# Fairness, votes against, and Condorcet(x)

Steve Eppley seppley at alumni.caltech.edu
Thu Apr 18 19:45:04 PDT 1996

```Bruce A. pointed out that there's a family of Condorcetish methods in
which the votes against a candidate include a term xq(i,j), where q
is the number of voters who rank i & j equally and x is a coefficient
ranging from 0 to 1.  Bruce suggests that the three reasonable values
for x are 0, .5, and 1, and he'd like to call all three of these
methods Condorcet methods.

Mike O. prefers that only the x=0 version be called the real Condorcet.

Mike also has been using a Dole,Clinton,Nader example where the
following is one of the variations:

46 Dole > Nader > Clinton
20 Clinton
34 Nader > Clinton > Dole

The pairings        Against the pair-loser (using x=0)
-----------------   ----------------------------------
Dole    < Clinton   54 against Dole
Clinton < Nader     80 against Clinton

The context for Mike's example was that the Dole voters were trying
to steal the election by reversing their sincere Clinton>Nader
preference.  But suppose their votes aren't a reversal but a sincere
ordering?  Is it still "fair" that Nader wins?

Since the Clinton voters are indifferent between Dole and Nader, why
should the Clinton voters' votes still be counted against Dole and
Nader if Clinton can't win?  They don't hurt Dole and Nader equally
in Condorcet: they hurt Dole's worst defeat but not Nader's worst
defeat.  Is this what the Clinton voters want?

Compare with the following example, in which the 20 Clinton voters
split evenly instead of all being indifferent:

46 Dole > Nader > Clinton
10 Clinton > Nader > Dole
10 Clinton > Dole > Nader
34 Nader > Clinton > Dole

The pairings        Against the pair-loser
-----------------   ----------------------
Dole    < Clinton   54 against Dole
Clinton < Nader     80 against Clinton

A circular tie, which Dole wins with only 54 against.

Perhaps it would be "fairer" to resolve circular ties using an
elimination scheme based on worst pairwise defeat:  Clinton, with 80
against, gets eliminated first.  Dole wins in both examples.  Which
method is fairer?

I realize that this elimination scheme might open the door to the
tactical voting which Mike alluded to, and rightly wants to negate.
(If so, I'd like to hear more about it.)  But is denying tactics a
sufficient reason to award Nader this victory?  I'd prefer a more
fundamental reason to declare the Nader victory fairer than a Dole
victory.  (The Clinton voters can already punish the Dole voters'
sincere indifference.)

I'm also wondering if there's a connection between this issue and
Bruce's other Condorcets.  If x=.5, then there would be 56 votes
against Nader in his worst defeat in the first example above, just
as in the second example.  Condorcet(.5) and Condorcet(1) would award
the win to Dole instead of Nader.  It's not clear to me why x=0 is
more reasonable than x=.5 or x=1.

Maybe each voter should be asked to specify, for each i=j pair,
what value of xij to use.  :-)

--Steve

```