[EM] some July 4 comments

[Bart Ingles]

"John B. Hodges" wrote:
> 
> >Kevin Venzke wrote:
> >
> >I think it is comparably bad to plurality, because it still
> >encourages two-party
> >dominance.  An electoral method that can't even avoid that, in my view, isn't
> >worth the effort to implement.
> 
> (JBH) Oh, really? I'd love to hear your reasoning on that. Even
> better would be some evidence. How many significant parties are there
> in Australia and Ireland? In ELECTORAL SYSTEMS, A Comparative
> Introduction, by David M. Farrell (2001) I find mention of seven
> different parties in Australia.

Don't we have a similar number of parties in the U.S. under the
plurality system?  There must be something more to the reference.

> Since all multicandidate elections are open to manipulation, the
> "spoiler effect" under IRV is nonzero; hypothetical cases can be
> constructed where voters would find it to their advantage to falsely
> rank a major party first. But I think any honest person would grant
> that IRV drastically reduces the "spoiler effect" relative to
> Plurality.

I think a fair statement would be to say that it reduces the spoiler
effect by roughly 50% in situations where choice of an election method
matters, in other words when there a three or more competitive
candidates.  If the final round is close, then its outcome likely
depends on whether the previous round was won by the candidate most
attractive to swing voters, versus the "spoiler".

With close races in both the next-to-last and final rounds, the
probability of the race being spoiled by the 3rd candidate is
approximately 50%.  If the next-to-last round was not close, then IRV
would likely yield the same winner as either Approval or Condorcet.  If
the final round was not close, then IRV would likely yield the same
winner as Approval, Condorcet, or Plurality.

But there is another effect which could also be called a "spoiler
effect", in that the possibility of a spoiler candidate affecting the
race has an effect on which candidates participate, and whether they can
gain support.  You could say that the probability of this 2nd kind of
spoiler effect is near 100%, even though by keeping small parties small
the likelihood of the first kind of spoiler is much reduced.


> Another point: Assume Condorcet-plus-some-completion-method; instead
> of two-party dominance, should we fear one-party dominance? Condorcet
> methods strongly tend to pick centrists. Could one party stake out
> the center and sit on it, unassailable? Or perhaps, might we see a
> competition of several "center" parties each vying to be
> indistinguishable from the others, so we routinely have a choice
> between Coke and Pepsi? What incentive do "center" parties have to
> listen to/coopt the proposals of "wing" parties? Under IRV the
> "center" can be squeezed from both sides, can be eliminated if a
> "wing" accumulates more second-choice votes from the "far wing", so
> we can be confident of at least two viable and meaningfully distinct
> choices. If a "center" party exists, it will be working hard to lure
> voters away from the wings, fighting the squeeze. Every party will
> have a reason to campaign for the second-choice votes of other
> parties near them. Can this be said for Condorcet-based systems? And
> on what grounds?

I think this may be a common mischaracterization of Condorcet winners. 
A Condorcet winner is not necessarily the most centrist, at least in the
sense of the following:


52  A > B > C
 8  B
40  C > B > A

Here all of the B voters appear closer to the center than the average A
voter.  But A's support includes the voter median, so A is the Condorcet
winner.

With multiple parties competing in an Approval or Condorcet election,
you are more likely to see something that looks like a Venn diagram with
a small amount of overlap in the center, rather than a bunch of
identical centrist parties competing for the same base.  Candidates need
to differentiate, if for no other reason than to attract support and
news coverage from a limited pool.  A candidate who sits in dead-center
plus or minus 25% has no particular advantage over a left- (or right-)
leaning candidate who appeals to voters in the minus 45%/plus 5% range
(where zero is the middle, and +/- 50 are the extremes).


> Since neither Condorcet-plus-whatever or Approval has ever been tried
> on any large scale, we do not know how they would work in practice.
> In CHAOTIC ELECTIONS! A Mathematician Looks at Voting, Donald G.
> Saari reports on the only serious experimental test of Approval, Page
> 53: in 1999 the Society for Social Choice and Welfare elected their
> president by AV, and ALSO asked each voter for a complete preference
> ranking of the candidates, as a "test of voting theory". There were
> three candidates, all highly regarded, so it was a competitive
> election. It turned out that the AV winner was not the Condorcet
> winner. It also turned out that only one voter listed a second choice
> in the AV election; since everyone knew the election was close, most
> chose to "bullet-vote" for their first choice. Saari speculates that
> AV will reduce to Plurality in close races.

I agree that AV should not be used for presidential elections before it
has been in place for some time at the local level.  In the 1999 SCCW
election you cite, five of the 71 voters cast approval votes for more
than one candidate.  Saari was apparently only looking at the subset of
voters who also chose to rank the candidates.

> Saari makes the point that, to get a definite predicted result for
> AV, you not only have to specify a profile of voter preferences, you
> ALSO have to specify some assumptions about voter behavior in
> choosing how many candidates to "approve". I.E in an election with
> five candidates, in AV the voter may vote for one, two, three, or
> four; which will they choose to do and why?

(1) You have to do that anyway.  With ranked ballots, you have to make
similar assumptions, not only about how many candidates will voters
rank, but in what order.  With AV and five candidates, there are four
admissible strategies.  The choice of which one depends not only on
strategic information, but on the voter's perception of utility for each
of the candidates.  
These utilities exist whether Dr. Saari chooses to recognize them or
not; they are generally revealed by the voter's choice of strategies,
even if not directly measurable.


> [...] So, basically what you have shown with this example [the IRV 
> nightmare scenario] is that pure center parties can get squeezed out 
> under IRV. To remain viable, a pure center party has to stay larger 

You may be missing the point.  It's not just Center that can get
squeezed out, but any candidate if other candidates share the same
constituency.

> than at least one wing, taken as a coalition. It has to poach voters 
> from at least one wing; it cannot allow itself passively to be 
> poached upon. In trying to poach from either wing it may lose some 
> voters to the opposite wing; probably the equilibrium solution 
> involves two parties glaring at each other over the 50-yard line, 
> each fighting also to guard their rear from additional parties. 
> ...

You appear to be correct about the equilibrium, which favors two
competitive parties.  Weber has shown this, among others.

> Postscript: It occurs to me that there may BE no equilibrium 
> solution. Because IRV essentially eliminates the spoiler effect, it 
> greatly reduces the effective "barriers to entry" of new parties.

You were right the first time.  In order to overcome the two-party
equilibrium, a new party not only has to overcome "barriers to entry",
it has to be perceived as being more viable than all but one other
party.

Bart