[EM] Arrow's theorem and cardinal voting systems

Rob Lanphier robla at robla.net
Thu Jan 9 23:02:00 PST 2020


Hi fdpk69p6uq,

I have to confess that your reply in this thread bothers me a little
bit.  More inline below....

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

On Thu, Jan 9, 2020 at 8:43 PM <fdpk69p6uq at snkmail.com> wrote:
> Didn't Arrow agree that rated systems aren't included?
>
> https://www.electionscience.org/commentary-analysis/voting-theory-podcast-2012-10-06-interview-with-nobel-laureate-dr-kenneth-arrow/

Are you saying that a single interview of an 90-year-old Kenneth Arrow
by a much younger interviewer with a possible bias on the matter
should be the final word on this subject?  How much of his
professional credibility did Arrow stake on that interview?  How much
preparation for that line of questioning do you think Arrow gave for
that interview?  Who's going to interview Gibbard?  Who's going to
interview Satterthwaite?

It was really clear to me a the point that Aaron Hamlin tried to get
Dr. Arrow's take on the "favorite betrayal criterion" that Dr. Arrow
wasn't actively reading this mailing list, and instead was enjoying
his waning years.  ;-)  It's interesting that Arrow had been here in
the Bay Area for a very long time, and witnessed San Francisco (and
Oakland, and others) move to Instant Runoff, and that he clearly had
some reservations about IRV.  He also seemed more concerned with
Electoral College and California's jungle primary than he did with any
of the municipal election reforms.

I really appreciate that Aaron did that interview before Dr. Arrow
died, and I told Aaron I was a little jealous, and was kicking myself
for not seeking Arrow out myself after I moved to San Francisco in
2011.  Given that, my assessment of the interview above probably seems
a bit harsh.  All I'm saying is that the interview wasn't set up for
the level of scrutiny necessary to establish rote truth.  I'm not
willing to accept that interview as definitive proof that Arrow's key
insight on voting systems is strictly limited to ordinal voting
systems, and that cardinal voting systems are provably free of any
sort of impossibility paradox.

Rob


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