[EM] Instant pairwise bracket

Rob Lanphier robla at robla.net
Sat Dec 1 23:15:33 PST 2018

Hi folks,

Check out this editorial from Harold Meyerson at the LA Times:
"A Democratic victory in 2020 demands a new form of primary"

Meyerson describes what a mess the 2020 Democratic primary for U.S.
President promises to be, with potentially up to 30 viable candidates
all competing for the Democratic Party nomination, and how even in a
field of 10-12 candidates, it's not hard to win with only 15% of the
vote. He openly muses about a tournament that would seem reasonably
certain to select the Condorcet winner in a crowded field (or at least
one of the candidates from the Smith set):

> I suppose the Democrats could adopt NCAA-like brackets, with the winner
> of the billionaires’ primary (which might feature Bloomberg, Tom
> Steyer and Starbucks’ Howard Schultz) facing off against the winner
> of the left primary (Sanders, Warren and maybe Brown), with the winner
> of that going up against the victor of the center-left senator bracket
> (Kirsten Gillibrand, Amy Klobuchar and Cory Booker), who...

...oooh, this is really appealing!  Is he about to describe a pairwise system?

> ... well, this system has problems, too.

Hrm....nope.  What is he about to propose?

> The one way to ensure that the nominee actually is favored by a majority
> of Democratic voters is for the party to adopt a form of ranked-choice
> voting.

D'oh!  He seems to be referring to Instant Runoff.  And indeed:
> Maine recently adopted such a system for federal offices.

He almost immediately points out the problems he sees with Instant
Runoff in a large field:
> If there really are 20 candidates on the early state ballots, I can’t
> see asking voters to rank them all, much less the computers to tally all
> those rankings. But in a field as densely populated as the Democrats’
> is shaping up to be, voters should be given the opportunity to cast their
> votes for win, place and show (and maybe fourth and fifth as well) —
> though if they just want to vote for one or two candidates, that should
> be their prerogative, too.

The system that Meyerson suggests seems to be a form of Borda voting.
He describes it somewhat, and it's clear he has something in mind, but
also acknowledges that there is plenty to be worked out.  I'm going to
guess that his editorial wasn't reviewed by an election method expert
before publication.  Hopefully it's gotten a lot more review since it
was published.

He's pretty clearly already familiar with Instant Runoff, but I think
there's an opportunity for advocates of other systems to suggest their
favorite alternative.  For example, I learned about this article from
Center for Election Science's feed on LinkedIn;

...where they said:
> Harold Meyerson rightly notes the need for a better voting method
> to conduct the Democratic primary in 2020, given the growing list
> of potential candidates. An even better solution than RCV? Approval
> voting. No vote splitting, no spoiler effect, and no costly new voting
> software or long waits to calculate winners. #Approvalvoting is
> the way to go.

Certainly, Approval is a really good choice.  Still, given the
direction Meyerson started to go, I'd like to riff on the NCAA runoff
idea.  A lonnng time ago (in 2006), I proposed a tournament-style
version (more about that below).  The NCAA-tournament idea and using
that as a framework for a method could allow us to create a really
good Condorcet-flavored proposal.  Here's a set of rules I cobbled
together tonight:

1.  Create a playoff bracket with room for all candidates, using rules
similar to the ones the NCAA uses for March Madness:

....or maybe on the ones Wimbledon uses:

In short, use a single-elimination tournament:

2.  Seed the candidates in the tournament such that all members of the
Smith set are guaranteed to advance to the final rounds.  I'm guessing
that the Copeland score could be used:

3. Calculate the winner of each contest using the standard ways of
inferring pairwise matchup results based on ranked/rated ballots

These steps may seem like a lot of theatrical extras (especially in
contests where there is a single Condorcet winner) but I think this
framework could provide a useful mental model for people whose eyes
glaze over when try to describe some of the mathematical
vulnerabilities of systems like Instant Runoff.

It seems like, with the right set of seeding rules, a system could be
devised that is provably equivalent to Tideman's Ranked Pairs or the
Schulze method, but yet would function in a way that is visually
similar to March Madness or Wimbledon.  Copeland's similarity to
Win-Loss-Tie records in sports could help guide people to agree on
mathematically-complicated ideas of fairness.

Like I say up above, I proposed a tournament-style election back in
2006 -- I found my proposal *after* I finished writing most of the
email above.  Here's my 2006 proposal:

I've slapped together a wiki page on electowiki.org where I plan to
flesh out my proposal:

...but regardless, I'm eager to read what folks think.


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