Tie breakers

[DEMOREP1 at aol.com]

One form (if not *the* form) of plain Condorcet tie breaker in a single
winner race computes the worst head to head defeats of the candidates in a
circular tie. The candidate with the lowest votes against him/her is deemed
the winner.

I have noted earlier and repeatedly that a first choice candidate in
Condorcet may be regarded as only slightly less absolutely evil than another
candidate. Example---  a absolute minus 98 percent candidate (X) is only
relatively less evil than a absolute minus 99 percent candidate (Z).

Thus, I suggest having a voter vote zero for all candidates that the voter
does not want elected. Example-- the voter could vote zero for both
candidates X and Z. All candidates with a majority zero vote against them
would lose. Thus, any surviving candidates would be initially ranked (1, 2,
3, etc. ) or unranked (blank) by the majority.

If the above tie breaker is to be used, then it should be modified to include
the zero votes in the votes against each candidate in computing the defeats. 
-------
The question of which tie breaker in head to head rankings is *best* is
another matter.
An array (spreadsheet) of the various candidate combinations will be
produced.
Example (assuming each v to be the votes which rank the candidate at the top
over the candidate at the left)
     A   B    C   D   E
A   x    v    v   v   v
B    v   x    v   v   v
C    v   v    x   v   v
D    v   v    v   x   v
E    v   v    v   v   x
Another summary would show the combinations with net results
such as
B A  20  15     5
B C  12   20   -8
B D  11   11     0
B E   21   9     12


If no candidate beats each other candidate head to head, then there must be a
tie-breaker. 
If the zero vote is being used, then each of the remaining candidates will be
ranked (1, 2, 3, etc.) or unranked (blank) by a majority of the voters.
Some candidates may lose all of their head to head combinations.
Each of the remaining candidates will tie, beat or lose to each other
remaining candidate head to head.

A tie breaker might be in one step (all but 1 candidate to lose) or
multi-step (1 or more candidates to lose at a time in a repetitive process).

Some tie breakers among the candidates in the tie breaker are obviously-- 
(a) the candidate with the lowest number of first choice votes to lose,
(b) votes for (in greatest win, in lowest win, in average win), 
(c) votes against (in greatest defeat, in lowest defeat, in average defeat)
(d) some combination of votes for and votes against (including an average of
votes in all pairings)
(e) limited approval (limiting the rankings- counting only 1 and 2 rankings
to produce a majority winner, counting only 1, 2 and 3 rankings to produce a
majority winner, etc.)
(f) the number of candidates beaten (and the number of candidates who beat a
given candidate).

Any tie breaker should be made usable for both single winner executive or
judicial elections and multi-winner executive or judicial elections (e.g. 2
or more sheriffs or judges in a given area).