# [EM] Instant 2-stage plurality/pairwise runoff

Steve Barney barnes992001 at yahoo.com
Wed Mar 13 20:26:55 PST 2002

```Adam Tarr (last name?):

It is not quite so obvious that the Instant 2-stage plurality/pairwise runoff,
or "instant two stage runoff" (ITTR), is better that IRV, overall. I am still
waiting for the mathematical proof, and quantification of the different
properties. If that is ever possible, it should be possible to quantify and
prove the differences between these particular 2 voting methods, as they are as
similar as can be.

I must point out that the IRV is more likely to choose the Condorcet Winner
when that candidate is not among the top 2 plurality vote getters. In such a
case, the CW's chances are ZERO with the ITTR, but they are much better than
that with the IRV. On the other hand, if the Condorcet Winner is among the top
2 plurality vote getters, the CW's chances are much better than zero with the
IRV. So, you see, it is not quite so obvious as it seemed at first blush that a
Condorcet Winner's chances are better with the ITTR than with IRV. Furthermore,
remember that the two methods are identical with 3 candidates. It may be that
the more candidates you have the less likely it is that the CW will be among
the top 2 plurality vote getters. Can somebody prove one of these 2 methods is
better than the other in any of these respects? I have already proven
(informally and in my own mind, at least) that the IRV is less manipulable than
the traditional (non-instant) 2-stage plurality/pairwise runoff with 4 or more
candidates, but I don't know how the instant version of that method compares to
IRV in that respect. I suspect that IRV is less manipulable than ITTR, too,
simply because it potentially involves more stages, and is, thus, more
complicated and harder to predict. Anyway, the comparison of these 2 instant
runoff methods seems to merit some attention, don't you think? Formal proofs
and illustative examples can be very useful and convincing.

SB

PS: Can we leave the Approval Vote method out of this, for now?

> Date: Tue, 12 Mar 2002 11:31:52 -0500 (EST)
> From: atarr at purdue.edu
> To: election-methods-list at eskimo.com
> Subject: Re: [EM] Instant 2-stage plurality/pairwise runoff
>
> Steve Wrote,
>
> > I am interested in the fact that the traditional 2 stage plurality
> > runoff will always choose a Condorcet Candidate, when one exists,
> > if that candidate is among the top 2 plurality candidates in the
> > first round. This suggests that we should consider an instant 2-stage
> > runoff procedure where preference ballots are used, and the top two
> > plurality candidates go into an instant pairwise vote.
>
> It does not suggest this.  The key problem is that one caveat you mention,
> "if
> that candidate is among the top 2 plurality candidates in the first round."
> We
> have no guarantee that this will be the case, and indeed it will not be the
> case
> in many scenarios.  In particular, the classic (on this list anyway) "left
> middle/right" scenario can cause middle, the obvious Condorcet winner, to
> finish
> last in the first round of plurality.  Demorep likes to use the stark Stalin
> Wahington/Hitler example to illustrate this.
>
> As an interesting side note, the nation of Sri Lanka (just south of India)
> recently switched over to such an instant two stage runoff (we called it ITTR
> in
> a thread a few months ago, for instant top two runoff).  Thus far, their ITTR
>
> elections have produced the same results that a plurality election would
> have.
> It should be interesting to watch.  ITTR is better than IRV, although both
> are