[EM] 02/06/02 - Adam's 02/02 example of three equalcandidates:

[Bart Ingles]

Adam Tarr wrote:
> 
> That's not really what the example was about.  I assumed a
> right,middle,left candidate (Bush, Gore, and Nader respectively in the
> example).  Gore voters broke both ways in their second choice, but not Bush
> or Nader voters.  The only time I mention a Bush or Nader voter voting for
> the other is at the end when I mention that a Bush voter could vote for
> Nader FIRST in an effort to win the election for Bush.
> 
> The example is not that far-fetched.  The only thing about it that was
> "rare" was that all three candidates were very close to one another in
> first preferences.

Minor point -- a close 3-way race is not necessary for this example to
show the problem you mention with IRV.  It's generally only necessary
that (1) the middle candidate has fewer 1st-choice votes than the two
"extreme" candidates, and (2) the extremes have less than 50% of
1st-choice votes.

If these conditions hold, then either the left or right voters will have
been better off voting for the lesser-evil centrist, depending on how
the center candidate's 2nd-choice votes break.

And then there's the situation where almost all of the voters are better
off voting for the lesser-evil (when there is a near-tie between the two
extreme candidates):

              --utility/rating--
      100                50                   0
      -----------------------------------------
45     A            B                         C
 5     B                 A                    C
 1     B                 C                    A
49     C            B                         A

A and C are in a dead heat, so that they can't predict whether their
favorite, or least favorite, will win.  They are both better off ranking
B first, rather than gambling on the outcome.  So 94% of the voters in
this election are better off ranking insincerely.

(I made A and C's 1st-choice totals slightly different to illustrate
that A and C need only be close in the final round for this situation to
exist -- so there's only one near-tie in this race, which is not all
that improbable).