First minus last tiebreaker

Fri Oct 30 15:42:43 PST 1998

Mr. Ingles wrote in part in Re: More Standards-

Even if the voters are completely sincere and rational, then to the extent
that they vote along ideological or partisan lines the "best candidates" will
be the same as the "worst candidates" when looking at the raw returns.  For
example, suppose two major factions of equal size vote ABCD and DCBA for
purely ideological or partisan reasons.  You end up with candidates A and D,
who are tied for both first and last place. In this case, all this really
means is that you have redundant information in the last half of the list.
D- The above suggests yet another head to head tiebreaker if there is/are no
Condorcet winner(s)--

subtract the opposite place votes (votes in 1st place minus votes in last
place, votes in 2nd place minus votes in 2nd to last place, etc.) to get net
results (First minus last tiebreaker- FMLT).


 9  DCBA
1 A, 1 B, -1 C, - 1 D
D and C lose, having net negatives. A wins.

The more general case, of course, for four choices (with all of the various
possible combinations of a voter voting for 1, 2, 3 or 4 choices) would be
    1-L    2-2L   Total
A   NA1  NA2      NAT
B   NB1   NB2      NBT
C   NC1   NC2      NCT
D   ND1   ND2      NDT

Each first minus last (1-L) amount (N1, N3, N5, N7) is less than half of the
votes- otherwise there would be a Condorcet Winner (CW).

Each N amount is positive, negative or zero.
One of the totals should be the highest positive (for a single winner case) or
highest positives (for a multiple winners case- such as 3 judges) in most
Truncated choices would be in last place- such as C > D > blank > (A=B)

If there are ties in the totals then back up 1 level.

Thus, each voter could vote his/her--
desired choices  compromise choices  opposed choices

A majority's desired choice(s) would presumably have net positive amounts.

The above assumes my standard YES majority approval of the choices going head
to head- such that the compromise choices of minority voters would move upward
in doing the head to head math.
Voter X votes
F > E > C > B > D > A
Only A, B, C and D get YES majorities of all the voters. 

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