C
C.Benham
Mon, Aug 14, 2023 4:09 AM
I think this is an interesting point. We can ask at a philosophical level what makes a good voting method. Is it just one that ticks the most boxes, or is it one that most reliably gets the "best" result?
Toby,
How are those two counter-posed? What do you think "the boxes" are about?
And that's partly because the premise of Condorcet is essentially built on a logical fallacy - basically that if A is preferred to B on more ballots that vice versa then electing A must
be a better result than electing B.
I'd be interested in reading your explanation of why you think that is a
"logical fallacy". What about if there are only two candidates?
I think generally while passing certain criteria is a good thing,..
Which ones do you have in mind?
Chris B.
Date: Sun, 13 Aug 2023 22:17:44 +0000 (UTC)
From: Toby Pereiratdp201b@yahoo.co.uk
To:"election-methods@lists.electorama.com"
Subject: Re: [EM] STAR
I think this is an interesting point. We can ask at a philosophical level what makes a good voting method. Is it just one that ticks the most boxes, or is it one that most reliably gets the "best" result? And what do we mean by best result? Are we working from the assumption that there is a best result to begin with (e.g. nearest the median, highest utility, closest possible to Condorcet winner) and looking for a method that most reliably picks that? I think generally while passing certain criteria is a good thing, occasional failures on multiple criteria isn't necessarily worse than strictly passing more criteria but also having worse failures than others. This is very hypothetical of course, and it does depend on the specific criteria.
However, if someone was naively looking at a list of criteria in isolation without knowing what was compatible with what, I think they would be more likely to put participation ahead of Condorcet than vice versa in a list of importance. But because participation is very hard to achieve (in simple terms you can have score, approval and some other awful methods), it's largely brushed under the carpet. Whereas, on the other hand, Condorcet is largely held up as the biggest deal of the lot on this mailing list. It's not that I think Condorcet is such a bad thing - I just don't think it's the be-all-and-end-all. In terms of voting reform, it can make sense to push for it because it makes intuitive sense, but in an ideal world where everyone was enlightened, I don't think it would have to be a deal-breaker. And that's partly because the premise of Condorcet is essentially built on a logical fallacy - basically that if A is preferred to B on more ballots that vice versa then electing A must
be a better result than electing B.
Toby
Toby wrote:
> I think this is an interesting point. We can ask at a philosophical level what makes a good voting method. Is it just one that ticks the most boxes, or is it one that most reliably gets the "best" result?
Toby,
How are those two counter-posed? What do you think "the boxes" are about?
> And that's partly because the premise of Condorcet is essentially built on a logical fallacy - basically that if A is preferred to B on more ballots that vice versa then electing A must
> be a better result than electing B.
I'd be interested in reading your explanation of why you think that is a
"logical fallacy". What about if there are only two candidates?
> I think generally while passing certain criteria is a good thing,..
Which ones do you have in mind?
Chris B.
> Date: Sun, 13 Aug 2023 22:17:44 +0000 (UTC)
> From: Toby Pereira<tdp201b@yahoo.co.uk>
> To:"election-methods@lists.electorama.com"
>
> Subject: Re: [EM] STAR
>
>
>
> I think this is an interesting point. We can ask at a philosophical level what makes a good voting method. Is it just one that ticks the most boxes, or is it one that most reliably gets the "best" result? And what do we mean by best result? Are we working from the assumption that there is a best result to begin with (e.g. nearest the median, highest utility, closest possible to Condorcet winner) and looking for a method that most reliably picks that? I think generally while passing certain criteria is a good thing, occasional failures on multiple criteria isn't necessarily worse than strictly passing more criteria but also having worse failures than others. This is very hypothetical of course, and it does depend on the specific criteria.
> However, if someone was naively looking at a list of criteria in isolation without knowing what was compatible with what, I think they would be more likely to put participation ahead of Condorcet than vice versa in a list of importance. But because participation is very hard to achieve (in simple terms you can have score, approval and some other awful methods), it's largely brushed under the carpet. Whereas, on the other hand, Condorcet is largely held up as the biggest deal of the lot on this mailing list. It's not that I think Condorcet is such a bad thing - I just don't think it's the be-all-and-end-all. In terms of voting reform, it can make sense to push for it because it makes intuitive sense, but in an ideal world where everyone was enlightened, I don't think it would have to be a deal-breaker. And that's partly because the premise of Condorcet is essentially built on a logical fallacy - basically that if A is preferred to B on more ballots that vice versa then electing A must
> be a better result than electing B.
> Toby
TP
Toby Pereira
Mon, Aug 14, 2023 8:41 AM
I think this is an interesting point. We can ask at a philosophical level what makes a good voting method. Is it just one that ticks the most boxes, or is it one >>that most reliably gets the "best" result?
How are those two counter-posed? What do you think "the boxes" are about?
I mentioned that there could be multiple low-level failures versus a few high-level failures, but also that it was a fairly hypothetical discussion. I'm not of the view that because of Jameson Quinn's simulations, it must be the case that the only way to get the best results is to sacrifice the strict passing of criteria. However, if we do define best in terms of utility or the median voter, I'm agnostic as to what method would best get these results in practice. But it is still interesting that STAR does well in Jameson's simulations. As for what the boxes are about, they are about ensuring that voting methods have sensible behaviour in certain situations, so I wouldn't expect them to necessarily negatively correlate with a "good" result.
And that's partly because the premise of Condorcet is essentially built on a logical fallacy - basically that if A is preferred to B on more ballots that vice versa >>then electing A must
be a better result than electing B.
I'd be interested in reading your explanation of why you think that is a
"logical fallacy". What about if there are only two candidates?
It's what I just replied to Kristofer - the fact that there's no way that you can consistently define society's preference in a way that you can determine whether society prefers A or B by looking at the pairwise comparison. It also doesn't make any difference if there are only two candidates. It's just that with two candidates, you won't notice it. If A and B are the only two candidates, then A might pairwise beat B and get elected. But if C also stood, B might be the winner under any of the sensible Condorcet methods that people on this mailing list consider. So is A preferred to B or vice versa? And is it the same answer regardless of whether C stood? Also if C was unsure about standing but ultimately did, how would we view the creation of a cycle? Would we say that it's bad that it messed up our majoritarian ideals? Or would we say that it's good because it gave us more information overall, and with this extra information B was ultimately rightly selected over A?
One of the reasons I bring this up is that there are some people who think that only a Condorcet method could even be considered democratic. I would counter this by saying that it's based on this logical contradiction. I would also counter it by saying that someone could equally say (perhaps have a greater claim) that a method cannot be democratic if it fails participation. This isn't to say that I don't like Condorcet methods, but I don't think it's a good idea to have them on a pedestal when discussing the best method to use in a situation. They are not the last word in democracy.
I think generally while passing certain criteria is a good thing,..
Which ones do you have in mind?
Two of the main ones I tend to look out for are monotonicity and independence of clones because they are obviously things we would want and they don't seem to be too restrictive in terms of methods they allow. But then with monotonicity, there is a family of criteria in addition to the "standard" one, some of which might be more restrictive than others. One criterion that I consider to be largely a box-ticking exercise is Local Independence of Irrelevant Alternatives. But other criteria such as participation and Independence of Irrelevant Alternatives look great in the abstract, but are very restrictive in terms of what they allow. Well, even methods that supposedly pass IIA in theory (e.g. approval, score) in no way pass them in practice.
On Monday, 14 August 2023 at 05:09:31 BST, C.Benham <cbenham@adam.com.au> wrote:
>Toby wrote:
>> I think this is an interesting point. We can ask at a philosophical level what makes a good voting method. Is it just one that ticks the most boxes, or is it one >>that most reliably gets the "best" result?
>Toby,
>How are those two counter-posed? What do you think "the boxes" are about?
I mentioned that there could be multiple low-level failures versus a few high-level failures, but also that it was a fairly hypothetical discussion. I'm not of the view that because of Jameson Quinn's simulations, it must be the case that the only way to get the best results is to sacrifice the strict passing of criteria. However, if we do define best in terms of utility or the median voter, I'm agnostic as to what method would best get these results in practice. But it is still interesting that STAR does well in Jameson's simulations. As for what the boxes are about, they are about ensuring that voting methods have sensible behaviour in certain situations, so I wouldn't expect them to necessarily negatively correlate with a "good" result.
>> And that's partly because the premise of Condorcet is essentially built on a logical fallacy - basically that if A is preferred to B on more ballots that vice versa >>then electing A must
>> be a better result than electing B.
>I'd be interested in reading your explanation of why you think that is a
>"logical fallacy". What about if there are only two candidates?
It's what I just replied to Kristofer - the fact that there's no way that you can consistently define society's preference in a way that you can determine whether society prefers A or B by looking at the pairwise comparison. It also doesn't make any difference if there are only two candidates. It's just that with two candidates, you won't notice it. If A and B are the only two candidates, then A might pairwise beat B and get elected. But if C also stood, B might be the winner under any of the sensible Condorcet methods that people on this mailing list consider. So is A preferred to B or vice versa? And is it the same answer regardless of whether C stood? Also if C was unsure about standing but ultimately did, how would we view the creation of a cycle? Would we say that it's bad that it messed up our majoritarian ideals? Or would we say that it's good because it gave us more information overall, and with this extra information B was ultimately rightly selected over A?
One of the reasons I bring this up is that there are some people who think that only a Condorcet method could even be considered democratic. I would counter this by saying that it's based on this logical contradiction. I would also counter it by saying that someone could equally say (perhaps have a greater claim) that a method cannot be democratic if it fails participation. This isn't to say that I don't like Condorcet methods, but I don't think it's a good idea to have them on a pedestal when discussing the best method to use in a situation. They are not the last word in democracy.
>> I think generally while passing certain criteria is a good thing,..
>Which ones do you have in mind?
Two of the main ones I tend to look out for are monotonicity and independence of clones because they are obviously things we would want and they don't seem to be too restrictive in terms of methods they allow. But then with monotonicity, there is a family of criteria in addition to the "standard" one, some of which might be more restrictive than others. One criterion that I consider to be largely a box-ticking exercise is Local Independence of Irrelevant Alternatives. But other criteria such as participation and Independence of Irrelevant Alternatives look great in the abstract, but are very restrictive in terms of what they allow. Well, even methods that supposedly pass IIA in theory (e.g. approval, score) in no way pass them in practice.
>Chris B.
Toby
F
fdpk69p6uq@snkmail.com
Wed, Aug 16, 2023 4:52 PM
On Mon, Aug 14, 2023 at 12:09 AM C.Benham wrote:
I think this is an interesting point. We can ask at a philosophical
level what makes a good voting method. Is it just one that ticks the most
boxes, or is it one that most reliably gets the "best" result?
The one that most reliably gets the best result in the real world. The
difficulty with this approach is accurately modeling human voting behavior
and the consequent utility experienced from the winner, but it's still the
better answer philosophically.
(Note that VSE predates Jameson Quinn by decades, and has had several
different names: https://en.wikipedia.org/wiki/Social_utility_efficiency)
And that's partly because the premise of Condorcet is essentially built
on a logical fallacy - basically that if A is preferred to B on more
ballots that vice versa then electing A must
be a better result than electing B.
I'd be interested in reading your explanation of why you think that is a
"logical fallacy". What about if there are only two candidates?
Ranked ballots can't capture strength of preference. It's possible for a
majority-preferred candidate to be very polarizing (loved by 51% and hated
by 49%), while the minority-preferred candidate is broadly-liked and has a
much higher overall approval/favorability rating. Which candidate is the
rightful winner?
https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html
"Suppose you and a pair of friends are looking to order a pizza. You, and
one friend, really like mushrooms, and prefer them over all other vegetable
options, but you both also really, really like pepperoni. Your other
friend also really likes mushrooms, and prefers them over all other
options, but they're also vegetarian. What one topping should you get?
Clearly the answer is mushrooms, and there is no group of friends worth
calling themselves such who would conclude otherwise. It's so obvious that
it hardly seems worth calling attention to. So why is it, that if we put
this decision up to a vote, do so many election methods, which are
otherwise seen as perfectly reasonable methods, fail? Plurality, top-two
runoffs http://en.wikipedia.org/wiki/Two-round_system, instant runoff
voting http://en.wikipedia.org/wiki/Instant-runoff_voting, all variations
of Condorcet's method http://en.wikipedia.org/wiki/Condorcet_method,
even Bucklin
voting http://en.wikipedia.org/wiki/Bucklin_voting; all of them,
incorrectly, choose pepperoni."
(And strength of preference is clearly a real thing in our brains. If you
prefer A > B > C, and are given the choice between Box 1, which contains B,
and Box 2, which has a 50/50 chance of containing A or C, which do you
choose? What if the probability were 1 in a million of Box 2 containing
C? By varying the probability until it's impossible to decide, you can
measure the relative strength of preference for B > C vs A > C.)
On Mon, Aug 14, 2023 at 12:09 AM C.Benham wrote:
> > I think this is an interesting point. We can ask at a philosophical
> level what makes a good voting method. Is it just one that ticks the most
> boxes, or is it one that most reliably gets the "best" result?
>
The one that most reliably gets the best result in the real world. The
difficulty with this approach is accurately modeling human voting behavior
and the consequent utility experienced from the winner, but it's still the
better answer philosophically.
(Note that VSE predates Jameson Quinn by decades, and has had several
different names: https://en.wikipedia.org/wiki/Social_utility_efficiency)
> And that's partly because the premise of Condorcet is essentially built
> on a logical fallacy - basically that if A is preferred to B on more
> ballots that vice versa then electing A must
> > be a better result than electing B.
>
> I'd be interested in reading your explanation of why you think that is a
> "logical fallacy". What about if there are only two candidates?
>
Ranked ballots can't capture strength of preference. It's possible for a
majority-preferred candidate to be very polarizing (loved by 51% and hated
by 49%), while the minority-preferred candidate is broadly-liked and has a
much higher overall approval/favorability rating. Which candidate is the
rightful winner?
https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html
"Suppose you and a pair of friends are looking to order a pizza. You, and
one friend, really like mushrooms, and prefer them over all other vegetable
options, but you both also really, *really* like pepperoni. Your other
friend also really likes mushrooms, and prefers them over all other
options, but they're also vegetarian. What one topping should you get?
Clearly the answer is mushrooms, and there is no group of friends worth
calling themselves such who would conclude otherwise. It's so obvious that
it hardly seems worth calling attention to. So why is it, that if we put
this decision up to a vote, do so many election methods, which are
otherwise seen as perfectly reasonable methods, fail? Plurality, top-two
runoffs <http://en.wikipedia.org/wiki/Two-round_system>, instant runoff
voting <http://en.wikipedia.org/wiki/Instant-runoff_voting>, all variations
of Condorcet's method <http://en.wikipedia.org/wiki/Condorcet_method>,
even Bucklin
voting <http://en.wikipedia.org/wiki/Bucklin_voting>; all of them,
incorrectly, choose pepperoni."
(And strength of preference is clearly a real thing in our brains. If you
prefer A > B > C, and are given the choice between Box 1, which contains B,
and Box 2, which has a 50/50 chance of containing A or C, which do you
choose? What if the probability were 1 in a million of Box 2 containing
C? By varying the probability until it's impossible to decide, you can
measure the relative strength of preference for B > C vs A > C.)
KM
Kristofer Munsterhjelm
Wed, Aug 16, 2023 5:54 PM
Ranked ballots can't capture strength of preference. It's possible for a
majority-preferred candidate to be very polarizing (loved by 51% and
hated by 49%), while the minority-preferred candidate is broadly-liked
and has a much higher overall approval/favorability rating. Which
candidate is the rightful winner?
https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html
"Suppose you and a pair of friends are looking to order a pizza. You,
and one friend, really like mushrooms, and prefer them over all other
vegetable options, but you both also really, /really/ like pepperoni.
Your other friend also really likes mushrooms, and prefers them over all
other options, but they're also vegetarian. What one topping should you
get?
Clearly the answer is mushrooms, and there is no group of friends worth
calling themselves such who would conclude otherwise. It's so obvious
that it hardly seems worth calling attention to. So why is it, that if
we put this decision up to a vote, do so many election methods, which
are otherwise seen as perfectly reasonable methods, fail? Plurality,
top-two runoffs http://en.wikipedia.org/wiki/Two-round_system, instant
runoff voting http://en.wikipedia.org/wiki/Instant-runoff_voting, all
variations of Condorcet's method
http://en.wikipedia.org/wiki/Condorcet_method, even Bucklin voting
http://en.wikipedia.org/wiki/Bucklin_voting; all of them, incorrectly,
choose pepperoni."
As a ranked voting guy, I'd say because incommensurability is a pain and
because it invites strategy by honest voters.
(Both of these incidentally are motivations for my attempt to make a
rated method that "takes von Neumann-Morgenstern utilities seriously".
But it's very difficult, mainly because strategic equilibria for
Approval result in the ordinal Condorcet winner being elected. See my
quick and dirty STAR ideas earlier.)
Point one: friends usually know what they mean when they say "that's
good!" or "that sucks". But suppose you have an electorate of 200
million. Some of these only rate totalitarian dictators a zero, while
others rate mildly unpleasant candidates a zero. Some of these only rate
true angels a ten, while others always rate their favorite frontrunner ten.
Now suppose the vote is so that A is the majority winner but B is ever
so slightly ahead by ratings. How do you know that B is truly the best
winner, and doesn't just have voters who tend to vote the whole range?
Point two: Now suppose you're an honest voter in this situation. The
ballot asks you for how much you like a candidate. What's the "right"
way to vote? How far do you lower the candidate you like the least? This
kind of ambiguity invites strategy and min/maxing, and in the case of
Range, further to voting Approval style (going "all the way" adapting
your scores to the situation).
My generalized STAR attempts thus reduce to majority rule in the
two-candidate case, because there's no way to absolutely calibrate the
different voters' scales. And I've been playing with lp norm
normalization among candidate triples, since that discourages
Approval-style voting. (IIRC, there are some arguments that l2
normalization incentivizes ratings whose intervals are proportional to
the utility differences, but I wouldn't be able to prove it.)
(And strength of preference is clearly a real thing in our brains. If
you prefer A > B > C, and are given the choice between Box 1, which
contains B, and Box 2, which has a 50/50 chance of containing A or C,
which do you choose? What if the probability were 1 in a million of Box
2 containing C? By varying the probability until it's impossible to
decide, you can measure the relative strength of preference for B > C vs
A > C.)
That's von Neumann-Morgenstern utilities, as I understand it. (From my
experience, sometimes it gets very hard to decide when you're close to
indifferent, though.)
The lottery information provides strength of preference up to an affine
scaling. So for each voter, there are two free parameters:
R(v, x) = a_v * U(v, x) + b_v
where R(v, x) is the voter's rating, a and b are constants, and U(v, x)
is voter v's (perceived) utility of getting x elected. The lottery
method gives us the ratio between the utilities (assuming risk
neutrality). But not a_v or b_v!
We can design the method so that it assumes every voter's scaling
constants are the same. That gives something like Range. Or we can
design it so that each voter's power is similar (OMOV), which gives
something that reduces to majority rule in the two-candidate case.
-km
On 8/16/23 18:52, fdpk69p6uq@snkmail.com wrote:
>
> Ranked ballots can't capture strength of preference. It's possible for a
> majority-preferred candidate to be very polarizing (loved by 51% and
> hated by 49%), while the minority-preferred candidate is broadly-liked
> and has a much higher overall approval/favorability rating. Which
> candidate is the rightful winner?
>
> https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html <https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html>
>
> "Suppose you and a pair of friends are looking to order a pizza. You,
> and one friend, really like mushrooms, and prefer them over all other
> vegetable options, but you both also really, /really/ like pepperoni.
> Your other friend also really likes mushrooms, and prefers them over all
> other options, but they're also vegetarian. What one topping should you
> get?
>
> Clearly the answer is mushrooms, and there is no group of friends worth
> calling themselves such who would conclude otherwise. It's so obvious
> that it hardly seems worth calling attention to. So why is it, that if
> we put this decision up to a vote, do so many election methods, which
> are otherwise seen as perfectly reasonable methods, fail? Plurality,
> top-two runoffs <http://en.wikipedia.org/wiki/Two-round_system>, instant
> runoff voting <http://en.wikipedia.org/wiki/Instant-runoff_voting>, all
> variations of Condorcet's method
> <http://en.wikipedia.org/wiki/Condorcet_method>, even Bucklin voting
> <http://en.wikipedia.org/wiki/Bucklin_voting>; all of them, incorrectly,
> choose pepperoni."
As a ranked voting guy, I'd say because incommensurability is a pain and
because it invites strategy by honest voters.
(Both of these incidentally are motivations for my attempt to make a
rated method that "takes von Neumann-Morgenstern utilities seriously".
But it's very difficult, mainly because strategic equilibria for
Approval result in the ordinal Condorcet winner being elected. See my
quick and dirty STAR ideas earlier.)
Point one: friends usually know what they mean when they say "that's
good!" or "that sucks". But suppose you have an electorate of 200
million. Some of these only rate totalitarian dictators a zero, while
others rate mildly unpleasant candidates a zero. Some of these only rate
true angels a ten, while others always rate their favorite frontrunner ten.
Now suppose the vote is so that A is the majority winner but B is ever
so slightly ahead by ratings. How do you know that B is truly the best
winner, and doesn't just have voters who tend to vote the whole range?
Point two: Now suppose you're an honest voter in this situation. The
ballot asks you for how much you like a candidate. What's the "right"
way to vote? How far do you lower the candidate you like the least? This
kind of ambiguity invites strategy and min/maxing, and in the case of
Range, further to voting Approval style (going "all the way" adapting
your scores to the situation).
My generalized STAR attempts thus reduce to majority rule in the
two-candidate case, because there's no way to absolutely calibrate the
different voters' scales. And I've been playing with lp norm
normalization among candidate triples, since that discourages
Approval-style voting. (IIRC, there are some arguments that l2
normalization incentivizes ratings whose intervals are proportional to
the utility differences, but I wouldn't be able to prove it.)
> (And strength of preference is clearly a real thing in our brains. If
> you prefer A > B > C, and are given the choice between Box 1, which
> contains B, and Box 2, which has a 50/50 chance of containing A or C,
> which do you choose? What if the probability were 1 in a million of Box
> 2 containing C? By varying the probability until it's impossible to
> decide, you can measure the relative strength of preference for B > C vs
> A > C.)
That's von Neumann-Morgenstern utilities, as I understand it. (From my
experience, sometimes it gets very hard to decide when you're close to
indifferent, though.)
The lottery information provides strength of preference up to an affine
scaling. So for each voter, there are two free parameters:
R(v, x) = a_v * U(v, x) + b_v
where R(v, x) is the voter's rating, a and b are constants, and U(v, x)
is voter v's (perceived) utility of getting x elected. The lottery
method gives us the ratio between the utilities (assuming risk
neutrality). But not a_v or b_v!
We can design the method so that it assumes every voter's scaling
constants are the same. That gives something like Range. Or we can
design it so that each voter's power is similar (OMOV), which gives
something that reduces to majority rule in the two-candidate case.
-km
CC
Colin Champion
Thu, Aug 17, 2023 7:37 AM
I think that bringing cardinal voting into the discussion is a red herring.
My contention is as follows. Suppose that we are given a set of
ballots (eg. a set of rankings of candidates) and an adequetely
specified generative model (eg. a jury model or a spatial model). Then
there is a mathematically identifiable rightful winner (I shall give an
example in a moment). The fact that given additional information (eg.
cardinal preferences) we might prefer a different candidate is
irrelevant - it is a question of there being a valid statistical
inference from the information given.
We might also consider the question of which is the best candidate
sub specie aeternitatis. This seems to me equally irrelevant. If there
exists such as thing as an objectively best candidate, then what makes
him objectively best is nothing to do with the voters' opinions.
Example of identifying the rightful winner: let the ballots come from a
Gaussian jury model. The candidates have valences (merits) drawn from a
standard univariate Gaussian, and each voter's assessment of the valence
of each candidate is a noisy estimate of the true merit, obtained by
adding an iid N(0,sigma) noise term to the true valence. A perfect
voting method will elect the candidate whose posterior expected valence
is greatest. This is a well defined and soluble mathematical problem.
CJC
On 16/08/2023 17:52, fdpk69p6uq@snkmail.com wrote:
On Mon, Aug 14, 2023 at 12:09 AM C.Benham wrote:
I think this is an interesting point. We can ask at a
philosophical level what makes a good voting method. Is it just
one that ticks the most boxes, or is it one that most reliably
gets the "best" result?
The one that most reliably gets the best result in the real world. The
difficulty with this approach is accurately modeling human voting
behavior and the consequent utility experienced from the winner, but
it's still the better answer philosophically.
(Note that VSE predates Jameson Quinn by decades, and has had several
different names:
https://en.wikipedia.org/wiki/Social_utility_efficiency
https://en.wikipedia.org/wiki/Social_utility_efficiency)
And that's partly because the premise of Condorcet is
essentially built on a logical fallacy - basically that if A is
preferred to B on more ballots that vice versa then electing A must
be a better result than electing B.
I'd be interested in reading your explanation of why you think
that is a
"logical fallacy". What about if there are only two candidates?
Ranked ballots can't capture strength of preference. It's possible for
a majority-preferred candidate to be very polarizing (loved by 51% and
hated by 49%), while the minority-preferred candidate is broadly-liked
and has a much higher overall approval/favorability rating. Which
candidate is the rightful winner?
https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html
https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html
"Suppose you and a pair of friends are looking to order a pizza. You,
and one friend, really like mushrooms, and prefer them over all other
vegetable options, but you both also really, /really/ like pepperoni.
Your other friend also really likes mushrooms, and prefers them over
all other options, but they're also vegetarian. What one topping
should you get?
Clearly the answer is mushrooms, and there is no group of friends
worth calling themselves such who would conclude otherwise. It's so
obvious that it hardly seems worth calling attention to. So why is it,
that if we put this decision up to a vote, do so many election
methods, which are otherwise seen as perfectly reasonable methods,
fail? Plurality, top-two runoffs
http://en.wikipedia.org/wiki/Two-round_system, instant runoff voting
http://en.wikipedia.org/wiki/Instant-runoff_voting, all variations
of Condorcet's method http://en.wikipedia.org/wiki/Condorcet_method,
even Bucklin voting http://en.wikipedia.org/wiki/Bucklin_voting; all
of them, incorrectly, choose pepperoni."
(And strength of preference is clearly a real thing in our brains. If
you prefer A > B > C, and are given the choice between Box 1, which
contains B, and Box 2, which has a 50/50 chance of containing A or C,
which do you choose? What if the probability were 1 in a million of
Box 2 containing C? By varying the probability until it's impossible
to decide, you can measure the relative strength of preference for B >
C vs A > C.)
Election-Methods mailing list - see https://electorama.com/em for list info
I think that bringing cardinal voting into the discussion is a red herring.
My contention is as follows. Suppose that we are given a set of
ballots (eg. a set of rankings of candidates) and an adequetely
specified generative model (eg. a jury model or a spatial model). Then
there is a mathematically identifiable rightful winner (I shall give an
example in a moment). The fact that given additional information (eg.
cardinal preferences) we might prefer a different candidate is
irrelevant - it is a question of there being a valid statistical
inference from the information given.
We might also consider the question of which is the best candidate
sub specie aeternitatis. This seems to me equally irrelevant. If there
exists such as thing as an objectively best candidate, then what makes
him objectively best is nothing to do with the voters' opinions.
Example of identifying the rightful winner: let the ballots come from a
Gaussian jury model. The candidates have valences (merits) drawn from a
standard univariate Gaussian, and each voter's assessment of the valence
of each candidate is a noisy estimate of the true merit, obtained by
adding an iid N(0,sigma) noise term to the true valence. A perfect
voting method will elect the candidate whose posterior expected valence
is greatest. This is a well defined and soluble mathematical problem.
CJC
On 16/08/2023 17:52, fdpk69p6uq@snkmail.com wrote:
>
> On Mon, Aug 14, 2023 at 12:09 AM C.Benham wrote:
>
> > I think this is an interesting point. We can ask at a
> philosophical level what makes a good voting method. Is it just
> one that ticks the most boxes, or is it one that most reliably
> gets the "best" result?
>
>
> The one that most reliably gets the best result in the real world. The
> difficulty with this approach is accurately modeling human voting
> behavior and the consequent utility experienced from the winner, but
> it's still the better answer philosophically.
>
> (Note that VSE predates Jameson Quinn by decades, and has had several
> different names:
> https://en.wikipedia.org/wiki/Social_utility_efficiency
> <https://en.wikipedia.org/wiki/Social_utility_efficiency>)
>
> > And that's partly because the premise of Condorcet is
> essentially built on a logical fallacy - basically that if A is
> preferred to B on more ballots that vice versa then electing A must
> > be a better result than electing B.
>
> I'd be interested in reading your explanation of why you think
> that is a
> "logical fallacy". What about if there are only two candidates?
>
>
> Ranked ballots can't capture strength of preference. It's possible for
> a majority-preferred candidate to be very polarizing (loved by 51% and
> hated by 49%), while the minority-preferred candidate is broadly-liked
> and has a much higher overall approval/favorability rating. Which
> candidate is the rightful winner?
>
> https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html
> <https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html>
>
> "Suppose you and a pair of friends are looking to order a pizza. You,
> and one friend, really like mushrooms, and prefer them over all other
> vegetable options, but you both also really, /really/ like pepperoni.
> Your other friend also really likes mushrooms, and prefers them over
> all other options, but they're also vegetarian. What one topping
> should you get?
>
> Clearly the answer is mushrooms, and there is no group of friends
> worth calling themselves such who would conclude otherwise. It's so
> obvious that it hardly seems worth calling attention to. So why is it,
> that if we put this decision up to a vote, do so many election
> methods, which are otherwise seen as perfectly reasonable methods,
> fail? Plurality, top-two runoffs
> <http://en.wikipedia.org/wiki/Two-round_system>, instant runoff voting
> <http://en.wikipedia.org/wiki/Instant-runoff_voting>, all variations
> of Condorcet's method <http://en.wikipedia.org/wiki/Condorcet_method>,
> even Bucklin voting <http://en.wikipedia.org/wiki/Bucklin_voting>; all
> of them, incorrectly, choose pepperoni."
>
> (And strength of preference is clearly a real thing in our brains. If
> you prefer A > B > C, and are given the choice between Box 1, which
> contains B, and Box 2, which has a 50/50 chance of containing A or C,
> which do you choose? What if the probability were 1 in a million of
> Box 2 containing C? By varying the probability until it's impossible
> to decide, you can measure the relative strength of preference for B >
> C vs A > C.)
>
> ----
> Election-Methods mailing list - see https://electorama.com/em for list info
FS
Forest Simmons
Thu, Aug 17, 2023 8:18 AM
The best methods that I know of for the friends context are minimum entropy
lottery methods characterized by max possible consensus (min entropy)
consistent with a proportional lottery method with higher entropy fallback
to disincentivize gratuitous defection.
Jobst's MaxParC (Max Partial Consensus) is the best example.
Too late to elaborate tonight.
fws
I'll
On Wed, Aug 16, 2023, 10:01 AM fdpk69p6uq@snkmail.com wrote:
On Mon, Aug 14, 2023 at 12:09 AM C.Benham wrote:
I think this is an interesting point. We can ask at a philosophical
level what makes a good voting method. Is it just one that ticks the most
boxes, or is it one that most reliably gets the "best" result?
The one that most reliably gets the best result in the real world. The
difficulty with this approach is accurately modeling human voting behavior
and the consequent utility experienced from the winner, but it's still the
better answer philosophically.
(Note that VSE predates Jameson Quinn by decades, and has had several
different names: https://en.wikipedia.org/wiki/Social_utility_efficiency)
And that's partly because the premise of Condorcet is essentially built
on a logical fallacy - basically that if A is preferred to B on more
ballots that vice versa then electing A must
be a better result than electing B.
I'd be interested in reading your explanation of why you think that is a
"logical fallacy". What about if there are only two candidates?
Ranked ballots can't capture strength of preference. It's possible for a
majority-preferred candidate to be very polarizing (loved by 51% and hated
by 49%), while the minority-preferred candidate is broadly-liked and has a
much higher overall approval/favorability rating. Which candidate is the
rightful winner?
https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html
"Suppose you and a pair of friends are looking to order a pizza. You, and
one friend, really like mushrooms, and prefer them over all other vegetable
options, but you both also really, really like pepperoni. Your other
friend also really likes mushrooms, and prefers them over all other
options, but they're also vegetarian. What one topping should you get?
Clearly the answer is mushrooms, and there is no group of friends worth
calling themselves such who would conclude otherwise. It's so obvious that
it hardly seems worth calling attention to. So why is it, that if we put
this decision up to a vote, do so many election methods, which are
otherwise seen as perfectly reasonable methods, fail? Plurality, top-two
runoffs http://en.wikipedia.org/wiki/Two-round_system, instant runoff
voting http://en.wikipedia.org/wiki/Instant-runoff_voting, all
variations of Condorcet's method
http://en.wikipedia.org/wiki/Condorcet_method, even Bucklin voting
http://en.wikipedia.org/wiki/Bucklin_voting; all of them, incorrectly,
choose pepperoni."
(And strength of preference is clearly a real thing in our brains. If you
prefer A > B > C, and are given the choice between Box 1, which contains B,
and Box 2, which has a 50/50 chance of containing A or C, which do you
choose? What if the probability were 1 in a million of Box 2 containing
C? By varying the probability until it's impossible to decide, you can
measure the relative strength of preference for B > C vs A > C.)
Election-Methods mailing list - see https://electorama.com/em for list
info
The best methods that I know of for the friends context are minimum entropy
lottery methods characterized by max possible consensus (min entropy)
consistent with a proportional lottery method with higher entropy fallback
to disincentivize gratuitous defection.
Jobst's MaxParC (Max Partial Consensus) is the best example.
Too late to elaborate tonight.
fws
I'll
On Wed, Aug 16, 2023, 10:01 AM <fdpk69p6uq@snkmail.com> wrote:
>
> On Mon, Aug 14, 2023 at 12:09 AM C.Benham wrote:
>
>> > I think this is an interesting point. We can ask at a philosophical
>> level what makes a good voting method. Is it just one that ticks the most
>> boxes, or is it one that most reliably gets the "best" result?
>>
>
> The one that most reliably gets the best result in the real world. The
> difficulty with this approach is accurately modeling human voting behavior
> and the consequent utility experienced from the winner, but it's still the
> better answer philosophically.
>
> (Note that VSE predates Jameson Quinn by decades, and has had several
> different names: https://en.wikipedia.org/wiki/Social_utility_efficiency)
>
> > And that's partly because the premise of Condorcet is essentially built
>> on a logical fallacy - basically that if A is preferred to B on more
>> ballots that vice versa then electing A must
>> > be a better result than electing B.
>>
>> I'd be interested in reading your explanation of why you think that is a
>> "logical fallacy". What about if there are only two candidates?
>>
>
> Ranked ballots can't capture strength of preference. It's possible for a
> majority-preferred candidate to be very polarizing (loved by 51% and hated
> by 49%), while the minority-preferred candidate is broadly-liked and has a
> much higher overall approval/favorability rating. Which candidate is the
> rightful winner?
>
>
> https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html
>
> "Suppose you and a pair of friends are looking to order a pizza. You, and
> one friend, really like mushrooms, and prefer them over all other vegetable
> options, but you both also really, *really* like pepperoni. Your other
> friend also really likes mushrooms, and prefers them over all other
> options, but they're also vegetarian. What one topping should you get?
>
> Clearly the answer is mushrooms, and there is no group of friends worth
> calling themselves such who would conclude otherwise. It's so obvious that
> it hardly seems worth calling attention to. So why is it, that if we put
> this decision up to a vote, do so many election methods, which are
> otherwise seen as perfectly reasonable methods, fail? Plurality, top-two
> runoffs <http://en.wikipedia.org/wiki/Two-round_system>, instant runoff
> voting <http://en.wikipedia.org/wiki/Instant-runoff_voting>, all
> variations of Condorcet's method
> <http://en.wikipedia.org/wiki/Condorcet_method>, even Bucklin voting
> <http://en.wikipedia.org/wiki/Bucklin_voting>; all of them, incorrectly,
> choose pepperoni."
> (And strength of preference is clearly a real thing in our brains. If you
> prefer A > B > C, and are given the choice between Box 1, which contains B,
> and Box 2, which has a 50/50 chance of containing A or C, which do you
> choose? What if the probability were 1 in a million of Box 2 containing
> C? By varying the probability until it's impossible to decide, you can
> measure the relative strength of preference for B > C vs A > C.)
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
FS
Forest Simmons
Thu, Aug 17, 2023 6:10 PM
Suppose voter utilities for three kinds of pizza are
60 A[100]>C[80]>>B[0]
40 B[100]>C[80]>>A[0]
Suppose the voters must choose by majority choice between pizza C and the
favorite pizza of a voter to be determined by randomly drawing a voter name
from a hat.
The random drawing method would give voter utility expectations of
60%100+40%0 for each A groupie, and
40%100+60%0 for each B groupie.
The max utility expectation would be 60.
On the other hand, if voters decide to go with the sure deal C, the assured
utility fo every voter will be 80.
Every rational voter faced with this choice will choose C.
Here we have an ostensibly random method that is sure to yield a consensus
decision when voters vote ratkonally.
More on this topic at
https://www.researchgate.net/figure/Properties-of-common-group-decision-methods-Nash-Lottery-and-MaxParC-Solid-and-dashed_fig3_342120971
fws
On Thu, Aug 17, 2023, 1:18 AM Forest Simmons forest.simmons21@gmail.com
wrote:
The best methods that I know of for the friends context are minimum
entropy lottery methods characterized by max possible consensus (min
entropy) consistent with a proportional lottery method with higher entropy
fallback to disincentivize gratuitous defection.
Jobst's MaxParC (Max Partial Consensus) is the best example.
Too late to elaborate tonight.
fws
I'll
On Wed, Aug 16, 2023, 10:01 AM fdpk69p6uq@snkmail.com wrote:
On Mon, Aug 14, 2023 at 12:09 AM C.Benham wrote:
I think this is an interesting point. We can ask at a philosophical
level what makes a good voting method. Is it just one that ticks the most
boxes, or is it one that most reliably gets the "best" result?
The one that most reliably gets the best result in the real world. The
difficulty with this approach is accurately modeling human voting behavior
and the consequent utility experienced from the winner, but it's still the
better answer philosophically.
(Note that VSE predates Jameson Quinn by decades, and has had several
different names: https://en.wikipedia.org/wiki/Social_utility_efficiency)
And that's partly because the premise of Condorcet is essentially built
on a logical fallacy - basically that if A is preferred to B on more
ballots that vice versa then electing A must
be a better result than electing B.
I'd be interested in reading your explanation of why you think that is a
"logical fallacy". What about if there are only two candidates?
Ranked ballots can't capture strength of preference. It's possible for a
majority-preferred candidate to be very polarizing (loved by 51% and hated
by 49%), while the minority-preferred candidate is broadly-liked and has a
much higher overall approval/favorability rating. Which candidate is the
rightful winner?
https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html
"Suppose you and a pair of friends are looking to order a pizza. You, and
one friend, really like mushrooms, and prefer them over all other vegetable
options, but you both also really, really like pepperoni. Your other
friend also really likes mushrooms, and prefers them over all other
options, but they're also vegetarian. What one topping should you get?
Clearly the answer is mushrooms, and there is no group of friends worth
calling themselves such who would conclude otherwise. It's so obvious that
it hardly seems worth calling attention to. So why is it, that if we put
this decision up to a vote, do so many election methods, which are
otherwise seen as perfectly reasonable methods, fail? Plurality, top-two
runoffs http://en.wikipedia.org/wiki/Two-round_system, instant runoff
voting http://en.wikipedia.org/wiki/Instant-runoff_voting, all
variations of Condorcet's method
http://en.wikipedia.org/wiki/Condorcet_method, even Bucklin voting
http://en.wikipedia.org/wiki/Bucklin_voting; all of them, incorrectly,
choose pepperoni."
(And strength of preference is clearly a real thing in our brains. If
you prefer A > B > C, and are given the choice between Box 1, which
contains B, and Box 2, which has a 50/50 chance of containing A or C, which
do you choose? What if the probability were 1 in a million of Box 2
containing C? By varying the probability until it's impossible to decide,
you can measure the relative strength of preference for B > C vs A > C.)
Election-Methods mailing list - see https://electorama.com/em for list
info
Suppose voter utilities for three kinds of pizza are
60 A[100]>C[80]>>B[0]
40 B[100]>C[80]>>A[0]
Suppose the voters must choose by majority choice between pizza C and the
favorite pizza of a voter to be determined by randomly drawing a voter name
from a hat.
The random drawing method would give voter utility expectations of
60%100+40%0 for each A groupie, and
40%100+60%0 for each B groupie.
The max utility expectation would be 60.
On the other hand, if voters decide to go with the sure deal C, the assured
utility fo every voter will be 80.
Every rational voter faced with this choice will choose C.
Here we have an ostensibly random method that is sure to yield a consensus
decision when voters vote ratkonally.
More on this topic at
https://www.researchgate.net/figure/Properties-of-common-group-decision-methods-Nash-Lottery-and-MaxParC-Solid-and-dashed_fig3_342120971
fws
On Thu, Aug 17, 2023, 1:18 AM Forest Simmons <forest.simmons21@gmail.com>
wrote:
> The best methods that I know of for the friends context are minimum
> entropy lottery methods characterized by max possible consensus (min
> entropy) consistent with a proportional lottery method with higher entropy
> fallback to disincentivize gratuitous defection.
>
> Jobst's MaxParC (Max Partial Consensus) is the best example.
>
> Too late to elaborate tonight.
>
> fws
>
> I'll
>
> On Wed, Aug 16, 2023, 10:01 AM <fdpk69p6uq@snkmail.com> wrote:
>
>>
>> On Mon, Aug 14, 2023 at 12:09 AM C.Benham wrote:
>>
>>> > I think this is an interesting point. We can ask at a philosophical
>>> level what makes a good voting method. Is it just one that ticks the most
>>> boxes, or is it one that most reliably gets the "best" result?
>>>
>>
>> The one that most reliably gets the best result in the real world. The
>> difficulty with this approach is accurately modeling human voting behavior
>> and the consequent utility experienced from the winner, but it's still the
>> better answer philosophically.
>>
>> (Note that VSE predates Jameson Quinn by decades, and has had several
>> different names: https://en.wikipedia.org/wiki/Social_utility_efficiency)
>>
>> > And that's partly because the premise of Condorcet is essentially built
>>> on a logical fallacy - basically that if A is preferred to B on more
>>> ballots that vice versa then electing A must
>>> > be a better result than electing B.
>>>
>>> I'd be interested in reading your explanation of why you think that is a
>>> "logical fallacy". What about if there are only two candidates?
>>>
>>
>> Ranked ballots can't capture strength of preference. It's possible for a
>> majority-preferred candidate to be very polarizing (loved by 51% and hated
>> by 49%), while the minority-preferred candidate is broadly-liked and has a
>> much higher overall approval/favorability rating. Which candidate is the
>> rightful winner?
>>
>>
>> https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html
>>
>> "Suppose you and a pair of friends are looking to order a pizza. You, and
>> one friend, really like mushrooms, and prefer them over all other vegetable
>> options, but you both also really, *really* like pepperoni. Your other
>> friend also really likes mushrooms, and prefers them over all other
>> options, but they're also vegetarian. What one topping should you get?
>>
>> Clearly the answer is mushrooms, and there is no group of friends worth
>> calling themselves such who would conclude otherwise. It's so obvious that
>> it hardly seems worth calling attention to. So why is it, that if we put
>> this decision up to a vote, do so many election methods, which are
>> otherwise seen as perfectly reasonable methods, fail? Plurality, top-two
>> runoffs <http://en.wikipedia.org/wiki/Two-round_system>, instant runoff
>> voting <http://en.wikipedia.org/wiki/Instant-runoff_voting>, all
>> variations of Condorcet's method
>> <http://en.wikipedia.org/wiki/Condorcet_method>, even Bucklin voting
>> <http://en.wikipedia.org/wiki/Bucklin_voting>; all of them, incorrectly,
>> choose pepperoni."
>> (And strength of preference is clearly a real thing in our brains. If
>> you prefer A > B > C, and are given the choice between Box 1, which
>> contains B, and Box 2, which has a 50/50 chance of containing A or C, which
>> do you choose? What if the probability were 1 in a million of Box 2
>> containing C? By varying the probability until it's impossible to decide,
>> you can measure the relative strength of preference for B > C vs A > C.)
>> ----
>> Election-Methods mailing list - see https://electorama.com/em for list
>> info
>>
>
FS
Forest Simmons
Fri, Aug 18, 2023 5:32 PM
It's been a while since I thought about this but here's something that
somebody with some number crunching resources should experiment with ... a
lottery method that I used to call "the ultimate lottery" back before Jobst
invented MaxParC, which arguably has at least an equal claim to
ultimateness:
Ballots are positive homogeneous functions of the candidate probability
variables. The homogeneity degree doesn't matter as long as all of the
ballots are of the same degree.
The candidate probabilities are chosen to maximize the product of the
ballots.
This candidate probability distribution can be realized as a spinner. The
spinner is spun to determine the winner.
How would this work for our pizza example?
For example, each voter's ballot could be her pizza desirability [score]
expectation as a function of the lottery probabilities.
Then each A faction voter would submit the same ballot ... namely the
function given by the expression
100pA+80pC, while each B faction voter would submit the expression
100pB+80pC.
When these ballots are multiplied together, we get the product
(100pA+80pC)^60×(100pB+80pC)^40.
The p values that maximize this product (subject to the constraint that
they are non-negative and sum to 100 percent) are pA=pB=0, and pC=100%.
The lottery that maximizes the expectation product is called the Nash
lottery after John Nash who first used this idea for efficient allocation
of limited resources.
Since expectations are linear combinations of the probabilities, they are
homogeneous of degree one ... one person, on vote. Their product is
homogeneous of degree n ... so n people, n votes.
Instead of using voter expectations for their ballots, the voters could
have used other homogeneous expressions ... for example, by simply
replacing each sum of products by a max of the same products.
The product of these modified ballots would be ...
[max(100pA,80pC)]^60
×[max(100pB,80pC)]^40.
Maximization of this product with the same constraints as before, yields
the same consensus distribution ... pC=100%.
This information is new in the sense that it has never been submitted for
official publication ... it's an exclusive bonus of Rob Lanphier's EM list
archive... first posted to this list back in 2011 after Jobst and I
published our 2010 paper on the use of mixed strategies for achieving
consensus.
Anyway, it turns out that using the Max operator in place of the Sum
operator yields a distribution with less entropy whenever the two
distributions are not identical.
Less entropy means less randomness, which means less chance, which in this
context, means more consensus.
In our example, the candidate distribution turned out to be 100 percent
candidate C ... zero randomness ... zero entropy ... 100 percent consensus.
Now you can see why I mentioned the need for number crunching capability
... experimenting with these ballot product maximizations requires some
serious number crunching.
The field is wide open. Is the Ultimate Lottery Method strongly monotonic?
For that matter, how about even the Nash Lottery?
Can MaxParC be formulated in terms of the Ultimate Lottery?
Somebody with some grad students should get them going on this!
fws
On Thu, Aug 17, 2023, 11:10 AM Forest Simmons forest.simmons21@gmail.com
wrote:
Suppose voter utilities for three kinds of pizza are
60 A[100]>C[80]>>B[0]
40 B[100]>C[80]>>A[0]
Suppose the voters must choose by majority choice between pizza C and the
favorite pizza of a voter to be determined by randomly drawing a voter name
from a hat.
The random drawing method would give voter utility expectations of
60%100+40%0 for each A groupie, and
40%100+60%0 for each B groupie.
The max utility expectation would be 60.
On the other hand, if voters decide to go with the sure deal C, the
assured utility fo every voter will be 80.
Every rational voter faced with this choice will choose C.
Here we have an ostensibly random method that is sure to yield a consensus
decision when voters vote ratkonally.
More on this topic at
https://www.researchgate.net/figure/Properties-of-common-group-decision-methods-Nash-Lottery-and-MaxParC-Solid-and-dashed_fig3_342120971
fws
On Thu, Aug 17, 2023, 1:18 AM Forest Simmons forest.simmons21@gmail.com
wrote:
The best methods that I know of for the friends context are minimum
entropy lottery methods characterized by max possible consensus (min
entropy) consistent with a proportional lottery method with higher entropy
fallback to disincentivize gratuitous defection.
Jobst's MaxParC (Max Partial Consensus) is the best example.
Too late to elaborate tonight.
fws
I'll
On Wed, Aug 16, 2023, 10:01 AM fdpk69p6uq@snkmail.com wrote:
On Mon, Aug 14, 2023 at 12:09 AM C.Benham wrote:
I think this is an interesting point. We can ask at a philosophical
level what makes a good voting method. Is it just one that ticks the most
boxes, or is it one that most reliably gets the "best" result?
The one that most reliably gets the best result in the real world. The
difficulty with this approach is accurately modeling human voting behavior
and the consequent utility experienced from the winner, but it's still the
better answer philosophically.
(Note that VSE predates Jameson Quinn by decades, and has had several
different names: https://en.wikipedia.org/wiki/Social_utility_efficiency
)
And that's partly because the premise of Condorcet is essentially
built on a logical fallacy - basically that if A is preferred to B on more
ballots that vice versa then electing A must
be a better result than electing B.
I'd be interested in reading your explanation of why you think that is
a
"logical fallacy". What about if there are only two candidates?
Ranked ballots can't capture strength of preference. It's possible for a
majority-preferred candidate to be very polarizing (loved by 51% and hated
by 49%), while the minority-preferred candidate is broadly-liked and has a
much higher overall approval/favorability rating. Which candidate is the
rightful winner?
https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html
"Suppose you and a pair of friends are looking to order a pizza. You,
and one friend, really like mushrooms, and prefer them over all other
vegetable options, but you both also really, really like pepperoni.
Your other friend also really likes mushrooms, and prefers them over all
other options, but they're also vegetarian. What one topping should you
get?
Clearly the answer is mushrooms, and there is no group of friends worth
calling themselves such who would conclude otherwise. It's so obvious that
it hardly seems worth calling attention to. So why is it, that if we put
this decision up to a vote, do so many election methods, which are
otherwise seen as perfectly reasonable methods, fail? Plurality, top-two
runoffs http://en.wikipedia.org/wiki/Two-round_system, instant runoff
voting http://en.wikipedia.org/wiki/Instant-runoff_voting, all
variations of Condorcet's method
http://en.wikipedia.org/wiki/Condorcet_method, even Bucklin voting
http://en.wikipedia.org/wiki/Bucklin_voting; all of them,
incorrectly, choose pepperoni."
(And strength of preference is clearly a real thing in our brains. If
you prefer A > B > C, and are given the choice between Box 1, which
contains B, and Box 2, which has a 50/50 chance of containing A or C, which
do you choose? What if the probability were 1 in a million of Box 2
containing C? By varying the probability until it's impossible to decide,
you can measure the relative strength of preference for B > C vs A > C.)
Election-Methods mailing list - see https://electorama.com/em for list
info
It's been a while since I thought about this but here's something that
somebody with some number crunching resources should experiment with ... a
lottery method that I used to call "the ultimate lottery" back before Jobst
invented MaxParC, which arguably has at least an equal claim to
ultimateness:
Ballots are positive homogeneous functions of the candidate probability
variables. The homogeneity degree doesn't matter as long as all of the
ballots are of the same degree.
The candidate probabilities are chosen to maximize the product of the
ballots.
This candidate probability distribution can be realized as a spinner. The
spinner is spun to determine the winner.
How would this work for our pizza example?
For example, each voter's ballot could be her pizza desirability [score]
expectation as a function of the lottery probabilities.
Then each A faction voter would submit the same ballot ... namely the
function given by the expression
100pA+80pC, while each B faction voter would submit the expression
100pB+80pC.
When these ballots are multiplied together, we get the product
(100pA+80pC)^60×(100pB+80pC)^40.
The p values that maximize this product (subject to the constraint that
they are non-negative and sum to 100 percent) are pA=pB=0, and pC=100%.
The lottery that maximizes the expectation product is called the Nash
lottery after John Nash who first used this idea for efficient allocation
of limited resources.
Since expectations are linear combinations of the probabilities, they are
homogeneous of degree one ... one person, on vote. Their product is
homogeneous of degree n ... so n people, n votes.
Instead of using voter expectations for their ballots, the voters could
have used other homogeneous expressions ... for example, by simply
replacing each sum of products by a max of the same products.
The product of these modified ballots would be ...
[max(100pA,80pC)]^60
×[max(100pB,80pC)]^40.
Maximization of this product with the same constraints as before, yields
the same consensus distribution ... pC=100%.
This information is new in the sense that it has never been submitted for
official publication ... it's an exclusive bonus of Rob Lanphier's EM list
archive... first posted to this list back in 2011 after Jobst and I
published our 2010 paper on the use of mixed strategies for achieving
consensus.
Anyway, it turns out that using the Max operator in place of the Sum
operator yields a distribution with less entropy whenever the two
distributions are not identical.
Less entropy means less randomness, which means less chance, which in this
context, means more consensus.
In our example, the candidate distribution turned out to be 100 percent
candidate C ... zero randomness ... zero entropy ... 100 percent consensus.
Now you can see why I mentioned the need for number crunching capability
... experimenting with these ballot product maximizations requires some
serious number crunching.
The field is wide open. Is the Ultimate Lottery Method strongly monotonic?
For that matter, how about even the Nash Lottery?
Can MaxParC be formulated in terms of the Ultimate Lottery?
Somebody with some grad students should get them going on this!
fws
On Thu, Aug 17, 2023, 11:10 AM Forest Simmons <forest.simmons21@gmail.com>
wrote:
> Suppose voter utilities for three kinds of pizza are
>
> 60 A[100]>C[80]>>B[0]
> 40 B[100]>C[80]>>A[0]
>
> Suppose the voters must choose by majority choice between pizza C and the
> favorite pizza of a voter to be determined by randomly drawing a voter name
> from a hat.
>
> The random drawing method would give voter utility expectations of
>
> 60%100+40%0 for each A groupie, and
> 40%100+60%0 for each B groupie.
>
> The max utility expectation would be 60.
>
> On the other hand, if voters decide to go with the sure deal C, the
> assured utility fo every voter will be 80.
>
> Every rational voter faced with this choice will choose C.
>
> Here we have an ostensibly random method that is sure to yield a consensus
> decision when voters vote ratkonally.
>
> More on this topic at
>
>
> https://www.researchgate.net/figure/Properties-of-common-group-decision-methods-Nash-Lottery-and-MaxParC-Solid-and-dashed_fig3_342120971
>
>
> fws
>
> On Thu, Aug 17, 2023, 1:18 AM Forest Simmons <forest.simmons21@gmail.com>
> wrote:
>
>> The best methods that I know of for the friends context are minimum
>> entropy lottery methods characterized by max possible consensus (min
>> entropy) consistent with a proportional lottery method with higher entropy
>> fallback to disincentivize gratuitous defection.
>>
>> Jobst's MaxParC (Max Partial Consensus) is the best example.
>>
>> Too late to elaborate tonight.
>>
>> fws
>>
>> I'll
>>
>> On Wed, Aug 16, 2023, 10:01 AM <fdpk69p6uq@snkmail.com> wrote:
>>
>>>
>>> On Mon, Aug 14, 2023 at 12:09 AM C.Benham wrote:
>>>
>>>> > I think this is an interesting point. We can ask at a philosophical
>>>> level what makes a good voting method. Is it just one that ticks the most
>>>> boxes, or is it one that most reliably gets the "best" result?
>>>>
>>>
>>> The one that most reliably gets the best result in the real world. The
>>> difficulty with this approach is accurately modeling human voting behavior
>>> and the consequent utility experienced from the winner, but it's still the
>>> better answer philosophically.
>>>
>>> (Note that VSE predates Jameson Quinn by decades, and has had several
>>> different names: https://en.wikipedia.org/wiki/Social_utility_efficiency
>>> )
>>>
>>> > And that's partly because the premise of Condorcet is essentially
>>>> built on a logical fallacy - basically that if A is preferred to B on more
>>>> ballots that vice versa then electing A must
>>>> > be a better result than electing B.
>>>>
>>>> I'd be interested in reading your explanation of why you think that is
>>>> a
>>>> "logical fallacy". What about if there are only two candidates?
>>>>
>>>
>>> Ranked ballots can't capture strength of preference. It's possible for a
>>> majority-preferred candidate to be very polarizing (loved by 51% and hated
>>> by 49%), while the minority-preferred candidate is broadly-liked and has a
>>> much higher overall approval/favorability rating. Which candidate is the
>>> rightful winner?
>>>
>>>
>>> https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html
>>>
>>> "Suppose you and a pair of friends are looking to order a pizza. You,
>>> and one friend, really like mushrooms, and prefer them over all other
>>> vegetable options, but you both also really, *really* like pepperoni.
>>> Your other friend also really likes mushrooms, and prefers them over all
>>> other options, but they're also vegetarian. What one topping should you
>>> get?
>>>
>>> Clearly the answer is mushrooms, and there is no group of friends worth
>>> calling themselves such who would conclude otherwise. It's so obvious that
>>> it hardly seems worth calling attention to. So why is it, that if we put
>>> this decision up to a vote, do so many election methods, which are
>>> otherwise seen as perfectly reasonable methods, fail? Plurality, top-two
>>> runoffs <http://en.wikipedia.org/wiki/Two-round_system>, instant runoff
>>> voting <http://en.wikipedia.org/wiki/Instant-runoff_voting>, all
>>> variations of Condorcet's method
>>> <http://en.wikipedia.org/wiki/Condorcet_method>, even Bucklin voting
>>> <http://en.wikipedia.org/wiki/Bucklin_voting>; all of them,
>>> incorrectly, choose pepperoni."
>>> (And strength of preference is clearly a real thing in our brains. If
>>> you prefer A > B > C, and are given the choice between Box 1, which
>>> contains B, and Box 2, which has a 50/50 chance of containing A or C, which
>>> do you choose? What if the probability were 1 in a million of Box 2
>>> containing C? By varying the probability until it's impossible to decide,
>>> you can measure the relative strength of preference for B > C vs A > C.)
>>> ----
>>> Election-Methods mailing list - see https://electorama.com/em for list
>>> info
>>>
>>
CC
Colin Champion
Fri, Aug 18, 2023 5:40 PM
Forest – I may be being slow, but... what problem are you trying to
solve? The problem which fpdk (quite plausibly, to my mind) said was
optimally solved by cardinal voting? Or the problem which I claimed was
optimally solved by decision theory? Or something to do with tactical
voting?
CJC
On 18/08/2023 18:32, Forest Simmons wrote:
It's been a while since I thought about this but here's something that
somebody with some number crunching resources should experiment with
... a lottery method that I used to call "the ultimate lottery" back
before Jobst invented MaxParC, which arguably has at least an equal
claim to ultimateness:
Ballots are positive homogeneous functions of the candidate
probability variables. The homogeneity degree doesn't matter as long
as all of the ballots are of the same degree.
The candidate probabilities are chosen to maximize the product of the
ballots.
This candidate probability distribution can be realized as a spinner.
The spinner is spun to determine the winner.
How would this work for our pizza example?
For example, each voter's ballot could be her pizza desirability
[score] expectation as a function of the lottery probabilities.
Then each A faction voter would submit the same ballot ... namely the
function given by the expression
100pA+80pC, while each B faction voter would submit the expression
100pB+80pC.
When these ballots are multiplied together, we get the product
(100pA+80pC)^60×(100pB+80pC)^40.
The p values that maximize this product (subject to the constraint
that they are non-negative and sum to 100 percent) are pA=pB=0, and
pC=100%.
The lottery that maximizes the expectation product is called the Nash
lottery after John Nash who first used this idea for efficient
allocation of limited resources.
Since expectations are linear combinations of the probabilities, they
are homogeneous of degree one ... one person, on vote. Their product
is homogeneous of degree n ... so n people, n votes.
Instead of using voter expectations for their ballots, the voters
could have used other homogeneous expressions ... for example, by
simply replacing each sum of products by a max of the same products.
The product of these modified ballots would be ...
[max(100pA,80pC)]^60
×[max(100pB,80pC)]^40.
Maximization of this product with the same constraints as before,
yields the same consensus distribution ... pC=100%.
This information is new in the sense that it has never been submitted
for official publication ... it's an exclusive bonus of Rob Lanphier's
EM list archive... first posted to this list back in 2011 after Jobst
and I published our 2010 paper on the use of mixed strategies for
achieving consensus.
Anyway, it turns out that using the Max operator in place of the Sum
operator yields a distribution with less entropy whenever the two
distributions are not identical.
Less entropy means less randomness, which means less chance, which in
this context, means more consensus.
In our example, the candidate distribution turned out to be 100
percent candidate C ... zero randomness ... zero entropy ... 100
percent consensus.
Now you can see why I mentioned the need for number crunching
capability ... experimenting with these ballot product maximizations
requires some serious number crunching.
The field is wide open. Is the Ultimate Lottery Method strongly
monotonic? For that matter, how about even the Nash Lottery?
Can MaxParC be formulated in terms of the Ultimate Lottery?
Somebody with some grad students should get them going on this!
fws
On Thu, Aug 17, 2023, 11:10 AM Forest Simmons
<forest.simmons21@gmail.com mailto:forest.simmons21@gmail.com> wrote:
Suppose voter utilities for three kinds of pizza are
60 A[100]>C[80]>>B[0]
40 B[100]>C[80]>>A[0]
Suppose the voters must choose by majority choice between pizza C
and the favorite pizza of a voter to be determined by randomly
drawing a voter name from a hat.
The random drawing method would give voter utility expectations of
60%100+40%0 for each A groupie, and
40%100+60%0 for each B groupie.
The max utility expectation would be 60.
On the other hand, if voters decide to go with the sure deal C,
the assured utility fo every voter will be 80.
Every rational voter faced with this choice will choose C.
Here we have an ostensibly random method that is sure to yield a
consensus decision when voters vote ratkonally.
More on this topic at
https://www.researchgate.net/figure/Properties-of-common-group-decision-methods-Nash-Lottery-and-MaxParC-Solid-and-dashed_fig3_342120971
<https://www.researchgate.net/figure/Properties-of-common-group-decision-methods-Nash-Lottery-and-MaxParC-Solid-and-dashed_fig3_342120971>
fws
On Thu, Aug 17, 2023, 1:18 AM Forest Simmons
<forest.simmons21@gmail.com <mailto:forest.simmons21@gmail.com>>
wrote:
The best methods that I know of for the friends context are
minimum entropy lottery methods characterized by max possible
consensus (min entropy) consistent with a proportional lottery
method with higher entropy fallback to disincentivize
gratuitous defection.
Jobst's MaxParC (Max Partial Consensus) is the best example.
Too late to elaborate tonight.
fws
I'll
On Wed, Aug 16, 2023, 10:01 AM <fdpk69p6uq@snkmail.com
<mailto:fdpk69p6uq@snkmail.com>> wrote:
On Mon, Aug 14, 2023 at 12:09 AM C.Benham wrote:
I think this is an interesting point. We can ask
at a philosophical level what makes a good voting
method. Is it just one that ticks the most boxes, or
is it one that most reliably gets the "best" result?
The one that most reliably gets the best result in the
real world. The difficulty with this approach is
accurately modeling human voting behavior and the
consequent utility experienced from the winner, but it's
still the better answer philosophically.
(Note that VSE predates Jameson Quinn by decades, and has
had several different names:
https://en.wikipedia.org/wiki/Social_utility_efficiency
<https://en.wikipedia.org/wiki/Social_utility_efficiency>)
And that's partly because the premise of Condorcet
is essentially built on a logical fallacy - basically
that if A is preferred to B on more ballots that vice
versa then electing A must
be a better result than electing B.
I'd be interested in reading your explanation of why
you think that is a
"logical fallacy". What about if there are only two
candidates?
Ranked ballots can't capture strength of preference. It's
possible for a majority-preferred candidate to be very
polarizing (loved by 51% and hated by 49%), while the
minority-preferred candidate is broadly-liked and has a
much higher overall approval/favorability rating. Which
candidate is the rightful winner?
https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html
<https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html>
"Suppose you and a pair of friends are looking to order a
pizza. You, and one friend, really like mushrooms, and
prefer them over all other vegetable options, but you both
also really, /really/ like pepperoni. Your other friend
also really likes mushrooms, and prefers them over all
other options, but they're also vegetarian. What one
topping should you get?
Clearly the answer is mushrooms, and there is no group of
friends worth calling themselves such who would conclude
otherwise. It's so obvious that it hardly seems worth
calling attention to. So why is it, that if we put this
decision up to a vote, do so many election methods, which
are otherwise seen as perfectly reasonable methods, fail?
Plurality, top-two runoffs
<http://en.wikipedia.org/wiki/Two-round_system>, instant
runoff voting
<http://en.wikipedia.org/wiki/Instant-runoff_voting>, all
variations of Condorcet's method
<http://en.wikipedia.org/wiki/Condorcet_method>, even
Bucklin voting
<http://en.wikipedia.org/wiki/Bucklin_voting>; all of
them, incorrectly, choose pepperoni."
(And strength of preference is clearly a real thing in our
brains. If you prefer A > B > C, and are given the choice
between Box 1, which contains B, and Box 2, which has a
50/50 chance of containing A or C, which do you choose?
What if the probability were 1 in a million of Box 2
containing C? By varying the probability until it's
impossible to decide, you can measure the relative
strength of preference for B > C vs A > C.)
----
Election-Methods mailing list - see
https://electorama.com/em <https://electorama.com/em> for
list info
Election-Methods mailing list - see https://electorama.com/em for list info
Forest – I may be being slow, but... what problem are you trying to
solve? The problem which fpdk (quite plausibly, to my mind) said was
optimally solved by cardinal voting? Or the problem which I claimed was
optimally solved by decision theory? Or something to do with tactical
voting?
CJC
On 18/08/2023 18:32, Forest Simmons wrote:
> It's been a while since I thought about this but here's something that
> somebody with some number crunching resources should experiment with
> ... a lottery method that I used to call "the ultimate lottery" back
> before Jobst invented MaxParC, which arguably has at least an equal
> claim to ultimateness:
>
> Ballots are positive homogeneous functions of the candidate
> probability variables. The homogeneity degree doesn't matter as long
> as all of the ballots are of the same degree.
>
> The candidate probabilities are chosen to maximize the product of the
> ballots.
>
> This candidate probability distribution can be realized as a spinner.
> The spinner is spun to determine the winner.
>
> How would this work for our pizza example?
>
> For example, each voter's ballot could be her pizza desirability
> [score] expectation as a function of the lottery probabilities.
>
> Then each A faction voter would submit the same ballot ... namely the
> function given by the expression
> 100pA+80pC, while each B faction voter would submit the expression
> 100pB+80pC.
>
> When these ballots are multiplied together, we get the product
> (100pA+80pC)^60×(100pB+80pC)^40.
>
> The p values that maximize this product (subject to the constraint
> that they are non-negative and sum to 100 percent) are pA=pB=0, and
> pC=100%.
>
> The lottery that maximizes the expectation product is called the Nash
> lottery after John Nash who first used this idea for efficient
> allocation of limited resources.
>
> Since expectations are linear combinations of the probabilities, they
> are homogeneous of degree one ... one person, on vote. Their product
> is homogeneous of degree n ... so n people, n votes.
>
> Instead of using voter expectations for their ballots, the voters
> could have used other homogeneous expressions ... for example, by
> simply replacing each sum of products by a max of the same products.
>
> The product of these modified ballots would be ...
>
> [max(100pA,80pC)]^60
> ×[max(100pB,80pC)]^40.
>
> Maximization of this product with the same constraints as before,
> yields the same consensus distribution ... pC=100%.
>
> This information is new in the sense that it has never been submitted
> for official publication ... it's an exclusive bonus of Rob Lanphier's
> EM list archive... first posted to this list back in 2011 after Jobst
> and I published our 2010 paper on the use of mixed strategies for
> achieving consensus.
>
> Anyway, it turns out that using the Max operator in place of the Sum
> operator yields a distribution with less entropy whenever the two
> distributions are not identical.
>
> Less entropy means less randomness, which means less chance, which in
> this context, means more consensus.
>
> In our example, the candidate distribution turned out to be 100
> percent candidate C ... zero randomness ... zero entropy ... 100
> percent consensus.
>
> Now you can see why I mentioned the need for number crunching
> capability ... experimenting with these ballot product maximizations
> requires some serious number crunching.
>
> The field is wide open. Is the Ultimate Lottery Method strongly
> monotonic? For that matter, how about even the Nash Lottery?
>
> Can MaxParC be formulated in terms of the Ultimate Lottery?
>
> Somebody with some grad students should get them going on this!
>
> fws
>
> On Thu, Aug 17, 2023, 11:10 AM Forest Simmons
> <forest.simmons21@gmail.com <mailto:forest.simmons21@gmail.com>> wrote:
>
> Suppose voter utilities for three kinds of pizza are
>
> 60 A[100]>C[80]>>B[0]
> 40 B[100]>C[80]>>A[0]
>
> Suppose the voters must choose by majority choice between pizza C
> and the favorite pizza of a voter to be determined by randomly
> drawing a voter name from a hat.
>
> The random drawing method would give voter utility expectations of
>
> 60%100+40%0 for each A groupie, and
> 40%100+60%0 for each B groupie.
>
> The max utility expectation would be 60.
>
> On the other hand, if voters decide to go with the sure deal C,
> the assured utility fo every voter will be 80.
>
> Every rational voter faced with this choice will choose C.
>
> Here we have an ostensibly random method that is sure to yield a
> consensus decision when voters vote ratkonally.
>
> More on this topic at
>
> https://www.researchgate.net/figure/Properties-of-common-group-decision-methods-Nash-Lottery-and-MaxParC-Solid-and-dashed_fig3_342120971
> <https://www.researchgate.net/figure/Properties-of-common-group-decision-methods-Nash-Lottery-and-MaxParC-Solid-and-dashed_fig3_342120971>
>
> fws
>
> On Thu, Aug 17, 2023, 1:18 AM Forest Simmons
> <forest.simmons21@gmail.com <mailto:forest.simmons21@gmail.com>>
> wrote:
>
> The best methods that I know of for the friends context are
> minimum entropy lottery methods characterized by max possible
> consensus (min entropy) consistent with a proportional lottery
> method with higher entropy fallback to disincentivize
> gratuitous defection.
>
> Jobst's MaxParC (Max Partial Consensus) is the best example.
>
> Too late to elaborate tonight.
>
> fws
>
> I'll
>
> On Wed, Aug 16, 2023, 10:01 AM <fdpk69p6uq@snkmail.com
> <mailto:fdpk69p6uq@snkmail.com>> wrote:
>
>
> On Mon, Aug 14, 2023 at 12:09 AM C.Benham wrote:
>
> > I think this is an interesting point. We can ask
> at a philosophical level what makes a good voting
> method. Is it just one that ticks the most boxes, or
> is it one that most reliably gets the "best" result?
>
>
> The one that most reliably gets the best result in the
> real world. The difficulty with this approach is
> accurately modeling human voting behavior and the
> consequent utility experienced from the winner, but it's
> still the better answer philosophically.
>
> (Note that VSE predates Jameson Quinn by decades, and has
> had several different names:
> https://en.wikipedia.org/wiki/Social_utility_efficiency
> <https://en.wikipedia.org/wiki/Social_utility_efficiency>)
>
> > And that's partly because the premise of Condorcet
> is essentially built on a logical fallacy - basically
> that if A is preferred to B on more ballots that vice
> versa then electing A must
> > be a better result than electing B.
>
> I'd be interested in reading your explanation of why
> you think that is a
> "logical fallacy". What about if there are only two
> candidates?
>
>
> Ranked ballots can't capture strength of preference. It's
> possible for a majority-preferred candidate to be very
> polarizing (loved by 51% and hated by 49%), while the
> minority-preferred candidate is broadly-liked and has a
> much higher overall approval/favorability rating. Which
> candidate is the rightful winner?
>
> https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html
> <https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html>
>
> "Suppose you and a pair of friends are looking to order a
> pizza. You, and one friend, really like mushrooms, and
> prefer them over all other vegetable options, but you both
> also really, /really/ like pepperoni. Your other friend
> also really likes mushrooms, and prefers them over all
> other options, but they're also vegetarian. What one
> topping should you get?
>
> Clearly the answer is mushrooms, and there is no group of
> friends worth calling themselves such who would conclude
> otherwise. It's so obvious that it hardly seems worth
> calling attention to. So why is it, that if we put this
> decision up to a vote, do so many election methods, which
> are otherwise seen as perfectly reasonable methods, fail?
> Plurality, top-two runoffs
> <http://en.wikipedia.org/wiki/Two-round_system>, instant
> runoff voting
> <http://en.wikipedia.org/wiki/Instant-runoff_voting>, all
> variations of Condorcet's method
> <http://en.wikipedia.org/wiki/Condorcet_method>, even
> Bucklin voting
> <http://en.wikipedia.org/wiki/Bucklin_voting>; all of
> them, incorrectly, choose pepperoni."
>
> (And strength of preference is clearly a real thing in our
> brains. If you prefer A > B > C, and are given the choice
> between Box 1, which contains B, and Box 2, which has a
> 50/50 chance of containing A or C, which do you choose?
> What if the probability were 1 in a million of Box 2
> containing C? By varying the probability until it's
> impossible to decide, you can measure the relative
> strength of preference for B > C vs A > C.)
> ----
> Election-Methods mailing list - see
> https://electorama.com/em <https://electorama.com/em> for
> list info
>
>
> ----
> Election-Methods mailing list - see https://electorama.com/em for list info
FS
Forest Simmons
Fri, Aug 18, 2023 8:50 PM
He posed a pizza choice among friends pronlem.. a problem of consensus as
opposed to "tyranny of the majority" ... how to find the best consensus
decision when a simple majority first place preference would not be ideal.
On Fri, Aug 18, 2023, 10:41 AM Colin Champion <
colin.champion@routemaster.app> wrote:
Forest – I may be being slow, but... what problem are you trying to solve?
The problem which fpdk (quite plausibly, to my mind) said was optimally
solved by cardinal voting? Or the problem which I claimed was optimally
solved by decision theory? Or something to do with tactical voting?
CJC
On 18/08/2023 18:32, Forest Simmons wrote:
It's been a while since I thought about this but here's something that
somebody with some number crunching resources should experiment with ... a
lottery method that I used to call "the ultimate lottery" back before Jobst
invented MaxParC, which arguably has at least an equal claim to
ultimateness:
Ballots are positive homogeneous functions of the candidate probability
variables. The homogeneity degree doesn't matter as long as all of the
ballots are of the same degree.
The candidate probabilities are chosen to maximize the product of the
ballots.
This candidate probability distribution can be realized as a spinner. The
spinner is spun to determine the winner.
How would this work for our pizza example?
For example, each voter's ballot could be her pizza desirability [score]
expectation as a function of the lottery probabilities.
Then each A faction voter would submit the same ballot ... namely the
function given by the expression
100pA+80pC, while each B faction voter would submit the expression
100pB+80pC.
When these ballots are multiplied together, we get the product
(100pA+80pC)^60×(100pB+80pC)^40.
The p values that maximize this product (subject to the constraint that
they are non-negative and sum to 100 percent) are pA=pB=0, and pC=100%.
The lottery that maximizes the expectation product is called the Nash
lottery after John Nash who first used this idea for efficient allocation
of limited resources.
Since expectations are linear combinations of the probabilities, they are
homogeneous of degree one ... one person, on vote. Their product is
homogeneous of degree n ... so n people, n votes.
Instead of using voter expectations for their ballots, the voters could
have used other homogeneous expressions ... for example, by simply
replacing each sum of products by a max of the same products.
The product of these modified ballots would be ...
[max(100pA,80pC)]^60
×[max(100pB,80pC)]^40.
Maximization of this product with the same constraints as before, yields
the same consensus distribution ... pC=100%.
This information is new in the sense that it has never been submitted for
official publication ... it's an exclusive bonus of Rob Lanphier's EM list
archive... first posted to this list back in 2011 after Jobst and I
published our 2010 paper on the use of mixed strategies for achieving
consensus.
Anyway, it turns out that using the Max operator in place of the Sum
operator yields a distribution with less entropy whenever the two
distributions are not identical.
Less entropy means less randomness, which means less chance, which in this
context, means more consensus.
In our example, the candidate distribution turned out to be 100 percent
candidate C ... zero randomness ... zero entropy ... 100 percent consensus.
Now you can see why I mentioned the need for number crunching capability
... experimenting with these ballot product maximizations requires some
serious number crunching.
The field is wide open. Is the Ultimate Lottery Method strongly monotonic?
For that matter, how about even the Nash Lottery?
Can MaxParC be formulated in terms of the Ultimate Lottery?
Somebody with some grad students should get them going on this!
fws
On Thu, Aug 17, 2023, 11:10 AM Forest Simmons forest.simmons21@gmail.com
wrote:
Suppose voter utilities for three kinds of pizza are
60 A[100]>C[80]>>B[0]
40 B[100]>C[80]>>A[0]
Suppose the voters must choose by majority choice between pizza C and the
favorite pizza of a voter to be determined by randomly drawing a voter name
from a hat.
The random drawing method would give voter utility expectations of
60%100+40%0 for each A groupie, and
40%100+60%0 for each B groupie.
The max utility expectation would be 60.
On the other hand, if voters decide to go with the sure deal C, the
assured utility fo every voter will be 80.
Every rational voter faced with this choice will choose C.
Here we have an ostensibly random method that is sure to yield a
consensus decision when voters vote ratkonally.
More on this topic at
https://www.researchgate.net/figure/Properties-of-common-group-decision-methods-Nash-Lottery-and-MaxParC-Solid-and-dashed_fig3_342120971
fws
On Thu, Aug 17, 2023, 1:18 AM Forest Simmons forest.simmons21@gmail.com
wrote:
The best methods that I know of for the friends context are minimum
entropy lottery methods characterized by max possible consensus (min
entropy) consistent with a proportional lottery method with higher entropy
fallback to disincentivize gratuitous defection.
Jobst's MaxParC (Max Partial Consensus) is the best example.
Too late to elaborate tonight.
fws
I'll
On Wed, Aug 16, 2023, 10:01 AM fdpk69p6uq@snkmail.com wrote:
On Mon, Aug 14, 2023 at 12:09 AM C.Benham wrote:
I think this is an interesting point. We can ask at a
philosophical level what makes a good voting method. Is it just one that
ticks the most boxes, or is it one that most reliably gets the "best"
result?
The one that most reliably gets the best result in the real world. The
difficulty with this approach is accurately modeling human voting behavior
and the consequent utility experienced from the winner, but it's still the
better answer philosophically.
(Note that VSE predates Jameson Quinn by decades, and has had several
different names:
https://en.wikipedia.org/wiki/Social_utility_efficiency)
And that's partly because the premise of Condorcet is essentially
built on a logical fallacy - basically that if A is preferred to B on more
ballots that vice versa then electing A must
be a better result than electing B.
I'd be interested in reading your explanation of why you think that is
a
"logical fallacy". What about if there are only two candidates?
Ranked ballots can't capture strength of preference. It's possible for
a majority-preferred candidate to be very polarizing (loved by 51% and
hated by 49%), while the minority-preferred candidate is broadly-liked and
has a much higher overall approval/favorability rating. Which candidate is
the rightful winner?
https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html
"Suppose you and a pair of friends are looking to order a pizza. You,
and one friend, really like mushrooms, and prefer them over all other
vegetable options, but you both also really, really like pepperoni.
Your other friend also really likes mushrooms, and prefers them over all
other options, but they're also vegetarian. What one topping should you
get?
Clearly the answer is mushrooms, and there is no group of friends worth
calling themselves such who would conclude otherwise. It's so obvious that
it hardly seems worth calling attention to. So why is it, that if we put
this decision up to a vote, do so many election methods, which are
otherwise seen as perfectly reasonable methods, fail? Plurality, top-two
runoffs http://en.wikipedia.org/wiki/Two-round_system, instant
runoff voting http://en.wikipedia.org/wiki/Instant-runoff_voting,
all variations of Condorcet's method
http://en.wikipedia.org/wiki/Condorcet_method, even Bucklin voting
http://en.wikipedia.org/wiki/Bucklin_voting; all of them,
incorrectly, choose pepperoni."
(And strength of preference is clearly a real thing in our brains. If
you prefer A > B > C, and are given the choice between Box 1, which
contains B, and Box 2, which has a 50/50 chance of containing A or C, which
do you choose? What if the probability were 1 in a million of Box 2
containing C? By varying the probability until it's impossible to decide,
you can measure the relative strength of preference for B > C vs A > C.)
Election-Methods mailing list - see https://electorama.com/em for list
info
He posed a pizza choice among friends pronlem.. a problem of consensus as
opposed to "tyranny of the majority" ... how to find the best consensus
decision when a simple majority first place preference would not be ideal.
On Fri, Aug 18, 2023, 10:41 AM Colin Champion <
colin.champion@routemaster.app> wrote:
> Forest – I may be being slow, but... what problem are you trying to solve?
> The problem which fpdk (quite plausibly, to my mind) said was optimally
> solved by cardinal voting? Or the problem which I claimed was optimally
> solved by decision theory? Or something to do with tactical voting?
> CJC
>
> On 18/08/2023 18:32, Forest Simmons wrote:
>
> It's been a while since I thought about this but here's something that
> somebody with some number crunching resources should experiment with ... a
> lottery method that I used to call "the ultimate lottery" back before Jobst
> invented MaxParC, which arguably has at least an equal claim to
> ultimateness:
>
> Ballots are positive homogeneous functions of the candidate probability
> variables. The homogeneity degree doesn't matter as long as all of the
> ballots are of the same degree.
>
> The candidate probabilities are chosen to maximize the product of the
> ballots.
>
> This candidate probability distribution can be realized as a spinner. The
> spinner is spun to determine the winner.
>
> How would this work for our pizza example?
>
> For example, each voter's ballot could be her pizza desirability [score]
> expectation as a function of the lottery probabilities.
>
> Then each A faction voter would submit the same ballot ... namely the
> function given by the expression
> 100pA+80pC, while each B faction voter would submit the expression
> 100pB+80pC.
>
> When these ballots are multiplied together, we get the product
> (100pA+80pC)^60×(100pB+80pC)^40.
>
> The p values that maximize this product (subject to the constraint that
> they are non-negative and sum to 100 percent) are pA=pB=0, and pC=100%.
>
> The lottery that maximizes the expectation product is called the Nash
> lottery after John Nash who first used this idea for efficient allocation
> of limited resources.
>
> Since expectations are linear combinations of the probabilities, they are
> homogeneous of degree one ... one person, on vote. Their product is
> homogeneous of degree n ... so n people, n votes.
>
> Instead of using voter expectations for their ballots, the voters could
> have used other homogeneous expressions ... for example, by simply
> replacing each sum of products by a max of the same products.
>
> The product of these modified ballots would be ...
>
> [max(100pA,80pC)]^60
> ×[max(100pB,80pC)]^40.
>
> Maximization of this product with the same constraints as before, yields
> the same consensus distribution ... pC=100%.
>
> This information is new in the sense that it has never been submitted for
> official publication ... it's an exclusive bonus of Rob Lanphier's EM list
> archive... first posted to this list back in 2011 after Jobst and I
> published our 2010 paper on the use of mixed strategies for achieving
> consensus.
>
> Anyway, it turns out that using the Max operator in place of the Sum
> operator yields a distribution with less entropy whenever the two
> distributions are not identical.
>
> Less entropy means less randomness, which means less chance, which in this
> context, means more consensus.
>
> In our example, the candidate distribution turned out to be 100 percent
> candidate C ... zero randomness ... zero entropy ... 100 percent consensus.
>
> Now you can see why I mentioned the need for number crunching capability
> ... experimenting with these ballot product maximizations requires some
> serious number crunching.
>
> The field is wide open. Is the Ultimate Lottery Method strongly monotonic?
> For that matter, how about even the Nash Lottery?
>
> Can MaxParC be formulated in terms of the Ultimate Lottery?
>
> Somebody with some grad students should get them going on this!
>
> fws
>
> On Thu, Aug 17, 2023, 11:10 AM Forest Simmons <forest.simmons21@gmail.com>
> wrote:
>
>> Suppose voter utilities for three kinds of pizza are
>>
>> 60 A[100]>C[80]>>B[0]
>> 40 B[100]>C[80]>>A[0]
>>
>> Suppose the voters must choose by majority choice between pizza C and the
>> favorite pizza of a voter to be determined by randomly drawing a voter name
>> from a hat.
>>
>> The random drawing method would give voter utility expectations of
>>
>> 60%100+40%0 for each A groupie, and
>> 40%100+60%0 for each B groupie.
>>
>> The max utility expectation would be 60.
>>
>> On the other hand, if voters decide to go with the sure deal C, the
>> assured utility fo every voter will be 80.
>>
>> Every rational voter faced with this choice will choose C.
>>
>> Here we have an ostensibly random method that is sure to yield a
>> consensus decision when voters vote ratkonally.
>>
>> More on this topic at
>>
>>
>> https://www.researchgate.net/figure/Properties-of-common-group-decision-methods-Nash-Lottery-and-MaxParC-Solid-and-dashed_fig3_342120971
>>
>>
>> fws
>>
>> On Thu, Aug 17, 2023, 1:18 AM Forest Simmons <forest.simmons21@gmail.com>
>> wrote:
>>
>>> The best methods that I know of for the friends context are minimum
>>> entropy lottery methods characterized by max possible consensus (min
>>> entropy) consistent with a proportional lottery method with higher entropy
>>> fallback to disincentivize gratuitous defection.
>>>
>>> Jobst's MaxParC (Max Partial Consensus) is the best example.
>>>
>>> Too late to elaborate tonight.
>>>
>>> fws
>>>
>>> I'll
>>>
>>> On Wed, Aug 16, 2023, 10:01 AM <fdpk69p6uq@snkmail.com> wrote:
>>>
>>>>
>>>> On Mon, Aug 14, 2023 at 12:09 AM C.Benham wrote:
>>>>
>>>>> > I think this is an interesting point. We can ask at a
>>>>> philosophical level what makes a good voting method. Is it just one that
>>>>> ticks the most boxes, or is it one that most reliably gets the "best"
>>>>> result?
>>>>>
>>>>
>>>> The one that most reliably gets the best result in the real world. The
>>>> difficulty with this approach is accurately modeling human voting behavior
>>>> and the consequent utility experienced from the winner, but it's still the
>>>> better answer philosophically.
>>>>
>>>> (Note that VSE predates Jameson Quinn by decades, and has had several
>>>> different names:
>>>> https://en.wikipedia.org/wiki/Social_utility_efficiency)
>>>>
>>>> > And that's partly because the premise of Condorcet is essentially
>>>>> built on a logical fallacy - basically that if A is preferred to B on more
>>>>> ballots that vice versa then electing A must
>>>>> > be a better result than electing B.
>>>>>
>>>>> I'd be interested in reading your explanation of why you think that is
>>>>> a
>>>>> "logical fallacy". What about if there are only two candidates?
>>>>>
>>>>
>>>> Ranked ballots can't capture strength of preference. It's possible for
>>>> a majority-preferred candidate to be very polarizing (loved by 51% and
>>>> hated by 49%), while the minority-preferred candidate is broadly-liked and
>>>> has a much higher overall approval/favorability rating. Which candidate is
>>>> the rightful winner?
>>>>
>>>>
>>>> https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html
>>>>
>>>> "Suppose you and a pair of friends are looking to order a pizza. You,
>>>> and one friend, really like mushrooms, and prefer them over all other
>>>> vegetable options, but you both also really, *really* like pepperoni.
>>>> Your other friend also really likes mushrooms, and prefers them over all
>>>> other options, but they're also vegetarian. What one topping should you
>>>> get?
>>>>
>>>> Clearly the answer is mushrooms, and there is no group of friends worth
>>>> calling themselves such who would conclude otherwise. It's so obvious that
>>>> it hardly seems worth calling attention to. So why is it, that if we put
>>>> this decision up to a vote, do so many election methods, which are
>>>> otherwise seen as perfectly reasonable methods, fail? Plurality, top-two
>>>> runoffs <http://en.wikipedia.org/wiki/Two-round_system>, instant
>>>> runoff voting <http://en.wikipedia.org/wiki/Instant-runoff_voting>,
>>>> all variations of Condorcet's method
>>>> <http://en.wikipedia.org/wiki/Condorcet_method>, even Bucklin voting
>>>> <http://en.wikipedia.org/wiki/Bucklin_voting>; all of them,
>>>> incorrectly, choose pepperoni."
>>>> (And strength of preference is clearly a real thing in our brains. If
>>>> you prefer A > B > C, and are given the choice between Box 1, which
>>>> contains B, and Box 2, which has a 50/50 chance of containing A or C, which
>>>> do you choose? What if the probability were 1 in a million of Box 2
>>>> containing C? By varying the probability until it's impossible to decide,
>>>> you can measure the relative strength of preference for B > C vs A > C.)
>>>> ----
>>>> Election-Methods mailing list - see https://electorama.com/em for list
>>>> info
>>>>
>>>
> ----
> Election-Methods mailing list - see https://electorama.com/em for list info
>
>
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
