Collective & individual "rationality" (was Re: [EM] Real usage of my site)

[Steve Eppley]

Augustin wrote:
> On Friday 27 Feb 2004 4:46 am, Eric Gorr wrote:
>> Apparently the Haifa Linux Club (Israeli Linux User Group
>> - http://www.haifux.org/) used my Condorcet voting
>> calculator to select their logo. There were 16 options
>> and 20 voters. I found it interesting that no cycles were
>> generated in this case.
-snip-
> That there was no cycle is understandable: the chosen design 
> is indeed much better than the other ones. It is actually 
> an Ideal Democratic Winner, so the outcome is 
> straightforward.
-snip-

The argument that the winner was much better than the rest 
only explains why there was a Condorcet winner (an 
alternative such that, for each of the other alternatives, 
some majority ranks it over the other).  It doesn't explain 
why there weren't any cycles among the lesser alternatives.

By the way, I counted only 15 alternatives when I pasted 
the votes Eric posted into my MAM calculator webpage. 
(My latest version of the calculator was installed today, 
linked at "http://www.alumni.caltech.edu/~seppley".)

On a somewhat unrelated subject: During the California 
governor recall election last year, there was a test of 
individual "rationality" (which I prefer to call 
transitivity, a term not as loaded).  A Caltech professor, 
Rod Kiwiet, surveyed about 1000 likely voters during the 
week before the election, and asked each voter to state a 
preference in each of the 6 pairings of the 4 major 
candidates.  Nearly every respondent stated 6 pairwise 
preferences that were transitive, consistent with some 
ordering of the 4 candidates.  The number of those who 
didn't was small enough that Rod said it could have been 
explained by typos by his staff.

What was most surprising is that Rod said such a study of 
individual transitivity in a major election had never been 
done before.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)