[EM] Instant pairwise bracket

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[EM] Instant pairwise bracket

Rob Lanphier
Hi folks,

Check out this editorial from Harold Meyerson at the LA Times:
"A Democratic victory in 2020 demands a new form of primary"
<https://www.latimes.com/opinion/op-ed/la-oe-meyerson-primary-ranking-20181129-story.html>

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;
<https://www.linkedin.com/feed/update/urn:li:activity:6473969393553543169>

...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:
<https://en.wikipedia.org/wiki/March_Madness>

....or maybe on the ones Wimbledon uses:
<https://en.wikipedia.org/wiki/Wimbledon_championship>

In short, use a single-elimination tournament:
<https://en.wikipedia.org/wiki/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:
<https://en.wikipedia.org/wiki/Copeland_method>

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:
<http://lists.electorama.com/pipermail/election-methods-electorama.com/2006-June/083675.html>

I've slapped together a wiki page on electowiki.org where I plan to
flesh out my proposal:
<https://electowiki.org/wiki/User:RobLa/runoff>

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

Rob
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Re: [EM] Instant pairwise bracket

Kristofer Munsterhjelm-3
On 2018-12-02 08:15, Rob Lanphier wrote:

> Hi folks,
>
> Check out this editorial from Harold Meyerson at the LA Times:
> "A Democratic victory in 2020 demands a new form of primary"
> <https://www.latimes.com/opinion/op-ed/la-oe-meyerson-primary-ranking-20181129-story.html>
>
> 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:

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.

> 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:
> <https://en.wikipedia.org/wiki/March_Madness>
>
> ....or maybe on the ones Wimbledon uses:
> <https://en.wikipedia.org/wiki/Wimbledon_championship>
>
> In short, use a single-elimination tournament:
> <https://en.wikipedia.org/wiki/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:
> <https://en.wikipedia.org/wiki/Copeland_method>
>
> 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.

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.

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.

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.
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Re: [EM] Instant pairwise bracket

Richard Lung
In reply to this post by Rob Lanphier
As said before, isn't approval voting essentially a rebranding of
cumulative voting. More is less: multiple x-votes (or scores) count
against each other. (Hence ranked choice necessary.)
And is it not so, that Condorcet principle is not an electoral system
but a cross-reference of some electoral system -- notably the use of
ranked choice voting.
Moreover, IRV and RCV and Approval voting are about, well, voting. There
is the mode of counting to consider. (Not that I'm suggesting you, in
particular, have not.)
from
Richard Lung.



On 02/12/2018 07:15, Rob Lanphier wrote:

> Hi folks,
>
> Check out this editorial from Harold Meyerson at the LA Times:
> "A Democratic victory in 2020 demands a new form of primary"
> <https://www.latimes.com/opinion/op-ed/la-oe-meyerson-primary-ranking-20181129-story.html>
>
> 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;
> <https://www.linkedin.com/feed/update/urn:li:activity:6473969393553543169>
>
> ...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:
> <https://en.wikipedia.org/wiki/March_Madness>
>
> ....or maybe on the ones Wimbledon uses:
> <https://en.wikipedia.org/wiki/Wimbledon_championship>
>
> In short, use a single-elimination tournament:
> <https://en.wikipedia.org/wiki/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:
> <https://en.wikipedia.org/wiki/Copeland_method>
>
> 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:
> <http://lists.electorama.com/pipermail/election-methods-electorama.com/2006-June/083675.html>
>
> I've slapped together a wiki page on electowiki.org where I plan to
> flesh out my proposal:
> <https://electowiki.org/wiki/User:RobLa/runoff>
>
> ...but regardless, I'm eager to read what folks think.
>
> Rob
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info


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Re: [EM] Instant pairwise bracket

Rob Lanphier
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 <[hidden email]> 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
<[hidden email]> 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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Re: [EM] Instant pairwise bracket

Andy Jennings
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 simulate.
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 <[hidden email]> 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 <[hidden email]> 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
<[hidden email]> 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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