Tiebreakers 2

[DEMOREP1 at aol.com]

Mr. Schulze's examples of Re: Near Clone Sets
Date:  Wed, Jun 10, 1998 8:05 AM EDT raise some more observations. 

Assume 5 choices in a circular tie. There are 10 groups for each pairing where
N = number of voters voting for the indicated ranking. The dashes indicate the
various combinations of the other 3 choices in the tie.

N1    A  B  -  -  -
N2    A  -  B  -  -
N3    A  -  -  B  -
N4    A  -  -  -  B
N5    -  A  B  -  -
N6    -  A  -  B  -
N7    -  A  -  -  B
N8    -  -  A  B  -
N9    -  -  A  -  B
N10   -  -  -  A  B

The reverse (switching A and B) would be another 10 groups (N11 to N20).

N11    B  A  -  -  -
N12    B  -  A  -  -
N13    B  -  -  A  -
N14    B  -  -  -  A
N15    -  B  A  -  -
N16    -  B  -  A  -
N17    -  B  -  -  A
N18    -  -  B  A  -
N19    -  -  B  -  A
N20    -  -  -  B  A

Note that each choice is in each vertical column 4 times (i.e. one less time
than the number of choices).
 
Simple Approval voting is the defacto sum of N1 to N10 plus the case where a
choice is last but acceptable- i.e. the reverse of the N1 to N4 groups (i.e.
N14, N17, N19, N20). 

The column totals would be
A     NIA  N2A  N3A  N4A  N5A
B     N1B  N2B  N3B  N4B  N5B

N1A = N1 + N2 + N3 + N4, 
N2A = N5  +N6 + N7 + N11, etc.

The sets of 20 combinations and totals involving the other candidates are
similar.

The general situation is that a minority cannot expect to win. Thus, a
minority will generally want to choose a compromise choice (the lesser evil of
the majority choices) after voting for its favorite minority choices who lose.

Example-- The voters for candidates W, Y and Z are in a minority.  The voters
for candidates G, H, K are in a majority. If there is a YES/NO majority vote
on each candidate, then W, Y and Z will presumably lose. Assume candidate H is
the lesser of 3 evils so far as the W, Y and Z voters are concerned. The
fourth choice H votes on the ballots of the W, Y and Z voters would become
first choice votes after W, Y and Z lost.

Bottom line-- 
1. Majority YES/NO vote on each choice. 
2. Do Head to Head for each choice getting a majority YES vote.
3. If there is no Condorcet head to head winner, then sum the first plus
second choice votes, the first plus second plus third choice votes (if
necessary), etc. to get a majority.

Note- If a choice has a majority of first choice votes, then he/she is a
Condorcet winner obviously.

Other possibilities--

Would successive dropping of votes based on column separations have any
meaning as a tiebreaker ?

N10   -  -  -  A  B
N8    -  -  A  B  -
N5    -  A  B  -  -
N1    A  B  -  -  -

N9    -  -  A  -  B
N6    -  A  -  B  -
N2    A  -  B  -  -

N7    -  A  -  -  B
N3    A  -  -  B  -

N4    A  -  -  -  B

Or, successively drop the lowest line number (e.g. assume N7 is lowest) ??

Would successive dropping of votes based on choice levels have any meaning ?

A     NIA  N2A  N3A  N4A  N5A   Total of N1A to N5A
B     N1B  N2B  N3B  N4B  N5B   Total of N1B to N5B

That is, drop the N5 votes from the totals (with the candidate with the
highest remaining votes being the winner) ???  If a tie continues then drop
the N4 votes, etc.