[EM] Instant Runoff Voting 3-candidate elections - pathologies considerably more common than you may have thought

Warren Smith warren.wds at gmail.com
Fri Sep 3 11:35:04 PDT 2010

On 9/3/10, Jack Nagel <nageljh at sas.upenn.edu> wrote:
> Dear Warren,
> Thank you for sending this interesting analysis.
> Could you recompute the 'total paradox probabilities' without
> including 'paradoxes' or 'pathologies' R, S, and T?

--yes... or you could, since all the necessary info to do so, is
available in the 'master table.'  (I admit it is a bit of a pain.)

Also, note T and S *ALREADY* were not included in the total paradox
probability and only  {Q, R, U, V, W, X, Y, Z} were, since I did not
regard T & S as 'paradoxes'
for this purpose.   So the only thing you need to remove is R.

You can just very easily look at the blue and yellow tables
at the 2 lines for "total" and "R" and see even if every R is
removed from the total (and even if we falsely assume R and everything
else disjoint)... it doesn't change a whole lot.  Actually R is
probably quite non-disjoint so
it probably changes a good deal less even than that.

> I think that
> would be a fairer test, for these reasons:
> It may be fair game to criticize IRV when Paradox Y occurs (failure
> to choose the Condorcet winner), because IRV advocates point to
> greater Condorcet efficiency as one of its advantages (although it's
> rather inconsistent for you and other advocates of score and approval
> voting to do so, because you do not embrace the Condorcet criterion
> when your favorite systems do not satisfy it).  Paradox Q is also OK,
> comparable to criticizing plurality for its vulnerability to spoiler
> effects.  Paradoxes U, V, W, and X all appear to be variations on
> non-monotonicity, so it's fair enough to include them.
> But unless I've missed something, S (existence of a Condorcet cycle)
> is a not a defect of IRV, but simply a property of the underlying
> preference configuration.

--I agree and already did agree which was why S was not in the total.

> Indeed, IRV, like plurality, has the
> practical advantage of hiding the existence of the cycle.
> And how can T (IRV and plurality winners differ) be a reason for
> criticizing IRV, when plurality winners are so often faulty from any
> of several normative standpoints (including your own)?  And R (the
> sniff test--IRV differs from all scoring rules), besides being a
> subset of T, again assumes as normative rules that are much debated.

--again I agree and already did agree and was why T was not in the total.
T is of interest for defining two different subpopulations of elections though.

You appear not to have said in your email why you do not like R(?),
but anyhow as I said if you remove R it won't change things a whole
lot since R is fairly rare.

Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
"endorse" as 1st step)

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