[EM] Upper-Bucklin naming (was: Median systems, branding....)

Jameson Quinn jameson.quinn at gmail.com
Fri Jun 14 17:52:09 PDT 2013

So. Abd and I now agree that a Bucklin system which uses just the
above-median votes to break ties is probably the best first step towards
median voting. I'd like to get the details worked out, so we can stop using
different terms ("Bucklin", "MJ", "GMJ") and settle on a single
clearly-defined proposal. I'd love to hear what others feel about these
issues (though this isn't really the place for debating whether some other
class of voting system, such as Score or Condorcet or whatever, is better
or worse than Bucklin/Median systems in general).

1. How to best express the system? Two equivalent definitions:

   - *Top-down*: "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 most votes above that level wins. If there are no votes above that
   level, the highest votes at or above that level wins."
   - *Bottom-up*: "Count the votes at the lowest grade against each
   candidate. If any candidates have a majority against, eliminate them from
   consideration. Continue adding in the next-lowest grade, until there is
   just one or zero candidates left. If there's one left, they win. Otherwise,
   if the last few candidates are eliminated together, choose whichever of
   that group was eliminated by the smallest majority against."

2. How many rating/grade/rank levels should be used, and how should they be
labeled? I'd suggest the following 5, along the lines of something Abd

A: Unequivocal support
B: Probable support (unless there's a candidate with majority "A" support)
C: Neutral (support or oppose, depending on other candidates' results)
D: Probable opposition (unless all other candidates have majority "F"
F: Unequivocal opposition

(I've relabeled the categories to help clarify their strategic meaning; for
instance, I changed "strong" to "unequivocal")

I would also be open to having blank votes count as "E" rather than "F",
but I think that's probably an unnecessary complication to begin with.

3. What should we call this system? Abd seemed happy with "Instant Runoff
Approval Voting". I'd be fine with that too, but before we settle on that,
we should look at the downsides:

   - FairVote has been moving away from "Instant Runoff / IRV" and towards
   "ranked choice/ RCV" in recent years. I don't know all of their reasons,
   but I suspect it is partially to do with the legalism of ballot initiative
   language. That is, IRV is technically neither instant nor a runoff, though
   it is certainly close on both counts.
   - It could lead to confusion between IRAV and IRV. That has its upsides
   — piggybacking on FairVote's existing publicity — but also its downsides —
   as we know, IRV is actually a pretty flawed system.

So I think we should have a poll with various options (using the system
itself to rate the options, of course). I'll start out with some proposals
and my votes:

-Descending Approval Threshold (DAT) Voting: A
-Descending Approval Threshold Adjudgment (DATA voting): B
-Majority Approval Threshold (MAT; note that the M could also be
backronymmed to "Median"): A
-Bucklin: F (not that we shouldn't say that this system is a Bucklin
system, just that that shouldn't be our only name for it)
-Bucklin-ER or ER-Bucklin: D (has already been used for other systems, not
a descriptive name)
-Graded Approval Threshold (GAT): C (Not bad, but not great)
-Majority Assignment of Grades (MAG): C (ditto)
-Graded Majority Approval (GMA): B (this one seems simple and descriptive)

Note that all of the above names could, in principle, apply to almost any
Bucklin system; but whichever one we pick, we'll arbitrarily define it as
being this system in particular.

Abd and anyone else who has an opinion: please vote among the above options.


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

> At 03:53 PM 6/13/2013, you wrote:
>> I just had a minor realization. As I said to Abd, his Bucklin-ER (as I
>> understand it) has slightly less resistance to the chicken dilemma than
>> GMJ, because the Bucklin-ER tiebreaker effectively ends up focusing
>> slightly below the median in the grade distribution, while GMJ focuses on a
>> region balanced around the median. Well, why not take that in the other
>> direction? Consider the following Bucklin system, tentativlely named:Â
>> uı|ʞɔnq-ᴚƎ:
>> 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 most
>> votes above that level wins. If there are no votes above that level, the
>> highest votes at or above that level wins.
> Now, this is familiar to me. I'm not searching right now, but I do think
> that this may have been a tiebreaker method with traditional Bucklin.
> Here, what it does is to award a win based on a plurality in the prior
> rank, but with the approval of a majority as shown by the next rank of
> approvals. Way cool. It incentivizes expressing preferences with some
> strength. If candidate count increases to that the limitation to three or
> four ranks is a problem, the number of ranks (ratings) may be increased.
>  Now consider a chicken dilemma where Y and Z must cooperate to defeat X.
>> If a Y voter rates Z at the second-to-bottom grade, then further strategy
>> simply will not help unless Z's median falls to 0 — which would mean
>> risking ann X win if Z's voters are similarly strategic. This is a
>> stronger, and more-simply-argued, bulwark against the chicken dilemma's
>> slippery slope than GMJ's.
> Indeed it is simpler, which is a powerful argument for it. You don't even
> have to mention "median."
> It *does have a problem*, which may show up in simulations. I'd prefer
> this method if completion in a single round is being insisted on. I'd want
> to see if the previous round winner and the plurality winner in the next
> round agree. If they do, easily, done. If not, then it could be time for a
> runoff.
> As stated, the method is not Condorcet compliant. In a runoff system or if
> the completion in the first round requires coincidence of the plurality
> winner at both ranks, I suspect it is Condorcet compliant *as to the
> evaluated ranks.* It's simple to extend that by using pairwise analysis on
> all the ranks.
>  GMJ still has certain advantages. Because it's cleaner and more
>> symmetrical in an abstract sense, its criterion compliances are slightly
>> better; and uı|ʞɔnq-ᴚƎ does not allow reporting via 1 number per
>> candidate. But these are minor, technical points. While I still have a
>> father's affection for GMJ, I think that uı|ʞɔnq-ᴚƎ is now my
>> favorite system.
> It could be quite good. I'd want to see simulation analysis of it by
> comparison with other methods.
>  Obviously the name needs fixing; I've left it with a deliberately
>> unusable one for now. I'd be happy to call it IRAV, or APV, or whatever
>> other people support in this thread.
> It's a Bucklin method! It merely deals with the issue of multiple
> majorities. As I've written, we should be so lucky as to have those. What
> this would do is to encourage, relatively, additional approvals at the
> lower rank. It is an additional LnH protection.
> Bucklin-ER/MMP? Multiple Majority Protection.
> Multiple Majorities occur because the majority is a bit over-eager to
> compromise. This method backs up if a multiple majority occurs. By doing
> so, it makes the so-called "chicken dilemma" less of a dilemma. The chicken
> dilemma is a fear of LnH failure. Do I vote for a compromise or do I
> continue to stand for my Favorite(s)?
> To make this more obvious and more *accurate*, consider the use of more
> ranks. With more approved ranks, a multiple majority becomes less likely,
> and a majority is cleanly found, more often. This, then, is a method of
> handling the rarer multiple majorities.
> And, did we mention, it is *easy to explain*?
> *Somebody* has been listening to my rantings.
> Thanks, Jameson. Great work.
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