# Head to Head 5/23/98

DEMOREP1 DEMOREP1 at aol.com
Sat May 23 20:41:01 PDT 1998

A.  For electing a single executive/ judicial officer, there is the following
possible method-
The voters vote YES or NO on each candidate and number vote for each candidate
1, 2, etc.
The YES/NO vote is done because number voting only shows relative approval but
does not show acceptability.

Assume A, B and C each get a majority YES vote and the number voting
produces--
20 ABC
15 ACB
17 BAC
18 BCA
16 CBA
19 CAB
105 total votes

The matrix is thus
A     B         C
A      X      54 *    52
B     51      X        55*
C     53*    50      X

* = Pair Winner (left over top)
No candidate wins all of his/her pairings (i.e. there is a so-called circular
tie).

One tie breaker would be to have the candidate getting the lowest votes in
his/her winning pairings to lose repeatedly.  I am not sure if such a
tiebreaker was meant by Condorcet due to his cryptic written comments.

Thus, C would lose (53 lowest win) and A would win.

B.   The above also applies with electing multiple executive/ judicial
officers.
Example-  Elect 4 sheriffs (i.e. the 4 highest choices of a voter count in
making comparisons among 4 person groups), 9 candidates each get a majority
YES.
Assume 1 candidate (such as D) wins in all of his/her combinations of 4
persons.  Such candidate would be elected.

Assume 5 other candidates are in various tie combinations (such as DBCF,
DAFG, DACE)
Such other candidates (B, C, F, A, G) would go head to head as in part A
above.

C. For legislative bodies, there would be multiple persons elected but only 1
choice counts.

Example- elect 5 persons in a district, 10 candidates.
There is no YES/NO vote.
Assume multiple ties involving 6 candidates (with 1 candidate winning in all
of his/ her combinations.  The other 5 candidates involved in the ties would
go head to head as in part A above.  The votes for losers get transferred to
the next remaining choice.

I suggest that the winners have a voting power in the legislative body equal
to the number of votes finally received.

D.  Thus, the head to head idea can be used in all types of candidate
elections.   In all of the above computers would generally have to do the sums
in the comparisons.

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