# New anti-spoiling method moots Gibbard-Satterthwaite?

DEMOREP1 at aol.com DEMOREP1 at aol.com
Tue Oct 28 16:47:56 PST 1997

```In Mr. Eppley's candidate withdrawal proposal there is---

Here's an example which should look familiar:

3 choices, 100 voters.
46: ACB       <--  these voters order-reversed their ABC?
10: BAC
10: BCA
34: CBA

The pairings (even if the basic method isn't pairwise):

prefer A     prefer B     prefer C
A vs B:           46L          54W
A vs C:           56W                       44L
B vs C:                        20L          80W

If the method will elect A given those votes, then candidate
C has a clear incentive to withdraw: presumably C's personal
preference order is similar to the preference orders of the
34 voters whose first choice is C.  This means that A is
C's "greater evil" and C would prefer the election of B.
If C withdraws then B will be elected since a majority
ranked B ahead of A.  Therefore C can improve the outcome,
in C's opinion, by withdrawing.

Candidate B can't change the outcome by withdrawing.  The
winner would still be A.

Candidate A wouldn't want to change the outcome by
withdrawing.
---------
D- I note again that rank order voting only shows relative support. How many
of the candidates can get majority approval (i.e. a majority of the voters
deem a candidate acceptable to hold the office) ?

In particular what makes the votes of the 46 voters who voted ACB suspect?
Any vote of any voter could be suspect as being order reversed.

One might guess that the last choice candidate of each of the voters is
unacceptable to the voter. If such was the case (i.e. the first 2 choices
indicate acceptability), then in the example
46: ACB
10: BAC
10: BCA
34: CBA
A gets 56, B gets 54 and C gets 90.

As I indicated around Jan. 1997 the obvious way to find out which candidates
(if any) have majority acceptability is a simple Yes or No vote on each
candidate (combined with the 1, 2, 3 rankings).

Candidates that get majority approval would go head to head. (In the example
A, B and C each get such majority approval- 56, 54 and 90).

Since there is a circular tie in the example, I suggest that the candidate
with the least number of first choice votes lose (in the example, B would
lose). The remaining candidates go head to head again. Thus A beats C, 56 to
44.

How many of the 34 CBA voters want C to withdraw ? How many of such 34 voters
"truly" wanted to vote BCA ?  With the massive cynicism about politics in the
U.S. I would suggest that among the last things needed is the last minute
manipulation of the election process by any of the candidates.  How much of
an uproar would there be if the likes of a Hitler or a Stalin were to be
elected by the last minute withdrawal of a Nixon or a McGovern ?

```