Condorcet pairs on the ballot

[Steve Eppley]

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? 

Now you're asking about sums, in general.  But we were talking about
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
to answer your same question again and again?)

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)