[EM] paradigms...

[Jobst Heitzig]

Dear colleagues!

Most of you will have noticed the ongoing discussion about cyclic
preferences I must admit to have started.

I don't think we should pursue that discussion further but instead have
a serious discussion about our *paradigms*.

What I mean by paradigm is this: From the discussion I think I
understand that there's mainly two interpretations of what a preference
is, and we should be aware of this ambivalence.

To me, the most basic notion any theory of elections or group choice
deals with is that of individual preference. Now, when I think about how
I myself usually make up my mind about what I want and what I don't
want, I come to the conclusion that at the core of this are
*comparisons*. I compare the options. How do I do that? I do it by
looking at what the differences are. And those differences are
differences between *pairs* of options. At the end, it frequently
happens that one option seems superior to all others, but that is still
a result of pairwise comparisons. It my also happen that I don't find a
single best option although I might well be able to decide between most
pairs of options.

Others may feel that they don't perform pairwise comparisons but look at
 all options simultaneously and find that some of the options sticks out
positively. So they directly find the best option.

These two versions of "preference" would be no problem if they could be
translated into each other. The problem is that they *cannot*!

I and many others, including researchers from various disciplines, have
shown that pairwise preferences do not always give a unique first
choice. On the other hand, Paul has tried to clarify that it is not
always correct to infer pairwise preferences from a ranking which
answers the question "what would be your first choice if the options you
have already ranked were unavailable".

Let me give an example which I hope is quite realistic. Suppose there
are two issues X and Y which I find equally important. On each issue,
there are two possible positions X1,X2 resp. Y1,Y2. Assume further that
there are candidates for each possible combination of these positions,
that is, candidates
	A: X1,Y1	B: X1,Y2
	C: X2,Y1	D: X2,Y2.
Now, suppose I'm quite confident that X1 is better than X2, but am very
unsure whether position Y1 or Y2 is better. That is, I'm an X-expert but
a Y-idiot. So, I would like to have A or B, depending on whether Y1 or
Y2 is better, which I don't know. Hence all I can say is that A>C and
B>D while all other pairwise comparisons will depend on issue Y which I
would rather have others decide upon. In a Hasse diagram, my pairwise
preferences look like this:

	A	B
	|	|
	C	D

Now, when I'm asked to make the whole decision alone, that is, which of
the four I would choose, I can only say, A or B. Hence, on a plurality
ballot, I would probably throw a coin and mark either A or B. Suppose
the coin tells me to mark A. Now, when I'm then asked which I would
choose when A was unavailable, I would say, B or C. Again throwing a
coin, I would consequently fill in B or C as my "2nd choice". Suppose
the coin told me to fill in B. Then I would be asked which I would
choose when both A and B were unavailable. I would fill in C or D with
equal probability, let's assume C. So my "ranking" would look like this
in the end: A>B>C>D. In an IRV setting, this makes sense I would say,
because IRV is in the same spirit as plurality, talking about "1st
choices" and so on. But in a pairwise setting such as Condorcet, such a
ballot is misleading since the Condorcet method would try to infer my
original pairwise preferences from the ranking, leading to the three
wrong assumptions A>B, A>D, B>C. This is because the ranking was
constructed by me for a different purpose, answering questions about
first choices instead of pairwise comparisons!

To put it positively: The nice thing about group decisions is that they
do *not* require each member of the group to have perfect information.
Most of the synergy in group decisions comes from the fact that one can
abstain from partial decisions, trusting the information other members
of the group have. In the example above, I can confidently trust in the
fact that other voters will know which of Y1,Y2 is better for society so
that I need not decide on that. But it would be nonsense to force me to
either keep my information about X secret or to pretend to have
information about Y which I don't have.


So, what I suggest is that we be aware of the different definitions of
preference and that we don't propose combinations of ballot and method
which belong to different realms.

Hoping to start some *constructive* discussion on this,
Jobst