# [EM] Sincere Condorcet Cycles

robert bristow-johnson rbj at audioimagination.com
Wed Dec 16 17:04:36 PST 2009

```On Dec 16, 2009, at 6:01 PM, Kristofer Munsterhjelm wrote:

> robert bristow-johnson wrote:
...
>> by the way, i can see how we can put 3 candidates on the 3 points
>> of an equilateral triangle (let's say it's centered at (0,0) and
>> we don't give a fig about rotation), and then from polling data of
>> voter preference, determine regions on the plane where a voter's
>> position in that region is logically consistent with their ordered
>> preference.  i am not sure how to do polling to put voters or
>> candidates on a 2-dim grid, just from information regarding who
>> they like and who they don't.
>
...
>
>> if the axes of the grid were to represent fundamental sociological
>> orientation, like liberal vs. conservative on the x-axis and
>> libertarian vs. communitarian (some might say "authoritarian") on
>> the y-axis based on questions about values and social issues.  and
>> then rate your candidates on the same basis and mark their
>> position.  in doing that, i am not sure that for two candidates
>> positioned diagonally (that would also have their equidistant
>> boundary line at a diagonal), it would not necessarily be the case
>> that some voter that is closer to A than to B would vote A>B.
>
> Yes, observation of the pattern of "wings" or political spectra is
> what leads to point 1 above. Though I'm not sure why someone who is
> closer to A than to B would not vote A>B. Do you mean that the grid
> would be insufficient to capture all the factors that might lead
> the voter to prefer B to A, or is there another reason?

well, i am not saying it would be common for a voter who is closer to
A than B to vote B>A, and i would say that it's reasonable in running
simulations on models to say simply that in a pairwise decision,
every voter votes for the candidate that they are closer to, given
some metric.  btw, there are other distance metrics than the
Euclidian (sqrt of sum of squares of components of each dimension),
there is the "taxicab norm" (sum of abs value of components) and what
we engineers call the "min-max norm" (the largest abs value of all
the components).  they all need to satisfy four criteria (the hardest
to prove would be the triangle inequality).

the reason i bring it up is that the choice of distance metric can
affect the outcome of a simulation, besides just how the 2-dim (or
more dims) grid gets defined, how different issues are weighted and
oriented (e.g. decriminalization of marijuana would be somewhere in
the libertarian/liberal corner, legalizing euthanasia might be mostly
libertarian with a slight tilt toward liberal, single-payer health
care and gun control would be in the communitarian/liberal corner,
restricting abortion might be in the communitarian/conservative
corner, the death penalty would be pretty much pure conservative,
increased police powers might be mostly conservative with a tilt
toward communitarian, etc.), and then based on some polling
questionaire and these weights and positions of *issues* in the issue
space, a voter or a candidate could be placed on the grid.  but, of
course, there are lots of subjective judgments (like i just did with
six issues) and it's a subjective judgment as to what norm to use to
measure distances.

those are some of the unknown factors in the model that might lead a
voter that is placed closer to A (by some distance metric, yet to be
decided) to still vote for B.  and then there are these random
personal factors; a voter might *personally* dislike a candidate that
he/she is politically well-aligned with, and would vote against such
a candidate for that reason.  i have actually run into a couple of
sorta conservative voters that voted for W in 2000, shed some of
their ignorance in the following 4 years, and even though their
positions on issues hadn't changed (still pro-death penalty, pro-war
on drugs, anti-abortion), they *hated* W by 2004.  i do not know
exactly how they voted in 2004, they might have voted for Kerry
(there were Howard Dean supporters, believe it or not) or they might
have stayed home.

i am not critical of making some assumptions (like a 2-dim issue
space or even measuring distances with the Euclidian norm), and there
are *many* assumptions (like exactly where on the grid, or in what
direction, does legalizing euthanasia lie?).  but i don't see it as
natural that all voters who primarily support candidate A, stand with
candidate A on all issues (which is what would be the case if they
lived at the same locus as A) nor will have the same second and third
choice as the other supporters of candidate A.  that i consider to be
pretty unnatural.

--

r b-j                  rbj at audioimagination.com

"Imagination is more important than knowledge."

```