# From Steve's Wasted non-rankings

Steve Eppley seppley at alumni.caltech.edu
Thu Dec 5 12:46:43 PST 1996

```Donald D wrote:
>Steve wrote:
>>How about an example, Donald, which shows why it's rational for
>>voters to vote for only one?
>
>Sure Steve - how about we use an example YOU put forward awhile back.
>
>                      46 AB
>                      20 B
>                      34 CB
>
>EVERYBODY - please note that Steve had one bloc of voters not
>making a second selection - that is the bloc that ends up winning
>this Condorcet election. This point will not go un-noticed by the
>voters - they are not stupid.

The point which has gone unnoticed by Donald (no matter how many
times it's posted here) is that only the *middle* bloc, if they're
sure they're the middle, doesn't hurt themselves by truncating.
(Truncation won't be the norm even for the middle bloc.  See
examples 5a, 5b, and 5c below.)

I expect most voters are not stupid enough to miss this point.

>Now suppose some of the A and B voters also decided not to make a

I presume that's a typo and you intended to write "A and C voters".

>second selection. B would lose if half of the voters for candidates
>A and C refused to make a second selection.

Ah, but who would win?  If the A voters don't rank B second, they're
helping C and not helping A.  Maybe Donald would do that, but few
would be this stupid.  If the C voters don't rank B second, they're
helping A and not helping C.  Few would be this stupid.

By not ranking a second choice, they're helping the candidates they
dislike more than their second choice.  The following family of
examples illustrate this.

1) The original example, tallied:
46 AB
20 B
34 CB
A    B    C
A         46   46L
B    54L       66L
C    34   34
---- ---- ----
score: 54    0   66   (Lower score is better.)

2) Like example 1 but half the A voters truncate:
23 A
23 AB
20 B
34 CB
A    B    C
A         46   23
B    54L       43L
C    34L  34
---- ---- ----
score: 54    0   43   (Compare with example 1.  The A voters foolishly
helped C by truncating.)

3) Like example 1 but half the C voters truncate:
46 AB
20 B
17 CB
17 C
A    B    C
A         46L  46L
B    37        66L
C    34   34
---- ---- ----
score:  0   46   66   (Compare with example 1.  The C voters foolishly
helped A by truncating.)

4) Like example 1 but half the A and C voters truncate:
23 A
23 AB
20 B
17 CB
17 C
A    B    C
A         46L  46L
B    37        43L
C    34   34
---- ---- ----
score:  0   46   46   (The C voters foolishly helped A by truncating.
It wasn't the A voters' truncation which helped
A beat B, as a comparison with example 3 shows.)

Donald thinks the B voters' truncation is what elected B.  He should
do the math.  Here are three scenarios:

5) Like example 1, but the B voters don't truncate.
5a) Assume all the B voters like A better than C:  B>A>C
46 AB
20 BA
34 CB
A    B    C
A         46   66L
B    54L       66L
C    34   34
---- ---- ----
score: 54    0   66   (Same scores as in example 1)

5b) Assume all the B voters like C better than A:  B>C>A
46 AB
20 BC
34 CB
A    B    C
A         46   66L
B    54L       46L
C    54   34
---- ---- ----
score: 54    0   66   (Same scores as in example 1)

5c) Assume half the B voters like C better than A and the other
half like A better than C.
46 AB
10 BA
10 BC
34 CB
A    B    C
A         46   66L
B    54L       56L
C    44   34
---- ---- ----
score: 54    0   66   (Same scores as in example 1)

These examples show how absurd Donald's argument is.  If Donald wants
to know why some of the scenarios posted in EM show the middle voters
truncating, he should ask and not let his imagination run wild.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)

```

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