Higher Majority Winner

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Higher Majority Winner

Craig Carey-2
Recent postings indicate the importance of getting a majority rule winner in
single winner elections using the Condorcet method.
Namely, (a) a majority disapproval vote will get rid of candidates not wanted
by an overall majority of the voters, and
(b) a candidate who is defeated head to head with each other candidate should
lose (i.e. is defeated by all head to head majorities) (the recent 3
Apples-Chocolate example).
There may be some overlapping in the above obviously but (b) should exist as
a second majority defense.

There are problems with strategic truncated voting.
Extreme Example
499 A, B
2 B
500 C
(The general extreme case is N, N-1 and 2 votes- a total of 2N + 1 votes)
Note- If there is a disapproval vote first, then -
the A and B voters combined could/would defeat C 501 to 500,
the B and C voters combined could/would defeat A 502 to 499 and
the C votes could/would not defeat B (due to second choice votes of A voters)
500 to 501 (i.e. B wins).

Note that the B voters do not vote for A (a one sided coalition).
Note that if 2 A voters truncate their ballots, that even B could/would be
defeated 500 t0 499.

If there is not a disapproval vote first, then
A beats B 499 to 2 margin 497
B beats C 501 to 500 margin 1
C beats A 500 to 499 margin 1
or a circular tie A>B>C>A.

Thus, C and A are each beat by 1 vote in their (only) defeats.
C beats A (assuming that the candidates with the equal lowest margins go head
to head again).

To discourage truncated voting (as in the above Extreme Example) I again
suggest that after a disapproval vote that each tie breaking round using head
to head Condorcet that the candidate with the lowest number of votes (first
choices plus additional choices) should lose.

If there is less truncated voting (i.e. more additional choices voted), then
a candidate with a higher plurality/majority would win.
 
In the example above, the first choice B voters (and even possibly the first
choice C voters) might be encouraged to vote second choices (possibly causing
A and C to each survive a majority disapproval test).

In a tie breaker situation among the candidates of a majority coalition, it
would seem that the candidate of the coalition with the lowest number of
votes should lose.

Note the above 2 against 1 example can be expanded- 3 against 2, 5 against 4,
etc.

I note again that one of the chief competitors to Condorcet is the top 2
runoff method (top 2 in a primary election go to a runoff primary election
(as used in several partisan elections in the U.S.) or to a general election
(as used in most nonpartisan elections in the U.S.) which respectively
produce a majority partisan nominee or a majority nonpartisan winner).

Condorcet avoids the defect of the top 2 runoff method that a eliminated
choice (third or lower) might beat each of the top 2 in head to head
pairings).
However, the Condorcet expanded remedy must try to maximize the possibility
that the winner is a majority of all voters winner.