[EM] cyclic preferences

[Paul Kislanko]

-----Original Message-----
From: James Green-Armytage

Dear Jobst,

	There are two separate issues here. 
	The first deals with whether a voting system should make allowances
for
irrational preferences.
	The second deals with whether cyclic preferences are irrational.
--------------------------

I have a different perspective, and I'll deal with the first one first.

"Irrational preferences" are only so because you say so. Here's my example
from a voter's perspective.

For simplicity, we'll assume only 3 candidates. I will choose one of them by
some complicated process that depends upon their position on numerous issues
compared to my position on those issues as modified by my assignment of
importance to the individual issues. Not even I know how the complex analog
computer that is my brain comes to that judgment of which of the three gets
to be first, but it has been trained in logic, so whomever is first is
likely a "rational" choice.

Now, if you ask me which of any of the three pairs of candidates I prefer,
the same process (logical, if not "rational") uses the same process to pick
between the elements of the subset. MY issues are still the same, and my
priorities are still the same, but without the third candidate the ratio of
agreement/disagreement is not the same as it was, because all of the issues
with which the missing candidate agrees more closely with my positions are
not included in the comparison. 

When all three are considered I might wind up with A>B>C, but if you take C
out of the equation the issues for which C was a better choice for ME than A
and B get added in to the equation for comparing A and B, and they were
"equally wrong" while C was in the mix, but I have to re-evaluate them when
only considering A and B, and they might even get different priorities.

In short, if A, B and C are all options, I might rank them A>B>C based upon
all of the issues, but if you take out B I might choose C>A on the remaining
issues because the relatively few issues I disagreed with C about have a
lower importance compared to the relatively few issues I disagreed with A
about.

To call my A>B>C in a full-ranking and my C>A in a pairwise comparison
"irrational" is not logical. It is only "irrational" in the context of a
voting system that presumes that pairwise preferences can be determined from
ranked ballots, which we know is impossible.

As far as the first point is concerned, I ask this question. Is it
"rational" to have a vote-COUNTING system that claims to be based on the
idea that it will pick the winner "as if" only 2 candidates were in the race
(the basis of Condorcet's theory) when the vote-COLLECTION method does not
ask for pairwise comparisons from the voters?

If you use my A>B>C to infer that I voted A>C you are using the counting
method to infer something I didn't say. And you'll count my vote differently
depending upon which meta-cycle -breaking method you use (Ranked Pairs gives
different results than Beatpath sometimes).

I would suggest it's much, much easier for the VOTER to express true
preferences if presented with "this, that, either, neither" explicitly for
each pairwise option. Such a vote COLLECTION method would not impair the
functionality of any vote COUNTING method (and would generally apply to any
to any method, including Approval). In Condorcet-based methods the results
would be much more accurate than any method-specific interpretation of the
matrix.

Quite frankly, I think that the idea that you can use a pairwise matrix to
COUNT votes but not to COLLECT votes is, if not "irrational", at least
"illogicical."

If cycles in personal preferences can be ignored because "they are
irrational" then any method that allows cycles to occur in the "counting"
part are equally irrational. That's why in the classical example the
Condorcet Winner is disapproved by 89 percent of the voters.