] cyclic preferences

[Paul Kislanko]

Adam Tarr

>>I will reiterate that allowing voters to cast cyclic ballots simply makes 
the method more complicated and increases the chance of a spoiled 
ballot.  Even if I didn't oppose it on theoretical grounds, I would oppose 
it on practical grounds.  Onward...
<<
It may make the collection system a little more complicated, but it makes
any Condorcet Method easier, since the voter directly specifies which of the
two cells in the matrix to add 1 to indicate her pair-wise preference. I
think this was the original point Jobst was making. 

And from the voter's perspective the "more complicated" collection is
actually easier (see below).

>>Jobst Heitzig wrote:

>1. Consider a voter who evaluates the candidates according to a number
>of aspects (or dimensions, criteria, issues, perspectives, whatever).
>Assume that these aspects are not "measurable" in a numerical way but
>that s/he can only tell whether a candidate is better than another
>according to that aspect or not. Also, assume that s/he cannot assign
>priorities to those aspects but considers them equally important.

Cannot, or will not?  Surely, with some thought, one can either attach 
differing relative importance to certain positions on certain issues, or 
can conclude that they are all equally important.  One or the other has to 
be true...<<

Technically, the same math that underlies Arrow's proof applies here. Of
course I can order my priorities strictly, but if there are more than 2
candidates and more than 2 issues, the sum of issue strength times candidate
position could still lead to inconsistent orderings of any subset of the
full candidate list. With all candidates in I could come up with a ranking,
but A > B > C doesn't mean I prefer to B to C if the issues for which A is
closest to my position are not more different from mine in a stict B is
closer than C order for all of them. In general that is not true.

>>  Assume
>further that for almost every pair X,Y of candidates there is an aspect
>in which X is better and another aspect in which Y is better. Most of
>you will agree that this situation is quite realistic, insn't it?

>That part, sure.

>>         Now, what preferences shall the voter express in this situation? 
> There
>are two natural ways: S/he will express the preference X>Y if and only
>if X is better than Y according to either ALL aspects, or according to
>MOST aspects. The preference relations which can result from the first
>rule  include all quasi-orders (= reflexive and transitive but not
>neccessarily total (="complete") relations), and those which can result
>from the second rule include all reflexive relations whatsoever, in
>particular, cyclic relations.

>Again, I reject the idea that a rational voter could ever make a decision 
simply by counting aspects/issues.  It is trivial to take a position and 
break it down into two sub-positions.  For example: you could say that I 
support legal abortions.  Or, you could say I disagree with the notion that 
a early-term fetus is an independent life, and that I believe that banning 
abortions is impractical.  Someone else may agree with both, neither, or 
only one of those two aspects.  But why should that breakdown make my 
opinion twice as important?

I didn't follow this at all. If my A>B>C ranking is based upon one of the
subsidiary aspects of the issues you've broken one issue into, I think it
shows how a rational voter like myself would switch X>Y to Y>X if a Z who
exactly matches my position on this most-important issue is not a part of
the comparison. Rather than a "a rational voter could never make a decision
based upon such things" I'd say that's exactly HOW a rational voter would
decide for that one issue which THREE of X>Y, Y>X, X>Z, Z>X, Y>Z, Z>Y come
closest to matching her pair-wise preferences. Far from not being rational,
doing it this way is the only way to decide such things at an individual
level. And to put the full ranking together I have do the same work for
EVERY issue. 

It doesn't make your opinion count any more than anybody else's, it's a
description of how you formed an opinion. I'd turn that completely around
and say why should the fact that my ranked ballot A>B>C be assumed by an
election method to consider that I'd prefer B to C if those were my choices?
Instead of inferring B>C, why not just ask me my pair-wise preference if
those were my choices? I'd "integrate over all issues" and I WOULD have a
well-defined preference, but it might or might not be B>C.


>>         To give a concrete example: 3 candidates X,Y,Z, 3 aspects 
> A1,A2,A3, and
>orderings X>Y>Z according to A1, Y>Z>X according to A2, Z>X>Y according
>to A3 (you all know this of course :-) The voter can either express no
>preference at all, or the cyclic preference X>Y>Z>X. Which gives us more
>information about his/her preferences? The latter, of course.

>Not necessarily.  If a voter truly feels that each issue has equal weight, 
then X=Y=Z (voted above or below other candidates) is a completely 
reasonable vote that tells us everything meaningful that voter has to 
say.  If the voter simply lacks the patience and rationality to resolve his 
or her preferences into a transitive ordering, then in my opinion his or 
her vote is just noise.

Well, in my opinion any voting method that INFERS a preference I don't have
is just garbage. You can insult my intelligence by calling me lazy, but as
was demonstrated a long time ago the more careful I am to do it "right" the
more likely the voting system is to get it wrong. I'd say the voting system
designers are the ones who don't have the patience and rationality to "do it
right."

>>2. Consider a voter who has children to care for who have no right to
>vote however. 

I'm staying out of this one because it's unnecessary to the basic argument,
and I don't think you have to have kids to vote in the interest of a future
generation.

But "onward" to the discussion about the practicalities.

Without regard to the mechanical implementation (it's trivially easy with
computers, slightly more complicated to do with punch-ballots, and no more
difficult than a standardized test if #2 pencils and optical scanners are
used) I'd collect pair-wise preferences this way.

My ideal ballot for a decision with more than 2 alternatives would have each
pair listed and these choices:
 X 
 Y
 Either X or Y
 Neither X nor Y

When I've answered that question for every pair of alternatives, without
inferring anything at all the counting system has collected what corresponds
to a ranked ballot if you want to use IRV, a 1:1 mapping to the pair-wise
results matrix if you want to use a Condorcet-style selection process, and
if you're using approval it's very specific.

When you get over a few candidates trying this with punch-outs would be
messy, but either the electronic or #2 pencil version would be very fast and
easy for the voter. 

My basic thought is that from a theoretical perspective it is worthwhile to
divorce the preference-collection process from the vote-counting process.
For one thing, it would make it a lot easier to analyze what the outcome
would've been under different methods, and from a purely practical
standpoint it would eliminate the sidebar discussions.

An academic statement that "intransitive cycles are irrational" ignores the
fact that irrational people have the right to vote, too, and any method that
has a built-in "discard the votes that the method designer considers
irrational" is decidedly not going to be popular with any rational voter
(the truly un-analytical won't notice, of course, but manipulating the sheep
by skewing the vote-counting machinery isn't more attractive to me than
doing so by spending millions on advertising).

>From a purely "academic" perspective, dividing an election method into its
"collect data" and "count votes" components simplifies a lot of the
comparative analysis. If the generalization of a ballot I suggested above is
used, you infer a ranked ballot, with or without truncation and compare IRV
to a Condorcet method that uses the derived ranked ballot and to a Condorcet
method that uses the explicit pair-wise preferences of each voter. That
would be a much more robust method, I'd think, since the same input would be
used by all systems.