# Condorcet pairs on the ballot

Steve Eppley seppley at alumni.caltech.edu
Fri Nov 22 12:43:31 PST 1996

```Donald D wrote:
>If we have an election we have votes to tally - either by hand or by
>a computer. Do you have some new way in which you do not have to
>collect them into sums?

vote-sums, which are a specific and unnecessary kind of sum.  Please
stop behaving so foolishly.

If the tally method is a pairwise method, all that has to be tallied
are two "pair-sums" for each pairing.

There's no need to tally "vote-sums" unless there's no room to store
the raw ballot data. (A \$20 2GB tape has enough room to store the raw
data of a huge election, by my calculations.)

It's possible that it would be more efficient to tally vote-sums as
an intermediate step to speed up the pairwise processing, but I
suspect that tallying vote-sums would itself be a very slow step.
(We've gone over this before issue before.  Did you skip reading
those messages?  Are you going to skip this as well, and expect us

With N candidates, there are (N x N-1) pair-sums to tally.  It's
convenient to store these in a square NxN array.  Each element [i,j]
of the array is a pair-sum which indicates how many people prefer
candidate i more than candidate j.  So the [i,j] and [j,i] elements
taken together indicate which candidate won the i vs. j pairing and
by how much.

Each element of the pairings array can be calculated without using
vote-sums.  Each ballot can be processed into the array by
incrementing each array element which needs to be incremented.

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

```