[EM] Median systems, branding, and activism strategy

Jameson Quinn jameson.quinn at gmail.com
Thu Jun 13 10:37:49 PDT 2013

2013/6/13 Abd ul-Rahman Lomax <abd at lomaxdesign.com>

> At 06:24 PM 6/12/2013, Jameson Quinn wrote:
>  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*" ????
> You can conceptualize Bucklin as a median system, because the first
> candidate to pass the majority post has the highest median vote. However,
> that's not how Bucklin was understood. It was seeking a majority, that's
> all. Explaining "median," and, particlarly, "graduated median," is a bit of
> a chore, as we have seen.
> This is something that is missing from many voting systems that have been
> designed with non-inutitive amalgamation process. I can read a description
> of how to amalgamate, but what I want to know, and I suspect most people
> will want to know, is the *sense* behind the system.

OK, whatever. I won't use the word "median" from now on, but rather talk
about "Bucklin systems" in general. To me, that's just provisional
terminology anyway. The point of this thread is to settle on common
terminology, not get bogged down discussing the provisional terms.

> ...
> But we proceed toward transformed systems one step at a time. It's hard to
> walk without taking steps, and running without steps will leave you
> face-down on the floor with a broken nose.

Right. And the only step I want to take here is to agree on a common
single-round Bucklin system to advocate and a common name for that system.

 <more snips>
>> 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.
> Who is "we." I call the system Bucklin.

I am suggesting that Bucklin advocates on this list, principally the two of
us, find a common system and a common term. I am confident that if the two
of us can agree, CES and others will follow.

> If CES or other activist organization wants to fix on a name, like IRAV,
> instant runoff approval voting, I'd support it. However, I *do* want to
> clearly connect with history. So a page might say:
> Instant Runoff Approval Voting
> (Bucklin, Grand Junction System, American Preferential Voting.)

I fully agree that we should connect with history in that way.

> And then any variation from, say, the Grand Junction System -- which is a
> *very specific name* -- would be explained. I.e., ER in all ranks, no
> sequential dropping of minor candidates. (Why in the world did Bucklin do
> that? Later, it was realized it was useless, and if it ever *did* make a
> difference, i.e., a minor candidate later got a plurality and the
> amalgamation ended, *why* would they refuse the win?)
>> 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.
> I'll stick with "naive."
>   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 dishonest.
> Bucklin is *not* a "stricly ranked system." It is "category ranking."
> I.e., Score. I'm sure you realize that Score uses a ranked ballot, right?
> I.e,. the scores are ranks, and it is merely that equal ranking is allowed,
> as well as empty ranks.

In Grand Junction, ties were not allowed in the first two ranks. That means
that system, while not fully a strict ranking system, shared some problems
common to such systems: it did not pass FBC and wasn't semi-honest. This is
a mathematical fact. If you think that the conclusions I draw from that
fact — that the Grand Junction system is not suitable for use today, and
therefore we should not call whatever system we propose for today simply
"Bucklin — are naive, that is your right.

>  So I wasn't being naive, but I may have been being over-technical and/or
>> cryptic.
> I'll stick with "naive," without denying the possible nature of the
> naivete. "over-technical" can be naive. I don't think you were cryptic,
> Jameson. You were *incorrect*. You collapsed "ranked thinking" with "ranked
> system." Ranked thinking is how I make choices, routinely. But I allow
> equal ranking, i.e., categorization. I.e.

See above.

Ranked systems that allow equal ranking are *not* the ranked systems that
> have been extensively analyzed. If they allow and value skipped ranks, they
> are *fully* not ranked systems, they are cardinal systems, what Arrow
> recently called "category" systems. Bucklin was, apparently, analyzed in
> Bayesian Regret simulations as if it were a ranked system.

You are right about that. But the Grand Junction system was not a cardinal
system in that sense; it was an ordinal/cardinal hybrid which had some
easily avoidable ordinal flaws.

>     * 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.
> What grades encourage is placing the candidates in absolute categories
> rather than relative ones. If the voter votes the highest category and the
> lowest, the voter is voting full power.


> What Jameson describes above is *not* the general case. I.e,. the voter,
> voting, does not know where the medians will lie, so voting the favorite,
> say, at lower than the top rating, *may* disempower the voter. Likewise at
> the other end, though the effect there is less obvious. The low end can
> make a difference if a majority is required, under some rules.

I agree with that as well. My contention is that voters who do this will
generally understand what they're doing and know that they're giving up
voting power; voters who want full voting power will intuitively span the
full range of grades (possibly skipping middle grades).

I do think that after a very few elections and, with polling, probably even
before the first election, the probable range for the winning median will
be pretty clear.

>> 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.
> I don't think so, yet.

OK. Well since I wasn't trying to make any of the points you seem to be
responding to here, there was a misunderstanding somewhere.

>  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?
> Perhaps. I have not *thoroughly analyzed GMJ.* Explain the difference.

OK. You ask the same question again below; I'll answer it here.

Here are the three equivalent GMJ definitions I posted in another message
in this thread:
1. Count the votes at the highest grade for each candidate. If any one
candidate has a majority, they win. If not, add in lower grades, one at a
time, until some candidate or candidates get a majority. If two candidates
would reach a majority at the same grade level, go back and add the votes
at that level in a graduated manner; that is, first add 10% of all votes at
that grade to each candidate, then 20%, stopping when exactly one candidate
has reached a majority; that candidate wins.

For the purposes of reporting results, a candidate's score is the grade
level they reached a majority at (their median), plus one half, minus the
fraction of the votes at that level which it took to reach a majority.
(This is the same number as the formula below gives.)

2. Calculate (median + (V> - V<) / (V= * 2)) for each candidate. The
highest score wins. V>, V<, and V= represent the number of votes above,
below, and at the median, respectively.

(If V= is zero, then (V> - V<) will also be zero by the definition of
"median", so in that case you can assume that V= is 1, or any other
non-zero number, to avoid division-by-zero problems.)

3. For each candidate, graph the cumulative grade distribution using
rectangles for each grade that meet at the corners. Draw a single line that
goes diagonally across each of the rectangles. The candidate who's line is
highest at the 50% mark is the winner. (This explanation makes more sense
if you see an example).

Here's a description of what I understand as your Bucklin-ER:
1. Count the votes at the highest grade for each candidate. If any one
candidate has a majority, they win. If not, add in lower grades, one at a
time, until some candidate or candidates get a majority. If two candidates
would reach a majority at the same grade level, then whichever has the
largest majority wins.

The difference here is ONLY the tiebreaker. The GMJ tiebreaker focuses on a
sort of "trimmed mean", that is to say, on an area around the center of the
distribution. The Bucklin-ER tiebreaker focuses on the next transition
below the median. Because that is slightly lower in the distribution, the
slope to the chicken dilemma is slightly slipperier with Bucklin-ER. It's
not a large effect.

Also, in order to give Bucklin-ER results, you need two numbers per
candidate ("Median of X with Y% majority") rather than just one as with
GMJ. Those are the differences.

> The *meaning* of a vote in a voting system is the effect it has. Any
> "name" for the vote is potentially misleading. Indeed, Approval voting is
> often criticized based on an assumed meaning of "I approve of this
> candidate," when the candidate may be a mere least-of-two-evils. The vote
> is an *action* of approval, not a sentiment or absolute judgment.

Right. And grading in GMJ or other Bucklin system is also an intentional
action as part of an election process, not merely an abstract assessment of

Start there. I've seen numerous attempts to explain GMJ, and they are are
> guaranteed, my sense, to lose most readers. Could be a problem with
> expression, but I'm suspecting that it's worse than that. Do not start, my
> advice, with tie-breaking. Start with what is simple and likely. Add
> tie-breaking rules later.

See above.

> But a tie in median grade is not based on "graduated median," and such
> ties are quite likely. This is very much a problem created by the use of
> median rather than sum-of-votes or average. And average creates a problem
> with what will be very common: unrated candidates.
> There is no such problem in Majority. Which is sum-of-votes, not "average
> vote." Someone who abstains by not voting for a candidate is treated as if
> they voted No. (In a real abstention, they do not vote in the election.)
> Nor is a blank in Majority treated as mid-rating. It is, quite simply, *not
> a consent to the election of that candidate.* And classical systems are
> looking for *explicit majority consent.*

So to you, if you get to counting grade G-1 without any majorities, and
then at grade G, X has 56% and Y has 54%, that's not a "tie", but two
candidates with the same median and different GMJ scores is. Sure, OK,

>  I can't understand exactly what you're saying about terms. But that's OK,
>> because which system is best is the first question.
> No. This is an implementation path, and such paths only rarely *begin
> with* the "best."

What I mean is, the best system to put at step 2; the one which will make
for the easiest transition 1->2, the least backsliding 2->1, and the most
energy for further steps if needed.

>   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
>> trivial.
> This is what I place as a later tweak, i.e., I go to five levels, i.e,.
> Range 4. There are then two unapproved categories and three approved ones.
>  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 argument.
> I've given it above. I would not *oppose* a letter-grade implementation,
> but would worry that it could lead to a backlash. It's not been tried in
> any public elections, and, as I've stated, it will, I expect, encourage
> relatively disempowered votes. But voters might wise up to that.

I think they would wise up. But we're pretty close to agreeing on this one.

>  3. Different tiebreaker. Advantages on either side:
>> ER-Bucklin: Simpler to explain.
> You do understand, I hope, that this is a *huge* advantage. The
> improvement in performance had better be major to justify this.
>  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.
> "Better chicken dilemma resistance"? It's essentially the same system, but
> grading *conceals* the choice to some extent. It's right out in the open
> and obvious with Bucklin. The only "strategy" that makes much sense with
> Bucklin is rank-skipping, which has a clear effect: it expresses preference
> strength.

I was only talking about the difference in tiebreakers, as explained above.

By the way: your bucklin-with-possible-runoffs proposals are immune from
the Chicken Dilemma; at worst, it would just cause a runoff which "honest"
votes could have avoided; and in that case, I can very much sympathize with
your argument that the Chicken-style votes are actually an "honest"
statement that the voter prefers a runoff to a premature compromise.

> Bucklin was a "preponderance of the votes" system, seeking a majority.
> Without a runoff process, it's a Plurality system, then. That is, after the
> amalgamation process is complete, the winner is the candidate with the most
> votes. That is *terminally simple,* and is very easily understood.
> With GMJ, there is the median vote, which will relatively often tie. Hence
> the G in GMJ. GMJ substitutes a graduated median for sum of votes. Thus
> each vote affects the "graduated median." So ties become rare.
> Both systems, as practical systems, would need to have rules for true
> tie-breaking.

Of course. But true ties are vanishingly rare in practice.

>  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.
> The appropriate agreement will certainly be wider, as happened with
> Approval as a first step. What I think is needed is a recognition that:
> 1. Bucklin uses a Range ballot.


> 2. Bucklin provides *limited* later-no-harm protection.


> 3. Same as above, Bucklin allows clean and vote-splitting-harmless
> expression of true favorite.


> I am *not* proposing Bucklin as an "ideal" or "perfect" voting system,
> though, for some contexts, it might be "good enough." If Bucklin uses a
> full range ballot (i.e., Range 4 or higher, say), the data is there to
> collect information on expressed relative utilities. Hence:
> 4. Bucklin will allow the collection of Range data. All this takes is
> counting all the votes, which, in my view, is a courtesy to voters as well
> as providing much better information to candidates and their supporters.

Agreed. In fact, the simplest way to count bucklin is to tally by grade
level, and publishing that data will give more than Range info, though less
than Condorcet.

> 5. Thus, Bucklin will foster the "nursery effect," often cited by Range
> supporters as a characteristic of Range voting.


> As to names, the name should not be misleading. Bucklin is not misleading.
> It's the name of a family of systems, though. IRAV might work. Bucklin
> *does* simulate a series of approval elections without eliminations but
> with voters being able to control the introduction of additional approvals.
> Bucklin-ER is what I generally have in mind, but I would not be opposed to
> an ordinary Bucklin system implementation, ER merely makes the system,
> under some conditions, a little more efficient. Non-ER Bucklin will result
> in the rejection of overvotes, and conflicts with Count All the Votes,
> which is my own fun name for Approval, that reduces it to what is actually
> done. No judgment, no sentiment about 'approval,' just the *facts.*
> Your vote will be counted. Period.

OK. So you favor the term IRAV. I think we could have consensus on that,
but I'd like to see if others have comments. Also, I don't want to start
actually using that term myself until we agree exactly what it means, that
is, until we choose a specific Bucklin system to advocate together.

> 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
>> tests.
> And the results?
See for instance http://rangevoting.org/StratHonMix.html. In a run with 50%
strategy where range BR is around 0.16, both "TopMedianRating" and Approval
have a BR around 0.20. If Median encouraged significantly less strategy, it
could easily have a BR in the neighborhood as Range.

>  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'm not "worried" about this, because *it will happen.* The *concern* is
> that some voters will do this without understanding that they are, thereby,
> disempowering themselves. The expression must be allowed. However, voters
> will have the option, at least in the U.S., to vote for a write-in
> candidate. If they want to bullet vote for the write-in, great. It is their
> choice.

Right. That will happen.

>  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.
> Do understand that this objection is essentially raised by *experts*. The
> classic Saari objection to Range Voting is based on an example where 99% of
> voters do that. The Saari objection is based on an idea that voters are
> supposed to make a choice. He's correct, but doesn't seem to understand
> that voters may choose to *strongly approve* of all candidates. Give them
> all an A! However, will these voters later have regret? When they see the
> results, will they be kicking themselves?
> These are *questions*, not declarations of Truth (TM).
>   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.
> No. "Historical curve" is a disempowering standard. The "curve" is the
> present candidate set, and if we want to be even more specific about it, it
> is the "expected set of possible winners." Someone who thinks that Obama is
> "objectively horrible" is only going to give him an A if he thinks that
> Obama is the *best* of all the possible winners. And even then it will
> grate.

I don't think we have to resolve all these issues. I see what you're saying
and disagree, but we're not far apart here, and it's a bit of a distraction
from the main point of the thread.

> "A" has an ordinary meaning to people. Above, it's acknowledged by Jameson
> that, in the voting system, it does not *actually mean that.* So why use
> it? Why not just label the category with the effect?
> 4. Maximum support.
> 3. Middle support.
> 2. Minimum support.
> 1. No support.
> 0. Maximum opposition.
> In fact, those could be labelled with the letters *as long as the meaning
> is clear.*
> A. Max
> B. Med
> C. Min
> D. No Pass
> F. Fail.
> I even used "fail" there. How's that? There should be no way for a
> candidate with majority (D or F) to pass, i.e., to win the election. An F
> is a maximum action toward including the candidate in a runoff. A D might
> provide some effect toward that.
Again, you're assuming runoffs. I support you there, but one step at a time.

>  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.
> Jameson, then you have not been paying attention, and you are not using
> independent thinking. I.e, you are being "ordinary." I'm expecting more
> from you. How about it?

I was reacting to your suggestion of reporting "a net grade point average".
As you know, score and bucklin are different systems, so there would be
(rare) cases where the winning Bucklin candidate did not have the highest
average. Would you still just report that?

If you're just reporting the average as a curiousity for folks like us,
great. But if you're using it to try to help explain the Bucklin results,
that's asking for trouble.

Again, this is a side point. We don't have to agree, but I wanted us to at
least understand each other.

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