# Condorcet's mathematical built-in bias

donald at mich.com donald at mich.com
Wed Dec 4 04:58:45 PST 1996

```Greetings Methods list,

DEMOREP1 wrote:
Thus, there can be a compromise candidate (such as M) who beats each other
Can IRO fans comprehend such compromise candidate possibility ?

Donald writes:
Not so fast DEMOREP1 - your success of the so called compromise candidate
depend in part on built-in mathematical bias.

Condorcet's pairing has a mathematical built-in bias that favors the low
candidate. On the first selection all candidates have a mathematical equal
chance at receiving votes. Each are free to receive between zero to one
hundred percent of the votes. But on the second and further selections
there is a bias that favors the low candidate of the first selection. On
the average the low candidate will receive more votes on the second
selection than the other candidates. Consider this example:

(  ) A            (  ) B          (  ) C
(  ) AB           (  ) BA         (  ) CA
(  ) AC           (  ) BC         (  ) CB
--------          --------        --------
49  A             41  B           10  C

Now - if one hundred people were to fill in the amounts, at random, that I
have left vacant so that the final totals will be  49 A  41 B  10 C  we
will find that on the average candidate C is going to receive more votes in
the second column of selections because C has more possible second
selections chances - 90 possible vote selections for C vs 59 for A and 51
for B. This is a built-in mathematical bias. Candidate C cannot help but to
gain more - no place to go but up.

Candidate C may have been the lowest on the first tally but as each
selection is used candidate C will be closing the gap with the others.
Condorcet's bias is part of the reason when pairwise selects the last
candidate to be the winner.

Another way to see this is as follows: Suppose there was a plurality
election in which no candidate received a majority and the election boss
told the voters: "We have no winner so you people are required to vote
again but this time you cannot vote for the same candidate - you must vote
for some other candidate."
Well - under these conditions the low candidate cannot help but get more
votes than he got in the first election - maybe even enough to win - but
running elections like this is absurded - like Condorcet is absurded.

It is improper to add second selections to first selections - Condorcet is
improper.

The voters of the last candidate are in the position of deciding which of
the two leading candidates will be the winner - but they and you have no
right to assume that the low cndidate should be the winner.

Donald,

```