[EM] Arrow's theorem and cardinal voting systems

fdpk69p6uq at snkmail.com fdpk69p6uq at snkmail.com
Thu Jan 9 20:42:59 PST 2020

Didn't Arrow agree that rated systems aren't included?


On Thu, Jan 9, 2020, 6:17 PM Rob Lanphier wrote:

> Hi folks,
> As some of you might have seen, Electowiki is a lot more active than
> it used to be.  I'm 99% convinced that's a good thing.  The 1% of me
> that has reservations is regarding how some advocates talk about
> Arrow's theorem.  I'm hoping you all can do one of the following:
> a)  change my view about Arrow's theorem, -or-
> b)  offer me some help in better articulating my view about Arrow's
> theorem.
> Many Score voting[1] activists claim that cardinal methods somehow
> dodge Arrow's theorem.  It seems to me that *all* voting systems (not
> a mere subset) are subject to some form of impossibility problem.
> Arrow's impossibility theorem deserved great acclaim for subjecting
> all mainstream voting systems of the 1950s to mathematical rigor, and
> it's clear that his 1950 paper and 1951 book profoundly influenced
> economics and game theory for the better.  His 1972 Nobel prize was
> well deserved.  It seems that it has become fashionable to find
> loopholes in Arrow's original formulation and declare the loopholes
> important.  Even if the loopholes exist, talking up those loopholes
> doesn't seem compelling, given the subsequent work by other theorists
> broaden the scope beyond Arrow's version.
> But, what the heck, let's actually talk about Arrow's original
> formulation.  I believe Score voting fails unrestricted domain:
> <https://en.wikipedia.org/wiki/Unrestricted_domain>
> In particular, let's say that 90% of voters prefer candidate A over
> candidate B:
> 90:A>B
> 10:B>A
> Arrow posits that there should only be one way to express that, and
> Score fails it.  In Score, it's possible to sometimes pick A, and
> sometimes pick B, depending on the score values on the ballots.  If
> Score *always* chose either A or B, then it would pass Universality.
> Score advocates claim that this isn't a bug, it's a *feature*.  If
> (for example), voters for A only mildly prefer A over B, but voters
> for B strongly detest A, then the correct social choice is B.
> However, it doesn't seem practical to inflict this level of nuance on
> voters.  I suspect that the first election where the Condorcet winner
> is beaten by a minority-preferred candidate (e.g. like what happened
> in Burlington 2009 [2]) will result in a repeal (like what happened in
> Burlington).  Back to the A/B example above, It's hard to imagine
> voters would consider the selection of "B" to be fair in a large
> election.
> It's fine to hold the opinion that Universality is an uninteresting
> criterion, and that therefore, Arrow's set of criteria isn't very
> interesting.  For example, a few years ago, we went through a phase
> where Condorcet advocates promoted "Local IIAC" as a IIAC[3] as a more
> interesting criterion, and advocating for Condorcet variants that meet
> that criterion.  Regardless, just because we find one criterion less
> compelling than another, we should talk accurately about the failed
> criterion.
> My way of thinking about Arrow's theorem (and being thankful for it)
> is to think of it like the physics of voting systems.  For example, in
> real-world physics, a "perfect" vehicle is impossible, because it's
> impossible to meet these criteria:
> * Goes faster than the speed of light
> * Has infinite capacity
> * Has a luxurious and comfortable passenger cabin
> * Fits in a small coat pocket
> * Is easy to produce
> * Is cheap (or even free)
> Just because a perfect vehicle is not possible, I'm glad
> transportation innovation didn't stop with Ford's Model T.  Of course,
> automobile sellers compete on the tradeoffs between the criteria
> above, and much public policy debate is about mode-of-transport
> tradeoffs between planes, trains and automobiles (and bicycles, and
> scooters, and and and...).  We need public policy debates around
> election method tradeoffs, too.
> I'm hoping we can try to stop trying to declare clever loopholes in
> Arrow's theorem, and just acknowledge the reality that *all* voting
> systems involve tradeoffs.  I hope we all can acknowledge that Arrow's
> central insight (there's no "perfect" system given perfectly
> reasonable criteria) is valid, and that it's only on the specifics of
> the exact criteria chosen for the 1951 proof that might be flawed.  I
> believe that election method activists should speak (and write) with
> clarity about the tradeoffs involved.  Whenever I see someone
> gleefully declare that Arrow's theorem doesn't apply to their voting
> method (and imply perfection), the credibility of the writer drops
> *precipitously* in my mind.
> Am I wrong?
> Rob
> p.s. I've been meaning to write this email for a while.  What inspired
> me to finally write it has been reading the current state of
> Electowiki and Wikipedia articles on the topic, like the "Arrow's
> impossiblity theorem" article on Electowiki[4]
> [1]: https://electowiki.org/wiki/Score_voting
> [2]: https://en.wikipedia.org/wiki/2009_Burlington_mayoral_election
> [3]: https://electowiki.org/wiki/IIAC
> [4]: https://electowiki.org/wiki/Arrow%27s_impossibility_theorem
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