Accumulated Choices Tie Breaker redo

[DEMOREP1 at aol.com]

The below was sent on 5/14/96 but I did not get a copy back from the server.
It has a direct bearing on whether x = 0, 1/2 or 1 in equal ranking cases.
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Another Condorcetish tie breaker has accumulated choices. 

Assuming that majority disapproved candidates lose and there is no initial
Condorcet winner (a candidate who beats each other candidate head to head),
then the choices can be accumulated until there is a majority winner.

Example:
23 A,B
17 A,C
5 B,A
32 B,C
21 C,A
3 C,B

61 A> 40 B
60 B> 41 C
56 C> 45 A
A>B>C>A
First choices    - A 40, B 37, C 24
Second choices-  A 26, B 24, C 49

If the first and second choices are combined there is
66 A, 63 B and 73 C. C would win with the highest majority.

Note to worst defeat-lowest votes against tie breaker folks-- the winner can
be different-- B would win with the worst defeat-lowest votes against tie
breaker versus C with accumulated choices.

In effect using accumulated choices as a tie breaker is a limited approval
voting starting with the first choice level and accumulating the choice
levels until there is a majority winner.

It should be noted that if any candidate survives a majority disapproval
vote, then any choice ranking (1, 2, etc.) indicates some relative degree of
approval (compared to lower ranked candidates). 

Having the accumulated choices tie breaker would encourage voting for
additional choices (i.e. discourage truncated voting) to get a majority
winner. If a voter's first choice does not initially win, then such choice
may win with accumulated choices from other voters. A voter's second (or
later) choice may well prove effective in electing a candidate. A later
choice would take effect only if there is no majority winner at the preceding
choice level.

For multi candidate executive and judicial elections (e.g. 2 or more sheriffs
or judges) a majority candidate would win at the earliest level possible
(i.e. would not lose if outvoted at a later choice level due to unfilled
positions). The remaining position(s) to be filled would be filled at a later
accumulated choice level.

For new folk--- total approval voting (voting for all the candidates that one
approves and having the candidate with the most votes winning) has a defect
if a majority of the voters give their first choice to one candidate (who
would beat each candidate head to head). Such candidate can lose in pure
approval voting- another candidate may get more accumulated votes at the
first and all lower levels. An extreme case being --
49 X, Y
1 X, Z
45 Y, Z
4 Z, Y

50 X> 49 Y
50 X> 49 Z
X is the Condorcet winner

With approval voting--
50 X, 98 Y, 50 Z
Y is the approval winner