# [EM] IRV vs Plurality (back to the pile count controversy)

James Gilmour jgilmour at globalnet.co.uk
Fri Jan 22 00:57:31 PST 2010

```robert bristow-johnson  > Sent: Friday, January 22, 2010 12:25 AM
> On Jan 21, 2010, at 7:05 PM, James Gilmour wrote:
>
> >>> N	Unique Preference Profiles
> >>> 2	4
> >>> 3	15
> >> ...
> >>
> >> then your calculation is mistaken.  the fact that you
> ostensibly need
> >> 4 piles when there are only two candidates should serve as a clue.
> >>
> >
> > If there are two candidates, A and B, then the possible unique
> > preference profiles are:
> > A
> > B
> > A>B
> > B>A
> >
>
>
> what, on a ballot, is the consequential difference in meaning between
> "A" and "A>B"?  what effect does a ballot marked "A>B" have over one
> marked just "A" (or vise versa) in *any* election method that uses
> ranked ballots?

In terms of "preference profiles" the question is completely irrelevant.  "A" and "A>B" are two different preference profiles.  So
the possible numbers of preference profiles for given numbers of candidates are, I think, correctly stated in the table in my
earlier post.

How the STV counting rules handle the two preference profiles "A" and "A>B" is a different matter.  Some STV counting rules handle
these two profiles identically.  But for some other STV counting rules the profiles "A" and "A>B" are handled differently.  This
second set of rules are those that prescribe the transfer of votes "to the bitter end", i.e. even after the winners have all been
determined.  Under this rule a ballot marked "A" would be treated differently from a ballot marked "A>B": at the last possible
transfer, the "A" ballot would become 'non-transferable (exhausted)', but the "A>B" ballot would be transferred to A.

This second rule is, of course, a stupid rule but that does not mean it has not been implemented in some jurisdictions, including,
sadly, Scotland.  It is also a highly undesirable rule because it means that my vote could, in some circumstances, be transferred to
the candidate I deliberately ranked last in the lowest possible place, e.g. 12th out of 12 candidates.  Following on from the
concept of 'Later No Harm' (which underpins the whole of contingency voting, as in IRV and STV-PR), it is very important to be able
to give a voter the absolutely assurance that under no circumstances will her vote ever be transferred to the candidate she has
ranked 12th out of 12.  Sadly, the stupid "transfer to the bitter end" rule undermines this.

James Gilmour

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```