[EM] paradigms...

[Dave Ketchum]

I will try to catch up by responding to several.

On Tue, 07 Sep 2004 09:23:34 +0200 Jobst Heitzig wrote:

> 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!


BIG thing I get from the above is a headache.  We are electing ONE PERSON, 
such as a mayor or governor.  Retreating for the moment from whatever you 
may be saying about pairwise:
      Given an IRV ballot I proceed as you describe above (except, if I am 
a serious voter, I will likely do less coin tossing).
      Given a Condorcet ballot I proceed in EXACTLY the same way, 
expecting IDENTICAL results, even though the debating may use different words.
      Correction - liking X1 better than X2, I do not need a coin toss to 
prefer B over C!
      Also, not caring as to C>D vs C<D, I should not vote a nonsense 
implied preference between them.
      Results can be different, for sometimes IRV does not look at all 
that a voter says, and sometimes this matters.

     Condorcet can easily permit voting A=B, which I will vote if 

permitted, since it better matches my desires.  IRV may permit such voting, 

but its counting is more difficult.
> 
> 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.


But, in your demonstration voting, you indicated a preference about Y that 
you admit here was nonsense.

> 
> 
> 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.


IF you manage to state preferences that I would see as mutually 
iconsistent, we then have the problem of doing resolution in an actual 
election.

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

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On Wed, 08 Sep 2004 22:58:48 +0200 Jobst Heitzig wrote:

> you wrote:
> 
>> However, let's assume that the ranking system in question allows you
>> to, rather than flipping a coin, simply rank A and B equally.  In
>> other words, declare them a tie.
> 
> 
> That would be fine as long as I could really do so! But as long as I can
> only express rankings I cannot do as you suggest! In a ranking, I cannot
> tie A=C, B=C, A=D, and B=D and simultaneously express A>B and C>D.
> 
Agreed that the target you offer is impossible, BUT, it has nothing to do 

with whether the sentence you are responding to is valid - and I see 

validity there.

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On Wed, 8 Sep 2004 19:22:11 -0500 Paul Kislanko wrote:


> I might think my hypothetical voter is illogical, too, but that's not the
> question. The question is can you reconstruct the original ballots from a
> pair-wise matrix? If not, then you can't claim a result based upon the
> pair-wise matrix is the "will of the people."
> 
My head aches again!  If I sum "ballots" in a "pair-wise matrix" I have 

simply done one step in determining the "will of the people" - but I sure 

DO NOT PROMISE to reconstruct any individual ballot from that sum.

-- 
  davek at clarityconnect.com    people.clarityconnect.com/webpages3/davek
  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
            Do to no one what you would not want done to you.
                  If you want peace, work for justice.