Truncated Votes clue
DEMOREP1 at aol.com
DEMOREP1 at aol.com
Sat Jul 18 14:47:16 PDT 1998
Truncated votes may provide a clue to a head to head circular tie tiebreaker.
The very simple case (i.e. Plurality)--
N1 A > blank > (B=C)
N2 B > blank > (A=C)
N3 C > blank > (A=B)
The last place totals-
A N2 + N3
B N1 + N3
C N1 + N2
One of such last place totals for a choice will be the highest (assuming no
ties). Should such choice lose ?
Should expanding upon Plurality change the loser ?
N1 A > B > C
N2 A > C > B
N3 B > A > C
N4 B > C > A
N5 C > A > B
N6 C > B > A
Assuming majority acceptability for each choice and a circular tie, then the
last 2 place votes are--
A N3 + N4 + N5 + N6
B N1 + N2 + N5 + N6
C N1 + N2 + N3 + N4
One of such 2 last place totals for a choice will be the highest (assuming no
ties). Should such choice lose ?
The above applies to 4 or more choices.
N1 A > blank > blank > ... > (B=C= ... =Y=Z)
etc.
N26 Z > blank > blank > ... > (A=B= ... =X=Y)
Expanded into a circular tie---
N1 A > B > C > ... > Z
N2 A > C > B > ... > W
etc.
N26f Z > Y > X > ... > A (26f= 26 factorial)
Note the possibility of clones (i.e. if N1= N2, then B and C are twins) (but
very unlikely in a large public election).
The sum of the votes in the last P places will produce one or more majorities
against. Should such choice(s) or only the highest majority against choice
lose successively ? See also the Reverse Bucklin series.
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