[EM] Median systems, branding, and activism strategy

Jameson Quinn jameson.quinn at gmail.com
Wed Jun 12 16:24:54 PDT 2013

2013/6/12 Abd ul-Rahman Lomax <abd at lomaxdesign.com>

> At 09:55 AM 6/12/2013, Jameson Quinn wrote:
>> As voting reform activists, we must work together as much as possible. In
>> general, that means that raising awareness should start with teaching
>> people about approval. Still, if someone is unsatisfied with the
>> expressivity of approval, we should have a backup offering.
> That is, we should have a plan for future improvement. Really, unless a
> place already has IRV in place, a more complex ballot is not the first step
> to take. It's like our decision to promote Approval. An obvious first step,
> a do-no-harm improvement. More complex ballots mean spending money.
> The actual reform we suggest should depend on local conditions. They vary.
>  Personally, I think that median systems offer the best backup offering in
>> that sense. That doesn't mean I intend to undercut people promoting Score
>> or Condorcet; just that I think median systems offer a good compromise
>> between expressivity and low rewards to strategy. From my perspective,
>> Score is great for honest voters, but for strategic voters it has exactly
>> the same expressivity problems that approval does. And Condorcet is too
>> complex — not just to describe in the abstract, but to present the results
>> of even a single election in a clear, intuitive form.
> Uh, Score systems can ba amagalamated as median or as average or as sum.

This isn't the misunderstanding I was talking about, but by saying "Score"
with a capital "S" I was referring to a summed or averaged system.

> The latter fits most closely with democratic traditions, it is just Count
> all the votes, i.e., Approval, plus the allowance of fractional voting.
> Median systems are introducing what appears to be, for public choice, an
> *entirely new* concept. So, the obvious question, why?

???? You are the one who likes Bucklin. Bucklin is a median system that's
nearly 100 years old. How is that "*entirely new*" ????

> And, remember, we are talking about first reforms, not the *ideal*.
>  But median systems have a problem. There are too many of them, and even
>> more names.
>> Off the top of my head, I can think of the following names:
>>    * Bucklin: A general class of median systems which are implemented via
>> a descending threshold. Also used to describe various specific ranked or
>> hybrid ranked/rated systems used during the progressive era. For instance,
>> some use "Bucklin" to mean "median using full or truncated rankings, using
>> the highest majority as a tiebreaker"; others mean the Grand Junction
>> system of "median using 3+1 numbered rank/grades with skipping allowed and
>> ties allowed at the third grade only; highest majority tiebreaker".
> Bucklin is a median system, that's true, but that is not the *concept.*

I don't even know what that means. In my book, making a distinction between
median systems on one hand and Bucklin systems on the other is
unsustainable. Any Bucklin system is a median system; and if you want to
define things so that there is a median system that isn't a Bucklin system,
that's a distinction without a difference.

And any poor performance of Bucklin would come, quite likely, from using
> median amalgamation. (I.e., a Bucklin ballot is really a Score ballot, and
> a score ballot can be used for Bucklin amalgamation, it is an obvious and
> simple extension.)

I literally cannot parse this at all.

>     * Majority Choice Approval (MCA): I've seen this applied to various
>> 3-rank median systems, but I think the canonical one is: "if there is a
>> majority top-rank, then the highest such; otherwise, the candidate with the
>> most non-bottom rankings."
>>    * Majority Judgment (MJ): as defined by Balinski and Laraki
>>    * Graduated Majority Judgment (GMJ): as defined by me.
>> There are also a number of possible descriptive "branding" terms for a
>> median / Bucklin system:
>>    * Instant Runoff Approval
> I created that one, because that is exactly what it is, and it simulates a
> series of descending cutoff Approval elections, hence a way-cool
> implementation, as a primary and runoff method in a two-round system, thus,
> if it has N approval grades, it simulates 2*N approval runoffs in the full
> two-election set. Jurisdictions that want to ensure majority approval can
> probably reach that, even with many candidates, in a two-round Bucklin
> system, and I've suggested that if the Range ballot is a little deeper,
> i.e, includes unapproved ranks, it can also, in the primary, be analysed
> for a beats-Range top two (or beats-Bucklin top two) winner, using the
> lower preferences, thus making the *system* Condorcet compliant, if a
> Condorcet winner must always be in the runoff. If a majority is found,
> depending on the wishes of the jurisdiction, the runoff may not be
> necessary.
> Increasingly, though, I've become aware of systems that *always* go to the
> general election. So the primary is just a unified primary, as distinct
> from party primaries. And with a good runoff method, and with write-ins
> allowed in the runoff, the electorate can still have three choices on the
> ballot, if certain conditions are met, plus write-ins that don't
> necessarily vote-split.
> What, I'd like to know, is not to like about this?

Runoff systems are great, and the intelligent runoffs you often propose are
great. They're also not what we're talking about. Are you saying that the
term "instant runoff approval" is a bad one because the system can be used
in combination with a runoff?

>     * Graded Instant Runoff
>>    * Descending Threshold Approval
>>    * Majority Threshold
>>    * Grade Voting
>>    * Majority-Based Grade Assignment
> Instant runoff Approval fully satisfies expectations. It is what the name
> implies.
... But now you're saying that Instant Runoff Approval is a good term? I
don't understand your larger point.

>  It seems to me that Median and Bucklin advocates should come to a
>> consensus on what specific system to promote, and what to call it. That
>> doesn't mean we should cease discussing the different systems in fora like
>> these; just that when promoting systems to the public, we should be on the
>> same page.
> Bucklin is widely known as Bucklin, the Grand Junction system, and it was
> simply called "preferential voting" in many places. It was also called
> "American Preferential Voting," to distinguish it from "foreign" systems
> (i.e, STV methods).
... and now the best term is "Bucklin"? Abd, I know you like to think out
loud. But we need to pick a term and stick with it.

>  Which system is best? I think the clear choices are MCA or GMJ, and I'd
>> personally favor GMJ. MCA is the simplest well-defined median system. GMJ
>> is good because:
>>    * Unlike the specific systems called "Bucklin", it has no vestige of
>> ranked thinking, and thus requires no dishonest strategy.
> That's naive.

I'm sorry, there's been a basic misunderstanding here, which has
repercussions throughout the rest of your reply below. When I said
"dishonest strategy", I didn't just mean "strategy"; I meant actively
preference-reversing strategy. In other words, "dishonest as opposed to
semi-honest" strategy, not "dishonest strategy as opposed to honest
voting". The fact that strictly ranked systems always require dishonest
strategy, while rated systems often don't, is a simple consequence of the
gibbard-saterthwaite theorem: in ranked systems, dishonest strategy is the
only kind that exists, so if there's always some strategy, it must be

So I wasn't being naive, but I may have been being over-technical and/or

>     * It's more expressive than MCA.
>>    * Unlike MJ, GMJ can easily be expressed in terms of a Bucklin-like
>> descending threshold, a single algebraic formula, or a graphing procedure.
>> (As far as I know, MJ can only be expressed in one way). GMJ is also easier
>> to "program" into a spreadsheet in my experience.
>>    * Unlike MJ, GMJ results can be succinctly and unambiguously expressed
>> as a single number for each candidate.
>>    * Unlike MJ, the GMJ winner for a given honestly-voted utility profile
>> tend to be stable as the number of evenly-spaced grading categories varies,
>> even in moderately "pathological" examples (such as a single-peaked versus
>> a two-peaked candidate).
>>    * However, the actual results will agree with other median systems in
>> almost all realistic cases.
>> What should we call it? GMJ isn't a horrible name, but if people prefer
>> to use one of the above "branding" terms or something similar, I'd be open
>> to discussing it.
> I *very much* dislike the use of letter grades that imply absolute
> ratings. It is essentially suggesting to the voter that they disempower
> themselves.

The only thing that disempowers a voter in a Bucklin system is if they vote
both of the top two distinct options on the same side of both the first and
second place medians. (I say "*distinct* options" to allow for the case
where the voter intentionally supported or opposed two near-clones.) I do
not think that grades encourage that any more than numbered categories. In
fact, because the range containing the top two grades would be more stable
from election to election with letter grades (or other non-comparative
categories, such as words), it would actually be less likely.

> The whole discussion about "dishonest strategy" is contaminated with
> judgment against the normal think we do with choices, our internal ratings
> are highly dependent on expectations *in the particular case*, and people
> who don't do that tend to be unhappy.

Again, this stems from the misunderstanding of what I meant to say above.

>  But I think it's important for us to join our voices in better harmony on
>> this. Abd, in particular: why do you continue to talk about "Bucklin" (ie,
>> the grand junction system) when there are better-designed,
>> more-clearly-defined Bucklin systems available today?
> The Grand Junction System is adequately defined, but the system I'd
> recommend now is Bucklin-ER, to start. Three ranks.
> All three ranks are approved ranks. In *some* elections, two ranks might
> be used.

So, you favor "Bucklin-ER" as a system over GMJ? Is that simply because of
the letter grades?

>  Jameson
>> ps. None of this message should be read as an attempt to abandon the
>> common effort to promote approval voting as a first step.
> This is very simple. Approval first. The obvious first and most
> significant objection to Approval, then, is addressed with ranked approval.
> There is a method, approval-IRV, that has the LnH behavior of IRV, if the
> voter wants that protection. But I actually think it harms voter behavior
> to encourage excessive fear of LnH.
> Look at the arguments for GMJ above. They will mostly be unintelligible to
> ordinary citizens who are not specialists in voting systems.

I've expressed them in technical terms, yes, because in this forum those
terms are understood. But I could explain most of them in simpler terms if
need be.

Anyway, the question isn't whether they're intelligible, it's whether
they're important. Please engage with them one by one.

> So, I see this as one reform path.
> 1. Approval.
> 2. Bucklin-ER, 3-rank. (Traditional Grand Junction system plus equal
> ranking *allowed* in all ranks.)

OK, stop here. We don't have to agree on steps 3-5. I largely do, but I
started this thread to talk about what specific system and terms to use for
step 2.

I can't understand exactly what you're saying about terms. But that's OK,
because which system is best is the first question. The differences between
my proposal (GMJ with letter grades) and your proposal (3 rank ER-Bucklin,
using the highest majority as a tiebreaker) are:

1. 5 levels versus 4. I think we'd both agree that this is relatively
2. Letter grades versus numbered "ranks". I think letter grades are clearly
better, and I've said a little bit about why above. I'd like to hear your
3. Different tiebreaker. Advantages on either side:
ER-Bucklin: Simpler to explain.
GMJ: More congruent with the Bucklin process. Slightly better chicken
dilemma resistance and strategy resistance in general. Easier to give the
results as numbers. Closer to MJ, which has a book about it.

Do you agree that it's worth trying to come to an agreement, and that both
of us should be ready to cede if necessary? How would you like to do this;
do you think third opinions would be good?

If we settle this question, we can move on to talking about names.


> 3. Full range ballot for Bucklin [adds . (*Range reporting starts, and
> Condorcet analysis becomes more complete*)
> 4. Runoff with pairwise leader included if different. Runoff if majority
> not found. Or unconditional runoff.
> 5. Range amalgamation substitutes for Bucklin amalgamation. Resolution may
> be increased if needed. Approval information is always collected.
> All of this works with runoff voting. We should *not* attempt to kill
> runoff voting as an *easy target*, and we should oppose FairVote attempts
> to do this, there is basic information about this to be included, and
> providing information for intelligent decisions is our job.
> (If it were practical, approval voting with repeated Bucklin ballots until
> a majority is found is a *highly sophisticated system*.)
> We don't know the Bayesian Regret performance of Bucklin, because the
> testing that was done, AFAIK, did not understand a Bucklin ballot as being
> a Range ballot, but treated it as a ranked ballot.

Warren did test a continuous median system. That is probably a better
approximation of rated Bucklin systems than what's called "Bucklin" in his

> The Bucklin ballot I'd see at the 3rd step could even have letters
> attached, it's really a Range 4 ballot, just as the step 2 ballot is that
> ballot without the elevated but unapproved rating of "1: included. So A is
> 4.0, as people expect. But I'd want to see the method in actual use
> *first*, to avoid misleading voters. If you really want to give all
> politicians a bad rating, then you should totally realize that you are
> disempowering yourself, not casting a full vote, to *make a choice.*

Oh, right. You're worried that people will rate everyone badly? I can
understand why people might have that impulse, but I think anybody who did
that would intuitively realize that they are giving up some voting power.
Also, it would be good to educate people that they're "grading on a
historical curve". Someone who thinks (say) that Obama is objectively
horrible but also in the top 15% of presidents historically, would be
perfectly justified in giving him an A on that latter basis.

> Bucklin could be reported, by the way, as a net grade point average for
> candidates, the values averaged would be the numbers of 0 plus 2-4. If the
> additional unapproved level of 1 is included on the ballot, it's then a
> complete Range set. And candidates can be given that single "grade" that
> Jameson wants. Voting is *choice*, not absolute rating.

????? what? You're suggesting running Score but calling it "Bucklin"?
Obviously not, but I'm confused.

I think I'll stop responding now because you're moving beyond Bucklin
systems to even more ideal options. That's fine and I agree with a lot of
what you say but it's not the topic I wanted to talk about here.

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