Ranking Array Math, Part 3

[DEMOREP1 at aol.com]

A. The plurality method can be put into a matrix, as follows. Example- 3
candidates, A, B, C. The first choice votes (and only votes) for each are--

  1A  1B  1C
The first choice votes can be put into a matrix.

A  X  1BA 1CA
B 1AB  X  1CB
C 1AC 1BC  X
The two amounts in each column are the same (i.e. 1AB= 1AC, 1BA= 1BC, 1CA=
1CB). Each one (1) can, of course, be dropped to produce the standard matrix.

B. With additional choices, the choice levels can be shown, as follows.
Standard 1, 2 and 3 ranking choices are made.

 2B  2C  2A  2C  2A  2B
 3C  3B  3C  3A  3B  3A
which produces the X over Y values of

 2BC 2CB 2AC 2CA 2AB 2BA

Combining the same X over Y values produces (T= Total)-

1AB + 2AB= ABT
1AC + 2AC= ACT
1BA + 2BA= BAT
1BC + 2BC= BCT
1CA + 2CA= CAT
1CB + 2CB= CBT

The amounts are put into the standard X over Y matrix.
A  X   BA  CA  ART
B  AB  X   CB  BRT
C  AC  BC  X   CRT
CT ACT BCT CCT  GT

RT= Row Totals, CT= Column Totals
GT= Grand Total
If there is a tie (such as AB>BA, BC>CB and CA>AC), then one or more of the
values can be the tie breaker.

C. The 3 election types (single executive/ judicial, multi- executive/
judicial, and legislative (proxy proportional representation)) can each be
deemed to be deemed variations of head to head contests ----

single executive/ judicial-- which of two candidates gets the most first
choice votes plus later choices from the other candidates where the voter has
one vote for one of the candidates,

multi (M)- executive/ judicial-- which of M plus 1 candidates gets the most
first choice votes plus later choices from the other candidates where the
voter has M votes (and one vote for each of the candidates),

legislative (S fixed seats) - which of S plus 1 candidates gets the most
first choice votes plus later choices from the other candidates where the
voter has one vote for one of the candidates.