[EM] A simple thought experiment.

[David L Wetzell]

Let's agree tentatively that Alternatives to IRV don't really outshine IRV
unless the number of competitive candidates exceeds 4.  Then, if we used a
1+ the output of a poisson dist'n to model the number of competitive
candidates in an election, it could shed some light on the debate.

Let's say that since Nate Silver tended to give Obama 2:1 odds over Romney
that we tend to have 1.5 competitive candidates in our current system so a
good starting parameter is 1 + the outcome of a poisson distribution with a
mean of .5.

Then,
=1-poisson(3, .5, 1)=.002, which would account for how most activists are
non-plussed by the debate over which single-winner election rule is the
best and willing to go with IRV since 1-poisson(1, .5, 1)=.01 and IRV wd
thereby reliably allow the number of candidates who aren't competitive but
able to make a difference to rise considerably.

But if IRV's use tends to increase the mean number of candidates say to 2
then 1-poisson(3, 1, 1)=.019, and 1-poisson(1, 1, 1)=.26.  Here, it seems
that
that IRV will still suffice most of the time and even when C is larger the
loss from a non-CW candidate winning wouldn't be that bad if (s)he isn't
that far off from the CW candidate.

But let's say instead we raised the mean to 2.5 then 1-poisson(3, 1.5,
1)=.066, and 1-poisson(1, 1.5, 1)=.44.  We'd still have all the advantages
with none of the down-falls in almost half of the time and in less than 10%
of the time would there be a situation where IRV could be significantly
improved upon.

But even if the number of competitive candidates did show potential to
balloon, as suggested by simulations and consuitations with experts, then
there'd be scope for switching from IRV to another election rule.  But in
the  current situation, C tends to be small and it's more important to
improve the quality than the quantity of competitive candidates, which can
be done by expanding significantly the number of non-competitive but
earnest candidates on the ballot and in the public square.

Also, the bottom line is that when you're advocating for a change in which
single-winner election rule alternative ought to be used, it's not right to
dump the burden of proof on IRV advocates.  The amount of time spent
marketing IRV already is a sunk cost and so the burden of proof for
switching ought to lie on the challengers not the defenders of the status
quo progressive electoral alternative to fptp.
dlw
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