Forest,
Given IRV's compliance with the "representativeness criteria" Mutual Dominant
Third, Majority for
Solid Coalitions, Condorcet Loser and Plurality; why should the bad look of
its "erratic behaviour"
be sufficient to condemn IRV in spite of these and other positive criterion
compliances such as
Later-no-Harm and Burial Invulnerability?
"....in the best of all possible worlds, namely normally distributed voting
populations in no more
than two dimensional issue space."
Why does that situation you refer to qualify as "the best of all possible
worlds" ?
Chris Benham
Forrest Simmons wrote (Wed. Nov.26):
Greg,
When someone asks for examples of IRV not working well in practice, they are
usually protesting against
contrived examples of IRV's failures. Sure any method can be made to look
ridiculous by some unlikely
contrived scenario.
I used to sympathize with that point of view until I started playing around
with examples that seemed natural
to me, and found that IRV's erratic behavior was fairly robust. You could vary
the parameters quite a bit
without shaking the bad behavior.
But I didn't expect anybody but fellow mathematicians to be able to appreciate
how generic the pathological
behavior was, until ...
... until the advent of the Ka-Ping Lee and B. Olson diagrams, which show
graphically the extent of the
pathology even in the best of all possible worlds, namely normally distributed
voting populations in no more
than two dimensional issue space.
These diagrams are not based upon contrived examples, but upon
benefit-of-a-doubt assumptions. Even
Borda looks good in these diagrams because voters are assumed to vote sincerely.
Each diagram represents thousands of elections decided by normally distributed
sincere voters.
I cannot believe that anybody who supports IRV really understands these
diagrams. Admittedly, it takes
some effort to understand exactly what they represent, and I regret that the
accompaning explanations are
too abstract for the mathematically naive. They are a subtle way of displaying
an immense amount of
information.
One way to make more concrete sense out of these diagrams is to pretend that
each of the "candidate"
dots actually represents a proposed building site, and that the purpose of each
simulated election is to
choose the site from among these options.
Each of the other pixels in the diagram represents (by its color) the outcome
the election would have (under
the given method) if a normal distribution of voters were centered at that
pixel.
So each pixel of the diagram represents a different election, but with the same
candidates (i.e. proposed
construction sites).
Different digrams explore the effect of moving the candidates around relative
to each other, as well as
increasing the number of candidates.
With a little practice you can get a good feel for what each diagram
represents, and what it says about the
method it is pointed at (as a kind of electo-scope).
On result is that IRV shows erratic behavior even in those diagrams where every
pixel represents an election
in which there is a Condorcet candidate.
My Best,
Forest
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