# Arrays

DEMOREP1 at aol.com DEMOREP1 at aol.com
Thu Apr 18 01:55:59 PDT 1996

```For the folks who are/were not math majors- an array is like a larger or
smaller checkerboard with rows and columns with each checkerboard square
being called a cell. An array is sometimes called a matrix. An array may also
be called a spreadsheet.

Thus in making Condorcet pairs an array/matrix/spreadsheet looks like---
Example (in 12 point Monaco)
5 Candidates- A, B, C, D, E

A   B   C   D   E
A    x   4   10  9   7
B    5   x   7   6   4
C    3   11  x   2   3
D    8   4   2   x   3
E    14  3   0   2   x

In Condorcet pairings (a.k.a. pairwise) the cells in the candidate vertical
columns may be deemed the cases when a voter ranks such candidate over the
candidates in the horizontal rows. Where C is the number of candidates, there
are (C x C)- C or C x (C-1) cells (candidate combinations). Thus, for
example,  B beats D in 4 votes, D beats B in 6 votes or D beats B by a net 2
votes.

Technically only one half of the matrix (the upper right or lower left part)
is needed with each cell being split into two parts with the votes for each
of the candidates ranked over the other candidate. There then would be (C x
(C-1))/2 cells (candidate combinations). Thus, in the B,D cell there would be
4,6.

```

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