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

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