[EM] Instant pairwise bracket

Andy Jennings elections at jenningsstory.com
Mon Dec 3 13:58:56 PST 2018

I have wondered about an instant pairwise bracket before.  What if you
simulated all possible brackets and selected the candidate that won the
most?  Does that turn out to be equivalent to Copeland or some other
Condorcet variant?

With 16 candidates, there would be 16!/2^15 = 638 million brackets to
With 32 candidates, there are 32!/2^31 = approx 10^26 or 2^86 brackets

Borderline untractable?

On Sun, Dec 2, 2018 at 2:55 PM Rob Lanphier <robla at robla.net> wrote:

> Hi Richard and Kristofer,
> I'm going to reply to both of you inline here, since my replies are
> related:
> On Sun, Dec 2, 2018 at 8:12 AM Richard Lung <voting at ukscientists.com>
> wrote:
> > As said before, isn't approval voting essentially a rebranding of
> > cumulative voting. [...]
> > Moreover, IRV and RCV and Approval voting are about, well, voting. There
> > is the mode of counting to consider.
> It's true that an IRV ballot looks very similar to a
> Condorcet/pairwise-system ballot (ranking some/all of the candidates),
> and an Approval ballot looks similar to a Cumulative ballot.  However,
> both IRV and Cumulative voting have stricter rules about what
> constitutes a spoiled ballot, and in general, it's reasonable for
> voters to understand the basics of how their ballot is tabulated.
> That is ultimately what has convinced me that Approval voting is a
> good-enough system.  It doesn't reliably produce the Condorcet winner
> if one exists (because the ballot isn't expressive enough) but the
> simplicity of the ballot and my rudimentary understanding of the
> research on the topic suggests Approval voting more reliably finds the
> Condorcet winner than IRV does, and more crucially, close elections
> would seem to result in more ideologically similar candidates than
> close IRV elections (and thus, candidates are more likely to respect
> the result of ballot recount battles)
> On Sun, Dec 2, 2018 at 6:34 AM Kristofer Munsterhjelm
> <km_elmet at t-online.de> wrote:
> > We may be angry at FairVote for appropriating the term "ranked-choice
> > voting"; but that just there is how it works. Get people to think ranked
> > ballots = IRV.
> Yeah, I'm not a fan of that tactic.  Moreover, I don't think that
> rebranding is a great strategy when they have mishaps like what
> happened in Burlington in 2009.  It seems fairly likely (to me) that
> sooner or later, we'll have another Burlington 2009-style mishap in a
> jurisdiction that uses "ranked choice" to describe Instant Runoff.
> Rebranding the system every 5-10 years doesn't seem like an effective
> long-term strategy.
> Kristofer also wrote:
> > I have a hunch that some criteria (independence of clones, mainly) in
> > combination with Condorcet/Smith depend upon doing at least n^2 pairwise
> > comparisons. If so, then the magic has to happen in the seeding, not in
> > the tournament itself, since playoff formats generally have log(n)
> > stages and do no more than n comparisons in each stage.
> I fear you're right.  I'm hoping there might be a seeding heuristic
> that might not be mathematically bulletproof, but would be considered
> fair enough that failures would be rare and respectable.  My hunch is
> that *any* election that has a Smith set with more than one candidate
> will be considered a "close" election.  In fact, as I think about it,
> it seems that calculating the Smith set and/or calculating the
> Copeland score for all candidates will be a critical part of finding a
> seeding algorithm that relatively uninformed voters would agree is
> fair.  People with a computer science or math background may be
> impressed with simplifying  the tabulation algorithm from O(n^2) to
> O(log(n), but most voters' eyes will glaze over at explanations
> involving improvements of [Big O] score for a tabulation algorithm,
> and that very few sports fans understand the seeding algorithms for
> large sports tournaments.
> [Big O]: https://en.wikipedia.org/wiki/Big_O_notation
> For example, I know very few people know the geeky intricacies of
> *exactly* how the NFL does it's seeding, but basically, the
> Win-Loss-Tie (Copeland score) plays a very important role, and
> whenever teams that have reasonably good Win-Loss-Tie records don't
> make the playoffs when other teams with relatively poor Win-Loss-Tie
> records do make it, it's considered a big ripoff (which seems to be
> why the NFL has gotten more generous with "wild card" games in
> addition to games involving division leaders) One voting system
> simplification that seems reasonable would be whether or not a
> candidate "makes the playoffs" (filtering), such that the magic can
> occur in a combination of the seeding and the filtering.
> Kristofer also wrote:
> > Of course, if we're talking practical methods, maybe eating the
> > imperfection bullet and accepting some clone dependence as long as it's
> > not too bad is the way to go. Or I could be wrong; it's only a hunch.
> I have a similar hunch.
> Kristofer also wrote:
> > The problem with doing n^2 comparisons by clever seeding is that the
> > complexity that (it's suspected, at least) makes Condorcet uninteresting
> > would just be moved into the seeding phase.
> That's what appeals to me about this tactic.  Seeding+filtering is
> known to be a hard problem, and most sports fans just accept that they
> don't fully understand it, and appreciate that there are nerds who
> seem to do a more-or-less trustworthy job at it.  Copeland seems to
> provide a good-enough filtering mechanism that most people do
> understand (and of course, that's an O(n^2) system). Moreover, they
> understand brackets, so a complicated Copeland tiebreaker could be
> understandable enough.
> Then again, this all assumes a ranked ballot as a given.  Ranked
> ballots seem to be very popular in the San Francisco Bay Area (and
> getting attention elsewhere in California), so for me, much of this is
> more about heading off another Burlington 2009 situation than it is
> about introducing a new tournament-style system in places where
> first-past-the-post is the exclusive status quo.  For the latter,
> Approval Voting seems like a better choice.
> Rob
> ----
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