What is the most useful definition of "monotonicity"?
Hi folks,
I don't think I've ever fully prerused the "Voting matters"[1] website
before, and realized how serious of a publication it was (or rather
"is"):
[1]: http://www.votingmatters.org.uk/
Maybe I did, but I forgot about it. It looks like there are several
interesting papers to read there.
Douglas Woodall published at least a couple of papers there. It also
seems that Woodall's definition of "monotonicity"[2] is the favorite
of many folks who like to discuss election methods. In particular, I
want to highlight Issue 3, paper 5 of "Voting matters":
[2]: http://www.votingmatters.org.uk/ISSUE3/P5.HTM
Here's Woodall's definition of monotonicity from that paper, which
breaks up monotonicity into nine different criteria:
Monotonicity. A candidate x should not be harmed if:
- (mono-raise) x is raised on some ballots without changing the orders of the other candidates;
- (mono-raise-delete) x is raised on some ballots and all candidates now below x on those ballots are deleted from them;
- (mono-raise-random) x is raised on some ballots and the positions now below x on those ballots are filled (or left vacant) in any way that results in a valid ballot;
- (mono-append) x is added at the end of some ballots that did not previously contain x;
- (mono-sub-plump) some ballots that do not have x top are replaced by ballots that have x top with no second choice;
- (mono-sub-top) some ballots that do not have x top are replaced by ballots that have x top (and are otherwise arbitrary);
- (mono-add-plump) further ballots are added that have x top with no second choice;
- (mono-add-top) further ballots are added that have x top (and are otherwise arbitrary);
- (mono-remove-bottom) some ballots are removed, all of which have x bottom, below all other candidates.
That's nine different criteria that all could be called
"monotonicity". This raises a few questions for me:
- Is Woodall's definition correct?
- Is Woodall's definition the most useful?
- Is Woodall's definition overly-complicated, or just
appropriately-complicated? - Does breaking up monotonicity into nine different criteria make it
easier to understand, or harder? - Was Woodall just copying his definition from someone else when
publishing those nine criteria? If so, who?
The reason why I ask: I want to improve the electowiki article about
monotonicity[3], and I'm wondering if emphasis on the nine criteria
above would help make the article clearer:
[3]: https://electowiki.org/wiki/Monotonicity
Should the electowiki community use Woodall's nine criteria as the
electowiki definition of "monotonicity"?
Rob
p.s. a YouTube video[4] posted to C4ES's Discord server is what
inspired me to compose this email:
[4]: https://youtu.be/OI232JSDwDg
p.p.s.: What I mean by "C4ES's Discord Server"[5] is the Discord
server that is operated by the Center for Election Science:
[5]: https://electionscience.org/discord
Hi Rob,
For what people usually mean when discussing monotonicity (such as in connection with IRV) this corresponds to Woodall's Mono-raise.
I'd say the criterion discussed second most often is Mono-add-top, a weaker form of Participation.
I don't see how Woodall can be wrong, it's his choice to define these criteria and characterize them as dealing with monotonicity. But to me, if you say a method "fails monotonicity," or "is monotone," you're either talking about Mono-raise or else you're being unclear. Inserting these into an article called "Monotonicity" could be unhelpful unless it's made clear that these are other criteria connected to the idea, and are used (as far as I know) primarily by Woodall.
Note that (at least in other articles) Woodall is/was largely concerned with which sets of properties are compatible with each other, and he didn't usually make statements judging the relative value of criteria. This leaves the job to other people to explain why we should care about a given property.
Kevin
Le dimanche 15 novembre 2020 à 20:32:50 UTC−6, Rob Lanphier <robla@robla.net> a écrit :
Hi folks,
I don't think I've ever fully prerused the "Voting matters"[1] website
before, and realized how serious of a publication it was (or rather
"is"):
[1]: http://www.votingmatters.org.uk/
Maybe I did, but I forgot about it. It looks like there are several
interesting papers to read there.
Douglas Woodall published at least a couple of papers there. It also
seems that Woodall's definition of "monotonicity"[2] is the favorite
of many folks who like to discuss election methods. In particular, I
want to highlight Issue 3, paper 5 of "Voting matters":
[2]: http://www.votingmatters.org.uk/ISSUE3/P5.HTM
Here's Woodall's definition of monotonicity from that paper, which
breaks up monotonicity into nine different criteria:
Monotonicity. A candidate x should not be harmed if:
- (mono-raise) x is raised on some ballots without changing the orders of the other candidates;
- (mono-raise-delete) x is raised on some ballots and all candidates now below x on those ballots are deleted from them;
- (mono-raise-random) x is raised on some ballots and the positions now below x on those ballots are filled (or left vacant) in any way that results in a valid ballot;
- (mono-append) x is added at the end of some ballots that did not previously contain x;
- (mono-sub-plump) some ballots that do not have x top are replaced by ballots that have x top with no second choice;
- (mono-sub-top) some ballots that do not have x top are replaced by ballots that have x top (and are otherwise arbitrary);
- (mono-add-plump) further ballots are added that have x top with no second choice;
- (mono-add-top) further ballots are added that have x top (and are otherwise arbitrary);
- (mono-remove-bottom) some ballots are removed, all of which have x bottom, below all other candidates.
That's nine different criteria that all could be called
"monotonicity". This raises a few questions for me:
- Is Woodall's definition correct?
- Is Woodall's definition the most useful?
- Is Woodall's definition overly-complicated, or just
appropriately-complicated? - Does breaking up monotonicity into nine different criteria make it
easier to understand, or harder? - Was Woodall just copying his definition from someone else when
publishing those nine criteria? If so, who?
The reason why I ask: I want to improve the electowiki article about
monotonicity[3], and I'm wondering if emphasis on the nine criteria
above would help make the article clearer:
[3]: https://electowiki.org/wiki/Monotonicity
Should the electowiki community use Woodall's nine criteria as the
electowiki definition of "monotonicity"?
Rob
p.s. a YouTube video[4] posted to C4ES's Discord server is what
inspired me to compose this email:
[4]: https://youtu.be/OI232JSDwDg
p.p.s.: What I mean by "C4ES's Discord Server"[5] is the Discord
server that is operated by the Center for Election Science:
[5]: https://electionscience.org/discord
Election-Methods mailing list - see https://electorama.com/em for list info
Monotonicity.
The transfer of surpluses in STV is monotonic. Not so the redistribution
of excluded candidates votes.
FAB STV is completely monotonic, because the votes are transferable, in
a (symmetric) exclusion count, as well as an election count. Hence the B
in FAB for a bi-nomial count. This does indeed make use of the binomial
theorem, for higher order counts. Normally, in an ordinary election, a
first order count would do. That is to say just an election count and an
exclusion count, unqualified by any higher order binomial theorem
refinements.
Regards,
Richard L.
On 16/11/2020 02:32, Rob Lanphier wrote:
Hi folks,
I don't think I've ever fully prerused the "Voting matters"[1] website
before, and realized how serious of a publication it was (or rather
"is"):
[1]: http://www.votingmatters.org.uk/
Maybe I did, but I forgot about it. It looks like there are several
interesting papers to read there.
Douglas Woodall published at least a couple of papers there. It also
seems that Woodall's definition of "monotonicity"[2] is the favorite
of many folks who like to discuss election methods. In particular, I
want to highlight Issue 3, paper 5 of "Voting matters":
[2]: http://www.votingmatters.org.uk/ISSUE3/P5.HTM
Here's Woodall's definition of monotonicity from that paper, which
breaks up monotonicity into nine different criteria:
Monotonicity. A candidate x should not be harmed if:
- (mono-raise) x is raised on some ballots without changing the orders of the other candidates;
- (mono-raise-delete) x is raised on some ballots and all candidates now below x on those ballots are deleted from them;
- (mono-raise-random) x is raised on some ballots and the positions now below x on those ballots are filled (or left vacant) in any way that results in a valid ballot;
- (mono-append) x is added at the end of some ballots that did not previously contain x;
- (mono-sub-plump) some ballots that do not have x top are replaced by ballots that have x top with no second choice;
- (mono-sub-top) some ballots that do not have x top are replaced by ballots that have x top (and are otherwise arbitrary);
- (mono-add-plump) further ballots are added that have x top with no second choice;
- (mono-add-top) further ballots are added that have x top (and are otherwise arbitrary);
- (mono-remove-bottom) some ballots are removed, all of which have x bottom, below all other candidates.
That's nine different criteria that all could be called
"monotonicity". This raises a few questions for me:
- Is Woodall's definition correct?
- Is Woodall's definition the most useful?
- Is Woodall's definition overly-complicated, or just
appropriately-complicated? - Does breaking up monotonicity into nine different criteria make it
easier to understand, or harder? - Was Woodall just copying his definition from someone else when
publishing those nine criteria? If so, who?
The reason why I ask: I want to improve the electowiki article about
monotonicity[3], and I'm wondering if emphasis on the nine criteria
above would help make the article clearer:
[3]: https://electowiki.org/wiki/Monotonicity
Should the electowiki community use Woodall's nine criteria as the
electowiki definition of "monotonicity"?
Rob
p.s. a YouTube video[4] posted to C4ES's Discord server is what
inspired me to compose this email:
[4]: https://youtu.be/OI232JSDwDg
p.p.s.: What I mean by "C4ES's Discord Server"[5] is the Discord
server that is operated by the Center for Election Science:
[5]: https://electionscience.org/discord
Election-Methods mailing list - see https://electorama.com/em for list info
Hi Kevin,
Thanks for the prompt and helpful reply! I think I know how I want
to go about editing the "Monotonicity" article on electowiki, but that
article needs a lot more work than just this addition.
More inline:
On Sun, Nov 15, 2020 at 6:59 PM Kevin Venzke stepjak@yahoo.fr wrote:
For what people usually mean when discussing monotonicity (such as in
connection with IRV) this corresponds to Woodall's Mono-raise.
Given that "Monotonicity" is more-or-less equivalent to "mono-raise"
(both by your reckoning, and by my previous understanding), I'd like
to use this as a tool to simplify the "Monotonicity" article on
electowiki, moving the more technical mathematical definitions out of
the summary of the article
I don't see how Woodall can be wrong, it's his choice to define these
criteria and characterize them as dealing with monotonicity. But to me,
if you say a method "fails monotonicity," or "is monotone," you're either
talking about Mono-raise or else you're being unclear. Inserting these
into an article called "Monotonicity" could be unhelpful unless it's made
clear that these are other criteria connected to the idea, and are used
(as far as I know) primarily by Woodall.
I've seen other folks use at least some of the nine criteria that
Woodall defines, so I'd like to define them somewhere on electowiki.
I'll give it some thought.
One relatively simple restatement comes from the Wikipedia article
about Arrow's theorem:
https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem
Here's the way that the Wikipedia article restates monotonicity:
"If any individual modifies his or her preference order by promoting a
certain option, then the societal preference order should respond only
by promoting that same option or not changing, never by placing it
lower than before. An individual should not be able to hurt an option
by ranking it higher."
More ways of thinking about it....
Note that (at least in other articles) Woodall is/was largely concerned
with which sets of properties are compatible with each other, and he
didn't usually make statements judging the relative value of criteria. This
leaves the job to other people to explain why we should care about a
given property.
Thanks for your advice! I'll give all of this more thought before I
make big changes to that electowiki article.
Rob
I think the scenarios where new ballots are added have more in common with participation than monotonicity, in terms of how it is normally understood in voting theory at least. Mono-add-top is just a specific case of participation.
Toby
On Monday, 16 November 2020, 02:32:50 GMT, Rob Lanphier robla@robla.net wrote:
Hi folks,
I don't think I've ever fully prerused the "Voting matters"[1] website
before, and realized how serious of a publication it was (or rather
"is"):
[1]: http://www.votingmatters.org.uk/
Maybe I did, but I forgot about it. It looks like there are several
interesting papers to read there.
Douglas Woodall published at least a couple of papers there. It also
seems that Woodall's definition of "monotonicity"[2] is the favorite
of many folks who like to discuss election methods. In particular, I
want to highlight Issue 3, paper 5 of "Voting matters":
[2]: http://www.votingmatters.org.uk/ISSUE3/P5.HTM
Here's Woodall's definition of monotonicity from that paper, which
breaks up monotonicity into nine different criteria:
Monotonicity. A candidate x should not be harmed if:
- (mono-raise) x is raised on some ballots without changing the orders of the other candidates;
- (mono-raise-delete) x is raised on some ballots and all candidates now below x on those ballots are deleted from them;
- (mono-raise-random) x is raised on some ballots and the positions now below x on those ballots are filled (or left vacant) in any way that results in a valid ballot;
- (mono-append) x is added at the end of some ballots that did not previously contain x;
- (mono-sub-plump) some ballots that do not have x top are replaced by ballots that have x top with no second choice;
- (mono-sub-top) some ballots that do not have x top are replaced by ballots that have x top (and are otherwise arbitrary);
- (mono-add-plump) further ballots are added that have x top with no second choice;
- (mono-add-top) further ballots are added that have x top (and are otherwise arbitrary);
- (mono-remove-bottom) some ballots are removed, all of which have x bottom, below all other candidates.
That's nine different criteria that all could be called
"monotonicity". This raises a few questions for me:
- Is Woodall's definition correct?
- Is Woodall's definition the most useful?
- Is Woodall's definition overly-complicated, or just
appropriately-complicated? - Does breaking up monotonicity into nine different criteria make it
easier to understand, or harder? - Was Woodall just copying his definition from someone else when
publishing those nine criteria? If so, who?
The reason why I ask: I want to improve the electowiki article about
monotonicity[3], and I'm wondering if emphasis on the nine criteria
above would help make the article clearer:
[3]: https://electowiki.org/wiki/Monotonicity
Should the electowiki community use Woodall's nine criteria as the
electowiki definition of "monotonicity"?
Rob
p.s. a YouTube video[4] posted to C4ES's Discord server is what
inspired me to compose this email:
[4]: https://youtu.be/OI232JSDwDg
p.p.s.: What I mean by "C4ES's Discord Server"[5] is the Discord
server that is operated by the Center for Election Science:
[5]: https://electionscience.org/discord
Election-Methods mailing list - see https://electorama.com/em for list info
Even the "most useful" monotonicity criterion isn't very important. Monotonicity strikes me as something to write about when one has a "publish or perish" job in academia.
Much more important than monotonicity are the incentives that the voting method induces on candidates who want to win... in particular whether candidates will want to take positions similar to the positions that the voters would collectively choose in a direct democracy. In other words, it should be a losing strategy for a candidate to take position X on some issue when there exists a position Y that a large majority prefer over X. A voting method has a much worse problem than non-monotonicity if a candidate has a good chance to win by taking minority-preferred positions (typically via a majority coalition comprised of those minorities).
Regards,
Steve
On 11/15/2020 9:32 PM, Rob Lanphier wrote:
Hi folks,
I don't think I've ever fully prerused the "Voting matters"[1] website
before, and realized how serious of a publication it was (or rather
"is"):
[1]: http://www.votingmatters.org.uk/
Maybe I did, but I forgot about it. It looks like there are several
interesting papers to read there.
Douglas Woodall published at least a couple of papers there. It also
seems that Woodall's definition of "monotonicity"[2] is the favorite
of many folks who like to discuss election methods. In particular, I
want to highlight Issue 3, paper 5 of "Voting matters":
[2]: http://www.votingmatters.org.uk/ISSUE3/P5.HTM
Here's Woodall's definition of monotonicity from that paper, which
breaks up monotonicity into nine different criteria:
Monotonicity. A candidate x should not be harmed if:
- (mono-raise) x is raised on some ballots without changing the orders of the other candidates;
- (mono-raise-delete) x is raised on some ballots and all candidates now below x on those ballots are deleted from them;
- (mono-raise-random) x is raised on some ballots and the positions now below x on those ballots are filled (or left vacant) in any way that results in a valid ballot;
- (mono-append) x is added at the end of some ballots that did not previously contain x;
- (mono-sub-plump) some ballots that do not have x top are replaced by ballots that have x top with no second choice;
- (mono-sub-top) some ballots that do not have x top are replaced by ballots that have x top (and are otherwise arbitrary);
- (mono-add-plump) further ballots are added that have x top with no second choice;
- (mono-add-top) further ballots are added that have x top (and are otherwise arbitrary);
- (mono-remove-bottom) some ballots are removed, all of which have x bottom, below all other candidates.
That's nine different criteria that all could be called
"monotonicity". This raises a few questions for me:
- Is Woodall's definition correct?
- Is Woodall's definition the most useful?
- Is Woodall's definition overly-complicated, or just
appropriately-complicated? - Does breaking up monotonicity into nine different criteria make it
easier to understand, or harder? - Was Woodall just copying his definition from someone else when
publishing those nine criteria? If so, who?
The reason why I ask: I want to improve the electowiki article about
monotonicity[3], and I'm wondering if emphasis on the nine criteria
above would help make the article clearer:
[3]: https://electowiki.org/wiki/Monotonicity
Should the electowiki community use Woodall's nine criteria as the
electowiki definition of "monotonicity"?
Rob
p.s. a YouTube video[4] posted to C4ES's Discord server is what
inspired me to compose this email:
[4]: https://youtu.be/OI232JSDwDg
p.p.s.: What I mean by "C4ES's Discord Server"[5] is the Discord
server that is operated by the Center for Election Science:
[5]: https://electionscience.org/discord
Election-Methods mailing list - see https://electorama.com/em for list info
Thanks Toby! Given the private and public responses I've gotten to my
question, and the deeper understanding of "the Monotonicity criterion"
that I'm developing, I think that it makes sense to figure out how
"the Woodall nine" (as I'll start calling them) map to "monotonicity"
when talking to people who understand matrix addition.
More below...
On Mon, Nov 16, 2020 at 2:17 AM Toby Pereira tdp201b@yahoo.co.uk wrote:
I think the scenarios where new ballots are added have more in common with
participation than monotonicity, in terms of how it is normally understood in
voting theory at least.
Let's use the Woodall Nine to talk about this. What would you say the
mapping is? I started coming up with my own version of the list
(which was serious), but this became a self-parody. The format of
each line is
- woodall-name - robla-named-criterion ("Proposed Wikipedia/electowiki Article")
Here's the mappings as I saw them on my first runthough:
- mono-raise - dont-muck-with-ballots-criterion ("Monotonicity (Classic)")
- mono-raise-delete - participation-criterion ("Monotonicity (Nuke ballots)")
- mono-raise-random - adding-random-ballots-causes-mayhem-criterion
("Monotonicity (Add random)") - mono-append - fill-in-ballot-bubbles-criterion ("Monotonicity (Add
preference)") - mono-sub-plump - replace-ballots-criterion ("Monotonicity (Erase preference)")
- mono-sub-top - replace-with-new-winner-criterion ("Monotonicity ()")
- mono-add-plump -
add-incompletely-ranked-ballots-to-cause-loss-criterion ("Monotonicity
(Add incomplete ballots)") - mono-add-top - add-top-scored-but-mostly-random-criterion
("Monotonicity (Add mostly random)") - mono-remove-bottom -
remove-bottom-ranked-Condorcet-loser-ballots-criterion ("Monotonicity
(Remove Condorcet loser haters)")
I think this thing needs to exist in the world, so I'm actually going
to keep working on it here:
https://electowiki.org/wiki/User:RobLa/Woodall-to-RobLa
Toby, I would love for you and others on this mailing list to come up
with more serious versions. I spent about an hour trying to be
serious when coming up with my mappings, and I think it was a valuable
exercise. My fear: there are many electoral reform advocates who will
say "I understand the monotonicity criterion". However, most of
those people wouldn't be able to answer this question: "what do YOU
mean when you say 'monotonicity criterion'?" My guess: they would
deflect, and say "I know someone who knows what it means, and I've
never really understood it, but I THINK it means this: xyz", and then
their "xyz" would be an oversimplified example involving Woodall's
"mono-raise" or perhaps "Participation" or something vaguely related
to Pareto efficiency. They probably don't understand very well, and
my hunch is that most people on this mailing list are overconfident
with THEIR understanding of "monotonicity".
When someone asks "What is the 'monotonicity criterion'?", it seems
the correct answer is to throw the question back at them: "before I
explain: do you know what 'monotonicity' is?". If it seems they
aren't very well-versed in advanced mathematics, and they aren't
familiar with what a monotonically-increasing sequence is, then assume
that it's time to back off the math jargon. I think "monotonicity
criterion" seems to be a terrible name for talking about electoral
reform.
That's the reason why I want to talk about the Woodall Nine. I'd like
to come up with layperson names for each of them, and possibly map
them to various criteria that have Wikipedia articles about them. If
there's not yet a Wikipedia article, maybe an electowiki article. If
there's not yet an electowiki article, maybe a section of an
electowiki article.
Responding to one last bit of your email:
Mono-add-top is just a specific case of participation.
Are there any other mono-woodall methods that are subsets of the
Participation criterion?
https://electowiki.org/wiki/Participation_criterion
Rob
I actually meant to say that mono-add-plump, not mono-add-top, that is just a specific case of participation. The new voter is only ranking one candidate, so if that causes the candidate to lose, then it is a failure of participation. But anyway, I think this is good work that you're doing. I'll have a look through your list.
Toby
On Tuesday, 17 November 2020, 08:59:30 GMT, Rob Lanphier robla@robla.net wrote:
Thanks Toby! Given the private and public responses I've gotten to my
question, and the deeper understanding of "the Monotonicity criterion"
that I'm developing, I think that it makes sense to figure out how
"the Woodall nine" (as I'll start calling them) map to "monotonicity"
when talking to people who understand matrix addition.
More below...
On Mon, Nov 16, 2020 at 2:17 AM Toby Pereira tdp201b@yahoo.co.uk wrote:
I think the scenarios where new ballots are added have more in common with
participation than monotonicity, in terms of how it is normally understood in
voting theory at least.
Let's use the Woodall Nine to talk about this. What would you say the
mapping is? I started coming up with my own version of the list
(which was serious), but this became a self-parody. The format of
each line is
- woodall-name - robla-named-criterion ("Proposed Wikipedia/electowiki Article")
Here's the mappings as I saw them on my first runthough:
- mono-raise - dont-muck-with-ballots-criterion ("Monotonicity (Classic)")
- mono-raise-delete - participation-criterion ("Monotonicity (Nuke ballots)")
- mono-raise-random - adding-random-ballots-causes-mayhem-criterion
("Monotonicity (Add random)") - mono-append - fill-in-ballot-bubbles-criterion ("Monotonicity (Add
preference)") - mono-sub-plump - replace-ballots-criterion ("Monotonicity (Erase preference)")
- mono-sub-top - replace-with-new-winner-criterion ("Monotonicity ()")
- mono-add-plump -
add-incompletely-ranked-ballots-to-cause-loss-criterion ("Monotonicity
(Add incomplete ballots)") - mono-add-top - add-top-scored-but-mostly-random-criterion
("Monotonicity (Add mostly random)") - mono-remove-bottom -
remove-bottom-ranked-Condorcet-loser-ballots-criterion ("Monotonicity
(Remove Condorcet loser haters)")
I think this thing needs to exist in the world, so I'm actually going
to keep working on it here:
https://electowiki.org/wiki/User:RobLa/Woodall-to-RobLa
Toby, I would love for you and others on this mailing list to come up
with more serious versions. I spent about an hour trying to be
serious when coming up with my mappings, and I think it was a valuable
exercise. My fear: there are many electoral reform advocates who will
say "I understand the monotonicity criterion". However, most of
those people wouldn't be able to answer this question: "what do YOU
mean when you say 'monotonicity criterion'?" My guess: they would
deflect, and say "I know someone who knows what it means, and I've
never really understood it, but I THINK it means this: xyz", and then
their "xyz" would be an oversimplified example involving Woodall's
"mono-raise" or perhaps "Participation" or something vaguely related
to Pareto efficiency. They probably don't understand very well, and
my hunch is that most people on this mailing list are overconfident
with THEIR understanding of "monotonicity".
When someone asks "What is the 'monotonicity criterion'?", it seems
the correct answer is to throw the question back at them: "before I
explain: do you know what 'monotonicity' is?". If it seems they
aren't very well-versed in advanced mathematics, and they aren't
familiar with what a monotonically-increasing sequence is, then assume
that it's time to back off the math jargon. I think "monotonicity
criterion" seems to be a terrible name for talking about electoral
reform.
That's the reason why I want to talk about the Woodall Nine. I'd like
to come up with layperson names for each of them, and possibly map
them to various criteria that have Wikipedia articles about them. If
there's not yet a Wikipedia article, maybe an electowiki article. If
there's not yet an electowiki article, maybe a section of an
electowiki article.
Responding to one last bit of your email:
Mono-add-top is just a specific case of participation.
Are there any other mono-woodall methods that are subsets of the
Participation criterion?
https://electowiki.org/wiki/Participation_criterion
Rob
Just to add to this - monotonicity looks at the fate of the candidate, whereas participation looks at the fate of the voter. But where only one candidate is listed on the ballot, their fates are intertwined.
On Tuesday, 17 November 2020, 09:19:22 GMT, Toby Pereira tdp201b@yahoo.co.uk wrote:
I actually meant to say that mono-add-plump, not mono-add-top, that is just a specific case of participation. The new voter is only ranking one candidate, so if that causes the candidate to lose, then it is a failure of participation. But anyway, I think this is good work that you're doing. I'll have a look through your list.
Toby
On Tuesday, 17 November 2020, 08:59:30 GMT, Rob Lanphier robla@robla.net wrote:
Thanks Toby! Given the private and public responses I've gotten to my
question, and the deeper understanding of "the Monotonicity criterion"
that I'm developing, I think that it makes sense to figure out how
"the Woodall nine" (as I'll start calling them) map to "monotonicity"
when talking to people who understand matrix addition.
More below...
On Mon, Nov 16, 2020 at 2:17 AM Toby Pereira tdp201b@yahoo.co.uk wrote:
I think the scenarios where new ballots are added have more in common with
participation than monotonicity, in terms of how it is normally understood in
voting theory at least.
Let's use the Woodall Nine to talk about this. What would you say the
mapping is? I started coming up with my own version of the list
(which was serious), but this became a self-parody. The format of
each line is
- woodall-name - robla-named-criterion ("Proposed Wikipedia/electowiki Article")
Here's the mappings as I saw them on my first runthough:
- mono-raise - dont-muck-with-ballots-criterion ("Monotonicity (Classic)")
- mono-raise-delete - participation-criterion ("Monotonicity (Nuke ballots)")
- mono-raise-random - adding-random-ballots-causes-mayhem-criterion
("Monotonicity (Add random)") - mono-append - fill-in-ballot-bubbles-criterion ("Monotonicity (Add
preference)") - mono-sub-plump - replace-ballots-criterion ("Monotonicity (Erase preference)")
- mono-sub-top - replace-with-new-winner-criterion ("Monotonicity ()")
- mono-add-plump -
add-incompletely-ranked-ballots-to-cause-loss-criterion ("Monotonicity
(Add incomplete ballots)") - mono-add-top - add-top-scored-but-mostly-random-criterion
("Monotonicity (Add mostly random)") - mono-remove-bottom -
remove-bottom-ranked-Condorcet-loser-ballots-criterion ("Monotonicity
(Remove Condorcet loser haters)")
I think this thing needs to exist in the world, so I'm actually going
to keep working on it here:
https://electowiki.org/wiki/User:RobLa/Woodall-to-RobLa
Toby, I would love for you and others on this mailing list to come up
with more serious versions. I spent about an hour trying to be
serious when coming up with my mappings, and I think it was a valuable
exercise. My fear: there are many electoral reform advocates who will
say "I understand the monotonicity criterion". However, most of
those people wouldn't be able to answer this question: "what do YOU
mean when you say 'monotonicity criterion'?" My guess: they would
deflect, and say "I know someone who knows what it means, and I've
never really understood it, but I THINK it means this: xyz", and then
their "xyz" would be an oversimplified example involving Woodall's
"mono-raise" or perhaps "Participation" or something vaguely related
to Pareto efficiency. They probably don't understand very well, and
my hunch is that most people on this mailing list are overconfident
with THEIR understanding of "monotonicity".
When someone asks "What is the 'monotonicity criterion'?", it seems
the correct answer is to throw the question back at them: "before I
explain: do you know what 'monotonicity' is?". If it seems they
aren't very well-versed in advanced mathematics, and they aren't
familiar with what a monotonically-increasing sequence is, then assume
that it's time to back off the math jargon. I think "monotonicity
criterion" seems to be a terrible name for talking about electoral
reform.
That's the reason why I want to talk about the Woodall Nine. I'd like
to come up with layperson names for each of them, and possibly map
them to various criteria that have Wikipedia articles about them. If
there's not yet a Wikipedia article, maybe an electowiki article. If
there's not yet an electowiki article, maybe a section of an
electowiki article.
Responding to one last bit of your email:
Mono-add-top is just a specific case of participation.
Are there any other mono-woodall methods that are subsets of the
Participation criterion?
https://electowiki.org/wiki/Participation_criterion
Rob
Hi Rob,
I'm not quite seeing the connection between the goal of renaming monotonicity, and the introduction (or popularization) of another eight criteria. Woodall still referred to it all as monotonicity, so how does his work help?
A couple of the criteria are so hard to satisfy that for most people it's probably not worth learning about them. Namely, Mono-raise-random and Mono-sub-top are apparently only satisfied by FPP and certain top-heavy Borda-like rules that Woodall didn't even see fit to name. His motivation for having these criteria was clearly not advocacy...
If you categorize the criteria, doing it by the operation performed gives the expected results I'd say:
modifying existing ballots: Mono-raise, Mono-raise-delete, Mono-raise-random, Mono-append. All four of these involve raising a candidate, except for the odd edge case that happens to exist within Woodall's framework, that "appending" the least liked candidate of the ballot could actually fail to raise him over anyone. If your framework doesn't support an "append" operation with that effect, then Mono-raise implies Mono-append, and Mono-raise-random implies all of the other three.
substituting ballots: Mono-sub-top and Mono-sub-plump can be categorized the same as Mono-raise because they can be conceived of as special cases (weaker forms) of Mono-raise-random and Mono-raise-delete respectively. (They aren't so much weaker though... Woodall doesn't offer any methods that satisfy the easier criterion of the pair and not the harder one.)
adding/dropping ballots: Mono-add-top, Mono-remove-bottom, Mono-add-plump. These are all implied by Participation (though Participation is much stronger than any of these). Note that you can rephrase Mono-remove-bottom to be about adding ballots.
Kevin
Le mardi 17 novembre 2020 à 02:58:35 UTC−6, Rob Lanphier <robla@robla.net> a écrit :
Thanks Toby! Given the private and public responses I've gotten to my
question, and the deeper understanding of "the Monotonicity criterion"
that I'm developing, I think that it makes sense to figure out how
"the Woodall nine" (as I'll start calling them) map to "monotonicity"
when talking to people who understand matrix addition.
More below...
On Mon, Nov 16, 2020 at 2:17 AM Toby Pereira tdp201b@yahoo.co.uk wrote:
I think the scenarios where new ballots are added have more in common with
participation than monotonicity, in terms of how it is normally understood in
voting theory at least.
Let's use the Woodall Nine to talk about this. What would you say the
mapping is? I started coming up with my own version of the list
(which was serious), but this became a self-parody. The format of
each line is
- woodall-name - robla-named-criterion ("Proposed Wikipedia/electowiki Article")
Here's the mappings as I saw them on my first runthough:
- mono-raise - dont-muck-with-ballots-criterion ("Monotonicity (Classic)")
- mono-raise-delete - participation-criterion ("Monotonicity (Nuke ballots)")
- mono-raise-random - adding-random-ballots-causes-mayhem-criterion
("Monotonicity (Add random)") - mono-append - fill-in-ballot-bubbles-criterion ("Monotonicity (Add
preference)") - mono-sub-plump - replace-ballots-criterion ("Monotonicity (Erase preference)")
- mono-sub-top - replace-with-new-winner-criterion ("Monotonicity ()")
- mono-add-plump -
add-incompletely-ranked-ballots-to-cause-loss-criterion ("Monotonicity
(Add incomplete ballots)") - mono-add-top - add-top-scored-but-mostly-random-criterion
("Monotonicity (Add mostly random)") - mono-remove-bottom -
remove-bottom-ranked-Condorcet-loser-ballots-criterion ("Monotonicity
(Remove Condorcet loser haters)")
I think this thing needs to exist in the world, so I'm actually going
to keep working on it here:
https://electowiki.org/wiki/User:RobLa/Woodall-to-RobLa
Toby, I would love for you and others on this mailing list to come up
with more serious versions. I spent about an hour trying to be
serious when coming up with my mappings, and I think it was a valuable
exercise. My fear: there are many electoral reform advocates who will
say "I understand the monotonicity criterion". However, most of
those people wouldn't be able to answer this question: "what do YOU
mean when you say 'monotonicity criterion'?" My guess: they would
deflect, and say "I know someone who knows what it means, and I've
never really understood it, but I THINK it means this: xyz", and then
their "xyz" would be an oversimplified example involving Woodall's
"mono-raise" or perhaps "Participation" or something vaguely related
to Pareto efficiency. They probably don't understand very well, and
my hunch is that most people on this mailing list are overconfident
with THEIR understanding of "monotonicity".
When someone asks "What is the 'monotonicity criterion'?", it seems
the correct answer is to throw the question back at them: "before I
explain: do you know what 'monotonicity' is?". If it seems they
aren't very well-versed in advanced mathematics, and they aren't
familiar with what a monotonically-increasing sequence is, then assume
that it's time to back off the math jargon. I think "monotonicity
criterion" seems to be a terrible name for talking about electoral
reform.
That's the reason why I want to talk about the Woodall Nine. I'd like
to come up with layperson names for each of them, and possibly map
them to various criteria that have Wikipedia articles about them. If
there's not yet a Wikipedia article, maybe an electowiki article. If
there's not yet an electowiki article, maybe a section of an
electowiki article.
Responding to one last bit of your email:
Mono-add-top is just a specific case of participation.
Are there any other mono-woodall methods that are subsets of the
Participation criterion?
https://electowiki.org/wiki/Participation_criterion
Rob
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