Copeland//Plurality --- can it beat IRV?
Dear All,
There is compelling reason why electoral reformers in the USA are promoting IRV. Firstly the monarchist mind-set on single districts, apparently shared as much in this group, as in American society, as a whole.
To the credit of Voter Choice Massachusetts, they see STV as a continuation of IRV. Multi-member constituencies are more important for democracy, as distinct from minimally democratic IRV or other single member systems.
A science cannot depend solely on mathematics (as was suggested in the nineties of string theory). That is just rationalistic scholasticism. Robert Heinlein, in one of his stories, said there are only mathematicians and peasants. If so, the scientific role of the earth-bound is under-rated.
Comment is free but facts are sacred. The fact is that STV, which has in common with IRV, premature exclusion of candidates, never the less, produces the election, mainly of first or high preferences. It may be non-monotonic, technically, but it is in fact a reliable system.
In my system of electoral thought, conventional STV (including Meek method)
Is zero order binomial stv. That is because it has only one of two rational terms, election count and exclusion count. That description is not meant to be a put-down: it is saying that traditional stv is not so much wrong, as the beginning of an approximation in counting.
My hand counts in binomial stv are just first order binomial stv: one rational election count combined with one rational exclusion count. Conventional stv has only one rational count; is a rationally uninomial count. And that is combined with merely an ordinal Last Past The Post exclusion count.
Binomial stv has greater continuity between single and multi-member districts, than IRV has with STV. This is because binomial stv puts Gregory method in the form of keep values, and, unlike Gregory method, keep values can be used for single districts as well as multiple seats per constituency.
Regards,
Richard Lung.
On 28 Jan 2022, at 12:53 pm, Toby Pereira tdp201b@yahoo.co.uk wrote:
I think the problem with these long threads is that there are rarely concluding thoughts at the end, so unless you're following very closely, you might miss the best stuff. Understandably people post stuff as it comes to them, so you get people's "stream of consciousness", but I think it would be good if, once a discussion is dying down, the main contributors then posted a summary of their overall thoughts and findings, and which things they would take forward.
Toby
On Friday, 28 January 2022, 09:12:17 GMT, Rob Lanphier roblan@gmail.com wrote:
On Thu, Jan 27, 2022 at 10:06 PM Forest Simmons
forest.simmons21@gmail.com wrote:
The name might be "Gross Loser Elimination"
The Gross Loser is the candidate that comes closest to being skunked in a pairwise matchup.
Ew, ick, what a gross loser! EWWW-W-W-W-W-W! :-D
I only have a cursory idea what y'all are talking about (and don't
bother trying to explain it; I may go back and do more than skim the
messages at some point, but I don't have the mental energy to spend on
this right now).
Regardless, I would love all of your help (everyone on EM-list) in
making electowiki more accessible to people new to electoral reform.
I think it's cool that Forest is trying to come up with names for this
new method that sounds marketable (sorta like "Ranked Robin").
However, my fear is that more names for minor variants of Llull's
method https://electowiki.org/wiki/Lllull's_method) is just going to
confuse people, given that Llull/Condorcet/Copeland has been around
for a while and yet hasn't taken the world by storm.
It could be that I need to study some more in order to participate in
this mailing list. It's been a long, long time since I've truly
wrapped my brain around linear algebra (which .... I didn't do very
well in that subject my first time around). I suppose I should
probably watch enough YouTube videos such that I've had enough of a
refresher in that topic to where I can follow the topic as fluidly as
you all seem to follow the discussions.
Regardless, we could use more editors helping us on electowiki, and
less voting method criteria or new methods to sort, because we're not
even CLOSE to sorting out everything that other editors have dumped on
electowiki over the past fifteen years or so. By "help", I should be
clear: we need people looking at existing articles with fresh eyes,
and improving them so that people new to electoral reform can
understand them. Let's make them as approachable as "Good Articles"
on English Wikipedia (which have a specific meaning:
https://en.wikipedia.org/wiki/Wikipedia:Good_articles)
Since I'm threadjacking, I'll finish by actually addressing Dr.
Carerra's original suggestion. Because I've been on this mailing list
for so long, I understand what "Copeland//Plurality" means (and I like
the idea of exploring that chain of methods for criterion compliance).
For those of us that like the Condorcet-winner criterion (CWC), some
sort of Copeland hybrid seems like a promising path toward an
explainable CWC system.
Rob
p.s. sorry if this email seems like I'm picking on either of you in
particular (Dr. Daniel Carrera or [TitleUnknown] Forest Simmons). I
just saw "gross loser" and it triggered the smartass in me, which then
provided me an entry point to speak to everyone active in this thread.
p.p.s. In reviewing before hitting "send", I realized I should read
more of the thread. I see now that y'all are talking about something
which MIGHT be better than BTR-IRV, and in general, I really like
Condorcet-winner-compliant alternatives to IRV that might be simple
enough to get people to rally behind. Riffing off of Copeland seems
promising, because sports junkies generally don't have an issue with
Win-Loss-Tie standings, and I think the Copeland-esque view of
Burlington 2009 election provides the clearest view of the unfairness
of what happened:
https://electowiki.org/wiki/2009_Burlington_mayoral_election#Pairwise_results
Election-Methods mailing list - see https://electorama.com/em for list info
Election-Methods mailing list - see https://electorama.com/em for list info
On 28.01.2022 13:53, Toby Pereira wrote:
I think the problem with these long threads is that there are rarely
concluding thoughts at the end, so unless you're following very closely,
you might miss the best stuff. Understandably people post stuff as it
comes to them, so you get people's "stream of consciousness", but I
think it would be good if, once a discussion is dying down, the main
contributors then posted a summary of their overall thoughts and
findings, and which things they would take forward.
That's a good idea, though I guess in some cases it could get a bit
difficult to determine when a conversation is over :-)
But for my threads, the exact spatial model one was discussing how we
could get a better approximation of the probability that a random
election in say a (10 voters, 4 candidates, 3 issues) spatial model will
be a particular given election. This would be useful for constructing
optimal strategically resistant methods in spatial models, and optimal
methods trading off between unmanipulability and VSE.
But unfortunately doing so seems to require determining a Voronoi map
for each instance of the spatial model (with candidates fixed); in
essence integrating over area of the intersection of some Voronoi
regions, over every possible position of the candidates in issue space.
Which looked pretty daunting to me, so I thought that the best we could
do is sampling the volume of the region with candidates fixed, and then
integrating that.
Then Daniel and Forest discussed ways to estimate this (I think? Or to
exactly evaluate something close to what I'm looking for), but my diff
eq skills are not nearly up to the task of following them.
There was also another thread where I was trying to extend my fpA-fpC
method to more than three candidates by making use of a recursive notion
inspired by IRV. I found a more elegant phrasing of the three-candidate
version (with a different tiebreaker when there's a pairwise tie), but
nothing conclusive out to four and beyond; though I do think the
recursive approach itself could be useful later. (Off-list I used the
recursive approach to find out that letting A's score be the minimum of
A's score in any three-candidate sub-election is monotone and preserves
DMT -- though it likely doesn't preserve DMTBR.)
And this thread (that I'm replying to) is about Copeland//Plurality and
IRV-flavored Condorcet methods. Forest suggested Minmax-elimination,
i.e. Raynaud. The "gross loser" he's referring to is, I think, by
Benham, which restores Plurality compliance to the method.
-km
Hi Forest,
Le vendredi 28 janvier 2022, 00:06:19 UTC−6, Forest Simmons forest.simmons21@gmail.com a écrit :
It is so omputationally simple that a small child can do it manually, given a
copy of the pairwise matrix:
Let k be the row containing the smallest entry in the entire matrix. [Too hard
for a small child to find?] Cross out both row k and column k. [Kids like this
kind of work.] Repeat until only one entry remains. Elect the candidate whose
row is not crossed out.
This method is due to Benham's modification of a non-Condorcet method whose
name slips my mind at the moment.
Sounds like it could be Chris' complicated "MinLV" Condorcet method which I
could imagine having been inspired by Woodall's "MinGS", which just elects
whichever candidate has the greatest minimum votes-for.
The name might be "Gross Loser Elimination"
The Gross Loser is the candidate that comes closest to being skunked in a pairwise
matchup.
Elect the candidate that remains after repeatedly eliminating the Gross Loser.
Eleven words ... perhaps the best possible RCV method that can be defined so
unambiguously and succinctly.
No need to mention Smith, but the fact remains it always elects a Smith member.
Here's a classic example of Chicken Defense:
49 C
26 A>B
25 B (sincere B>C)
B subverts the sincere CW (A) by a chicken defection that creates a cycle
A>B>C>A
RP, Schulze, MinMax, River, etc reward the defector by breaking the cycle at the
A>B step, which is the weakest majority (26 to 25), allowing the defector to win
with impunity.
Here is some criticism of that.
-
The method doesn't know whether anybody is strategizing, so the method
punishes the B voters even when they themselves believe they are sincere. -
The method does not only punish the strategizers, it punishes the entire
majority. The A voters as well are confronted with an incentive: to NOT vote for
A next time, or to at least rank B above A. We have a very similar incentive in
FPP.
Somehow one needs to show that it's more likely that this punishment threat
causes the whole B faction to add on sufficient A preferences, than that the
majority decides before the election not to play with fire, and they withdraw
one of the candidates.
Personally I think this punishment dynamic does nothing but deter nomination.
- Look at what happens if we switch the sizes of the A>B and B factions. Now B
wins and is NOT punished for defecting. This tells me that we didn't actually
fix the issue, because "not both" factions are required to cooperate. A faction
that "knows" they are the larger of the two, is exempt.
Probably the only real "chicken dilemma-proof" method is DSC. There if the
majority does not form a mutual majority, they just aren't going to win.
Kevin
Great summary!
Update on Hamiltonian MonteCarlo (HMC) that Da will and I were considering
... it is more adapted to sampling constant energy states.
Putting aside the HMC/ergodicity idea for now, we can still use the
"electo-potential" idea for finding different kinds of equilibria...
depending on which L_p norm is understood in the steepest descent equation
dr/dt=-grad V(r),
Where the "electo-potental" V(r) is defined as
V(r)=Sum(over voter positions R) of the product ||R-r||f(R), where f(R) is
the fraction of the voters concentrated at R.
It looks like the L_1 norm is most suitable for an issue space in the form
of a Cartesian product of issue axes.
Also argmin{||gradV at k|| : k in K}, where K is the set of candidates,
seems to be a previously unknown Smith efficient election method.
It should be highly manipulation resistant because the norm of grad V at k
is possibly the best measure of the combined voter pull on candidate k away
from its position in "electo-space".
El sáb., 29 de ene. de 2022 5:35 a. m., Kristofer Munsterhjelm <
km_elmet@t-online.de> escribió:
On 28.01.2022 13:53, Toby Pereira wrote:
I think the problem with these long threads is that there are rarely
concluding thoughts at the end, so unless you're following very closely,
you might miss the best stuff. Understandably people post stuff as it
comes to them, so you get people's "stream of consciousness", but I
think it would be good if, once a discussion is dying down, the main
contributors then posted a summary of their overall thoughts and
findings, and which things they would take forward.
That's a good idea, though I guess in some cases it could get a bit
difficult to determine when a conversation is over :-)
But for my threads, the exact spatial model one was discussing how we
could get a better approximation of the probability that a random
election in say a (10 voters, 4 candidates, 3 issues) spatial model will
be a particular given election. This would be useful for constructing
optimal strategically resistant methods in spatial models, and optimal
methods trading off between unmanipulability and VSE.
But unfortunately doing so seems to require determining a Voronoi map
for each instance of the spatial model (with candidates fixed); in
essence integrating over area of the intersection of some Voronoi
regions, over every possible position of the candidates in issue space.
Which looked pretty daunting to me, so I thought that the best we could
do is sampling the volume of the region with candidates fixed, and then
integrating that.
Then Daniel and Forest discussed ways to estimate this (I think? Or to
exactly evaluate something close to what I'm looking for), but my diff
eq skills are not nearly up to the task of following them.
There was also another thread where I was trying to extend my fpA-fpC
method to more than three candidates by making use of a recursive notion
inspired by IRV. I found a more elegant phrasing of the three-candidate
version (with a different tiebreaker when there's a pairwise tie), but
nothing conclusive out to four and beyond; though I do think the
recursive approach itself could be useful later. (Off-list I used the
recursive approach to find out that letting A's score be the minimum of
A's score in any three-candidate sub-election is monotone and preserves
DMT -- though it likely doesn't preserve DMTBR.)
And this thread (that I'm replying to) is about Copeland//Plurality and
IRV-flavored Condorcet methods. Forest suggested Minmax-elimination,
i.e. Raynaud. The "gross loser" he's referring to is, I think, by
Benham, which restores Plurality compliance to the method.
-km