# N minus 1 or Reverse Plurality

DEMOREP1 at aol.com DEMOREP1 at aol.com
Sat Jul 25 20:15:34 PDT 1998

```Another limited Approval type tiebreaker is N minus 1.

If there is a circular tie, then change the number of ranked votes to unranked
The choice having the lowest number of votes in the first N minus 1 places
would lose or the plurality choice in last place loses.    Redo the head the

Truncated choices would be in a last place tie.
Example a voter votes BE with 5 choices--
B > E > (blank) > (blank) > (A=C=D)

The major point is that the first N minus 1 ranked votes have a continuing
effect as the tiebreaker.  However, such a tiebreaker would seem to have the
major strategy problems of simple Plurality.

Which unranked majority has the least strategy problems as a circular
tiebreaker (especially with 4 or more tied choices)----

Left to right (Bucklin)
Halfway left to right or right to left (N/2 or halfway Bucklin)
Right to left (Reverse Bucklin) ?

The above assumes my standard YES/NO vote on candidates in executive and
judicial elections but is not used in p.r. elections.

It should be noted that having a choice removed in a circular tie is the same
as if the remaining choices are to be elected (e.g. 5 to be elected, 6 choices
in a tie).

Example (from  Re: Condorect sub-cycle rule, Sat, Oct 4, 1997 12:18 PM EDT by
Markus Schulze)--

25 BCDFEA
24 CDFEAB
20 ABFECD
15 EABCDF
4 ECABDF
100

A:B=67:33
A:C=35:65
A:D=51:49
A:E=20:80
A:F=51:49
B:C=68:32
B:D=72:28
B:E=45:55
B:F=76:24
C:D=100:0
C:E=49:51
C:F=80:20
D:E=49:51
D:F=80:20
E:F=31:69

A>B>C>D>F>E>A

First 5 choices
A  75
B  76
C 100
D  80
E 100
F  69 loses  (F is the plurality in last place)
500

A:B=67:33
A:C=35:65
A:D=51:49
A:E=20:80
B:C=68:32
B:D=72:28
B:E=45:55
C:D=100:0
C:E=49:51
D:E=49:51

D is a Condorcet loser.

A:B=67:33
A:C=35:65
A:E=20:80
B:C=68:32
B:E=45:55
C:E=49:51

E is the Condorcet winner.

If Reverse Bucklin is used however, then--
Last 2     Last 3

A   49        57
B   28        32
C   20        15
D   47        51
E    25       69
F    31       56
200      300
No majority against in last 2 places.
E has highest majority against in last 3 places.

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