[EM] diagram for IRV

Forest Simmons fsimmons at pcc.edu
Fri Jun 8 10:01:03 PDT 2001

Here's a diagram that I used in a FairVote Oregon meeting to help explain
why the spoiler effect is almost inevitable in the evolution of a third
party under the auspices of IRV: 

percieved  2nd place

   |   CW loses       :
   |   first round    :  win both rounds
   |                  :
   |                  :
   |        _         :  win first round only
   |        /|        :
   |       /          :
   |start /           :
          perceived first place viability

The horizontal and vertical axes represent percieved first round and
second (last)  round "viability" of the third party candidate, assuming
that the race boils down to a three way race. 

The dotted lines represent the win/lose cutoffs for the two respective

In the early days of growth of the third party, its candidate will be
represented by a point near the lower left of the diagram. As the third
party gains support in subsequent elections its candidate will move in a
general north easterly direction.

If the path happens to cross the two dotted lines simultaneously (in the
upper right corner of the rectangle), then everything is hunky dory.  But
how likely is that?

It is much more likely that your third party favorite will cross the
vertical dotted line before it crosses the horizontal dotted line or

The first case (vertical before horizontal) comes up, for example, when
your second choice still has more final round viability than your first
choice (i.e. the third party positioned on the diagram), but not enough to
survive the first round without your first place support. 

This is the case when you have clear strategic incentive to vote your
second choice over your favorite.

As I have explained elsewhere, this case is more likely in the natural
evolution than the other case.  In a nutshell, the third party grows at
the expensive of its natural allies, without whose support it cannot
survive the final round.

The "horizontal before vertical" case suffers from other problems. Your
first place choice actually has enough strength to beat the IRV winner,
but doesn't make it to the final round because of lack of first place
support.  This can be caused by a media shutout like the one suffered by
Nader, or it can be caused by fear of the two extreme candidates that the
voters think they have to vote against as their top priority, or whatever.

It is in this case that your third party favorite might be the Condorcet
winner, but still loses the election.

The purpose of this diagram is to counteract the claim of IRV advocates
that IRV's problems are only apt to occur in hypothetical examples. The
diagram shows that the win region is separated from the start region by
two dotted lines, just as surely as conception and birth are separated by
a period of painful labor in a time line diagram of pregnancy.

There is a negligible probability that both dotted lines will be crossed
simultaneously, so IRV is almost surely going to give one of the
unsatisfactory results that comes from crossing one of the lines before
the other.

This diagram doesn't prove that IRV picks the wrong winner, but it does
provide a graphical explanation of why the spoiler problem (especially) is
not just a negligible possibility.


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