[EM] Instant pairwise bracket

Rob Lanphier robla at robla.net
Sun Dec 2 13:54:30 PST 2018

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.


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