# [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 11:43:35 PDT 2010

```(continued)
in fact, to be precise, you can look at the 4 lines of the pink table
involving R, optionally with a subset of {S,T} added (which is why 4
lines), ONLY, to see how much Nagel should subtract off the total.
Binary = 01**000000
where * means either 1 or 0.
You'll see the subtraction is of a very small amount.
(Some lines missing since zero prob.)

On 9/3/10, Warren Smith <warren.wds at gmail.com> wrote:
> 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
> "endorse" as 1st step)
> and
> math.temple.edu/~wds/homepage/works.html
>

--
Warren D. Smith