Condorcet pairs on the ballot

Steve Eppley seppley at alumni.caltech.edu
Tue Nov 19 08:55:09 PST 1996

```Donald posted another joke proposal without a smiley:

>I have a very good suggestion on how to improve the pairing in
>Condorcet elections.
>
>I suggest that we put the pairs on the ballot instead of
>constructing the pairs after the election.

This would make the ballot huge is there are a reasonable number of
candidates running.  The number of pairings goes as the square of the
number of candidates.  (N * N-1 / 2)

Rather than make things easier for the voters, it would make voting
far more tedious.  Rankings are a very convenient shorthand for the
voters, and they have the same meaning if we make the reasonable
assumption that preferences are transitive (i.e., A>B>C implies
A>B, B>C, and A>C).

>The first advantage of doing the pairs on the ballot is that we do
>not have to deal with the many combinations of Vote-Sums.

Only someone who can't get Instant Runoff out of his fevered brain
would tally vote-sums.

>A four candidate election would have as many as sixty-four
>combinations - two hundred for a five candidate race. But, by
>putting the pairs on the ballot the pairing results are given
>directly without dealing with any combinations of Vote-Sums.

A 4-candidate election would have 4*3/2 = 6 pairings for each voter
to mark.  A 10-candidate election would have 10*9/2 = 45 pairings.
The voter can save a lot of time by using the shorthand implied by
rankings.

>The second advantage is that this way is more honest because the
>voters would be actually comparing the candidates one to one instead
>of merely indicating second choices.

No, there'd be less honesty by letting voters vote each pairing
separately, if you accept that honest votes obey the transitive
assumption.

>Third: If the people vote for the pairs directly maybe we will have
>fewer circular ties.

Because it would be so tedious, voter turnout would fall and those
who do vote would leave a lot of pairings unvoted.  The number of
circular ties would increase, not fall.

>Some of you have blamed the voters for circular ties, I do not
>know if this is true, but this way the voters may show more
>responsibility. We may be able to get the ties down below fifty
>percent.

It's not a question of blame.  It's a question of whether society is
so divided that there isn't a satisfactory compromise running.

If there are circular ties, they'll be among the few candidates close
to the political center.  There's no magic in "50%".

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

```