These preferences give rise to a Condorcet paradox, because A is preferred to B,
which is preferred to C, which is preferred back to A again.
No candidate is preferred to both of the other candidates by a majority.
The fact that a majority of the group prefers A to B and
a majority prefers B to C does not imply that a majority prefers A to C.
These preferences give rise to Condercet cycling because if
pairwise voting continued until a clear winner arose, the voting would never end.
It would keep cycling.
Condorcet cycling emphasizes the importance of procedure.
The person who sets the agenda can determine the outcome.
An agenda setter who wants candidate B to win would just need to have an initial
vote between A and C, and have the winner of that contest,
which would be C, then face off and lose to candidate B.
The Condorcet paradox is also related to the Arrow impossibility theorem,
which proves that there is no satisfactory voting method, or
for that matter a nonvoting method, of aggregating preferences.
Ken Arrow, by the way, is a real hero of mine in economics.
There was a time when he left a message
on an old time answering machine asking me to give a paper, and
I still have that tape recording of his voice.
That's how much of a fanboy I am.
The third perversity I'm gonna talk about is Simpson's Paradox,
which has direct application to questions about how to best test for discrimination.
The 11th Circuit wrote that the paradox raises the possibility of quote,
illusory disparities in improperly aggregating data
that disappear when the data are disaggregated, unquote.
For example, scholars analyzing 1973 admissions data from
the University of California at Berkeley uncovered quote,
a clear but misleading pattern of bias against female applicants, unquote.
Because the uncontrolled aggregate analysis showed that women applicants
have an lower overall acceptance rate than men applicants,
even though many of the departments admitted women at a higher rate than men.