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FS

Forest Simmons

Fri, May 6, 2022 4:19 AM

There were several 3-slot methods I was considering when I started this
thread, but the main one was a version of median judgment first proposed by
Andy Jennings in his dissertstion more than a decade ago. A few years ago
Adrien Fabre independently published the method as "Usual Judgment." And
last month I discovered the method independently in the case of three
judgment categories.

As soon as I made a graphic available showing the helical ramp
interpolation that characterizes the method, the versions of Jennings and
Fabre were brought to my attention. Both of them contemplated more than
three categories.

A Wikipedia article (Highest Median Voting Rules) comparing various median
judgment methods (rightly) affirms that among the known median judgment
methods, Usual Judgment dominates the others in criteria compliances ...
resolving nagging imperfections (lack of Reverse Symmetry and Participation
compliances) of Majority Judgment, for example.

However, the article pointed out that the perfection of Usual Judgment,
especially in the intricacies of its general case tie breaking procedure,
might put too high a demand on the attention span of the average voter.

This kind of "problem" is a public relations problem only for methods whose
proponents make too big a deal of the elegance of the arcane intricacies
that do not concern the lay citizen.

When someone picks up a proposal like MAM, for example, from this EM list
and tries to sell it to the public without filtering out the technical
discussions designed to persuade the other EM experts ... Big Mistake!

In the case of Usual Judgment restricted to the case of three judgment
categories (the 3-slot case that I am proposing), it would be hard to
complicate the tie breaking process ... though somebody with unusual talent
for confusing things might mess it up.

The following is a bare bones introduction. Somebody else can decide on the
names of the three categories and their definitions.

For now let's call them generically Top, Between, & Bottom.

Usual Judgment is designed to output a finish order for the candidates.
Someday we can get into that, but for now even mentioning that,
gratuitously and prematurely pushes to the limit valuable attention span
(slash) willpower (slash) compassion fatigue

So here we go ...

If some candidate is judged Top on more than half of the ballots, elect the
candidate judged Top on the greatest majority of ballots.

Else-If every candidate is judged Bottom on more than half of the ballots,
elect the one judged bottom on the fewest ballots.

Otherwise, elect (from among the candidates with neither a Top nor Bottom
majority) the one with the largest score obtained by dividing the
difference of its Top and Bottom counts by its Between level count.

That's it for the lay person description other than some examples and
heuristic explanations to show how it works ... don't complicate it by
trying to forestall all possible questions ... that's a software engineer
reflex that we have to hold in check.

While explaining the method, you may point out how it respects majority
rule: if some candidate is judged Top level on more than half of the
ballots, then she will be elected except when (as may happen) there is
another candidate with a greater majority of Top level judgments ... which
should be good news for the electorate!

If somebody asks how truncations (abstentions) are counted, you can answer
that they are treated the same way that truncations are treated in other
popular methods like IRV, Ranked Pairs, Range, Borda, etc... and for the
same reason ... to dodge the Dark Horse dilemma ... an abstention is
treated as a Bottom judgment, just as an abstention is treated as below any
ranked candidate on ranked choice ballots. Why would Borda, for example
give it a rank half way between first and last?

If somebody asks ... "Why the division by the Between level count?"... It
serves to accentuate the difference between Top and Bottom counts to make
ties less likely.

Beyond that (for extremely persistent, curious questioners) this division
is required for continuity of results at the boundaries of the three cases
[which is necessary for Participation Criterion compliance, one of those
compliances whose lack has given other median judgment methods like
Majority Judgment some mild public relations grief].

At this juncture a graphic from Andy's dissertation would be worth a
thousand words.

Who else has a suggestion to share?

-Forest

El lun., 2 de may. de 2022 12:47 p. m., Forest Simmons <
forest.simmons21@gmail.com> escribió:

While people are playing with election methods based on three level
ballots, I would like to suggest another way to generate these three level
ballots to reinforce my main contention... that three levels are easier to
generate than two.

This method transforms standard sets of Universal Domain style, ranked
preference, ordinal ballots into 3 level ballots, which you may consider as
cardinal, grade, or judgment category ballots as you so desire. A creative,
accepting, brainstorming environment is what this thread is all about!

First generate a table of pairwise defeats and ties to consult while
making a second (final) pass through the input ballots.

Then for each candidate k and each ballot B, decided whether B increments
the Top, Bottom, or Mid level count of candidate k as follows:

If on ballot B candidate k outranks some candidate j that is not defeated
by any candidate ranked above k, then increment the Top level count of
candidate k.

ElseIf some candidate j ranked above k is not defeated by any candidate
that is outranked by k, then increment the Bottom level count of candidate
k.

Else increment the Mid level count of candidate k.

Isn't that much simpler than any (two level) approval DSV method that
you've ever heard of?

Of course, for three levels, Implicit Three Level would be even simpler:
just count the ranked ballot Tops, Bottoms, and Middles without the
possibility of dipping down or reaching up into the middle ranks for
additional approvals or disapprovals. But where's the fun in that?

Now keep grokking a good election method (besides simple Score and
"Explicit Approval" ... the low hanging fruit already grabbed up my Rob
Lanphier) based on three level ballots.

Thanks.

-Forest

El dom., 1 de may. de 2022 8:00 p. m., Forest Simmons <
forest.simmons21@gmail.com> escribió:

El sáb., 30 de abr. de 2022 8:58 p. m., Rob Lanphier roblan@gmail.com
escribió:

Hi Forest,

Thanks for the food for thought (really.... I took a long time
composing this email). My hunch is that you're proposing something
awfully similar to "explicit approval" as devised by the folks in the
Wikimedia community, but more inline below:

On Sat, Apr 30, 2022 at 12:42 PM Forest Simmons
forest.simmons21@gmail.com wrote:

On paper Approval has the best standard criteria compliances of any
method. On top of that it has all around simplicity going for it. Yet
nobody likes it,

That's a peculiar definition of "nobody":

https://electionscience.org/commentary-analysis/approval-voting-americas-favorite-voting-reform/

and the most common complaint from experts and lay
citizens alike is that the definition of "approval" is so vague that
it could drive an indecisive person to distraction: There is no clear
guideline for partitioning the candidates into two distinct categories
with a crisp boundary between them.

I agree with this complaint, and stated it as my objection for many
years, but I've gotten over it. I'll restate a couple heuristics that
I posted in a reddit comment recently:

https://www.reddit.com/r/EndFPTP/comments/u1qguy/recordsetting_15_candidates_vie_for_fargo_city/i4eb3sw/

HEURISTIC A:

Find the candidate which seems likely to get elected, and that the
voter is afraid will win. That's the "fear anchor" candidate.
For each candidate on the ballot, decide:
2a. if the candidate is better than the "fear anchor", then vote for them
2b. if the candidate is NOT better than the "fear anchor", then DO NOT
vote for them

HEURISTIC B:
If the "frontrunner" is a good candidate, then vote for them. If not,
then don't. Then decide on whether to vote for a candidate based on
how they compare to the frontrunner (if better, then "YES"; if not
better, then "NO").

Michael Ossipoff had a couple of other good ones: 1. Approve whomever you
would vote for in a FPTP Plurality election election as well as everyone
you like better. 2. Approve every candidate that you prefer over another
trip to the polls.

Joe Weinstein: approve or disapprove X depending on whether you the
winner is more likely to be worse than X or better than X.

Rob Legrand: Approve down to the most likely winner ... inclusive only if
the runner-up is worse.

I don't to tip my hand yet ... I want people to grapple with it
themselves.

In close second is the related complaint about lack of expressive power
... in particular the inability to distinguish favorite, compromise,
and anti-favorite with three separate levels of ballot support.

I think this is what the appeal of STAR voting is. But it's also what
I liked about the form of explicit approval that Wikimedia Foundation
used to use for many of its elections:
https://electowiki.org/wiki/Explicit_approval_voting

My hunch is that the Wikimedia folks got it right with their
tabulation method. They had three levels for each candidate (Support
/ Abstain / Oppose) and then used the formula below to tabulate:

Support / (Support + Oppose)

...and then relying on a per-candidate. Default was "abstain", and
the quota was recalculated for each candidate. The system was biased
against candidates that didn't elicit either strong support or strong
opposition (since those candidates would have a difficult time meeting
quota, since abstentions didn't count), but it seemed like a
reasonable level of work to place on voters (to research candidates)
and on candidates (to campaign, and increase their name recognition)

Weirdly, English Wikipedia doesn't have an article for "Explicit
approval voting", but it has "Combined approval voting":
https://en.wikipedia.org/wiki/Combined_approval_voting

...which appears to select equivalent winners to Score voting with +0,
+1, and +2 (integers) as the only options..

Regardless, are you proposing a fourth tabulation method?

"Definite Dis/Approval" (DD/A) addresses head on the basis for
these complaints with judgment style ballot instructions... "mark as
definitely approved (DA) only the candidates that you are absolutely
sure that you want to support" ... "mark as definitely disapproved
(DD) only the candidates that you very strongly feel to be unsuitable
for the position." Otherwise, mark the remaining candidates as
either ... "somewhere in the middle (Mid) between strongly suitable
and strongly unsuitable" or "No basis (NB) for an opinion." A blank
(i.e.abstemtion/undecided) is counted with the NB's.

What if I'm not sure? Then most definitely it would be dishonest to
mark DA or DD. If you cannot decide between NB and Mid, then leave it
blank ... the ultimate expression of "Undecided".

Now suppose that for each candidate k, you have the total counts DA(k),
DD(k), Mid(k), and NB(k), and no other information.

How would you use those totals to decide the single winner?
How would you construct a finish order if need be?
How would you resolve ties?

Why come up with a new name and a new set of complicated jargon if you
haven't answered these questions yet (especially since "Mid(k)" and
"NB(k)" seem to be equivalent, and "NB" in my mind means "nota bene")?
Explicit Approval, Combined Approval, and STAR voting answer your
questions in three different ways, and all three of them have worthy
cases for them (and against them). Perhaps a good starting point is
to come up with your own answers to each of those questions, and then
express your case using the language already used to describe one (or
more) of those election methods.

Sorry if the tone of my email seems negative. It just seems to me
that much of the discussion on this mailing list is between people who
want to invent their own jargon and their own election methods. I've
been guilty of it myself (e.g. when several of us devised MATT and MAF
in discussions on this mailing list back in 2018)[1][2][3]. Back in
2018 (after having spent many weekends the prior summer in California
knocking on doors outside my district), and then one weekend tabling
for the Center for Election Science, I came to realize that approval
voting could solve problems in the California primaries, and tried to
come up with a system that was simple enough, and didn't have the
appearance of a difficult algebra problem photocopied from a linear
algebra textbook. Can you (or someone on this list) come up with a
system that's suitable for replacing the "blanket primary"[4] we have
here in California?

Rob
[1]:
http://lists.electorama.com/pipermail/election-methods-electorama.com//2018-November/thread.html
[2]:
http://lists.electorama.com/pipermail/election-methods-electorama.com//2018-December/thread.html
[3]: https://electowiki.org/wiki/Approval-based_primary_election_methods
[4]: https://electowiki.org/wiki/Blanket_primary

There were several 3-slot methods I was considering when I started this thread, but the main one was a version of median judgment first proposed by Andy Jennings in his dissertstion more than a decade ago. A few years ago Adrien Fabre independently published the method as "Usual Judgment." And last month I discovered the method independently in the case of three judgment categories. As soon as I made a graphic available showing the helical ramp interpolation that characterizes the method, the versions of Jennings and Fabre were brought to my attention. Both of them contemplated more than three categories. A Wikipedia article (Highest Median Voting Rules) comparing various median judgment methods (rightly) affirms that among the known median judgment methods, Usual Judgment dominates the others in criteria compliances ... resolving nagging imperfections (lack of Reverse Symmetry and Participation compliances) of Majority Judgment, for example. However, the article pointed out that the perfection of Usual Judgment, especially in the intricacies of its general case tie breaking procedure, might put too high a demand on the attention span of the average voter. This kind of "problem" is a public relations problem only for methods whose proponents make too big a deal of the elegance of the arcane intricacies that do not concern the lay citizen. When someone picks up a proposal like MAM, for example, from this EM list and tries to sell it to the public without filtering out the technical discussions designed to persuade the other EM experts ... Big Mistake! In the case of Usual Judgment restricted to the case of three judgment categories (the 3-slot case that I am proposing), it would be hard to complicate the tie breaking process ... though somebody with unusual talent for confusing things might mess it up. The following is a bare bones introduction. Somebody else can decide on the names of the three categories and their definitions. For now let's call them generically Top, Between, & Bottom. Usual Judgment is designed to output a finish order for the candidates. Someday we can get into that, but for now even mentioning that, gratuitously and prematurely pushes to the limit valuable attention span (slash) willpower (slash) compassion fatigue So here we go ... If some candidate is judged Top on more than half of the ballots, elect the candidate judged Top on the greatest majority of ballots. Else-If every candidate is judged Bottom on more than half of the ballots, elect the one judged bottom on the fewest ballots. Otherwise, elect (from among the candidates with neither a Top nor Bottom majority) the one with the largest score obtained by dividing the difference of its Top and Bottom counts by its Between level count. That's it for the lay person description other than some examples and heuristic explanations to show how it works ... don't complicate it by trying to forestall all possible questions ... that's a software engineer reflex that we have to hold in check. While explaining the method, you may point out how it respects majority rule: if some candidate is judged Top level on more than half of the ballots, then she will be elected except when (as may happen) there is another candidate with a greater majority of Top level judgments ... which should be good news for the electorate! If somebody asks how truncations (abstentions) are counted, you can answer that they are treated the same way that truncations are treated in other popular methods like IRV, Ranked Pairs, Range, Borda, etc... and for the same reason ... to dodge the Dark Horse dilemma ... an abstention is treated as a Bottom judgment, just as an abstention is treated as below any ranked candidate on ranked choice ballots. Why would Borda, for example give it a rank half way between first and last? If somebody asks ... "Why the division by the Between level count?"... It serves to accentuate the difference between Top and Bottom counts to make ties less likely. Beyond that (for extremely persistent, curious questioners) this division is required for continuity of results at the boundaries of the three cases [which is necessary for Participation Criterion compliance, one of those compliances whose lack has given other median judgment methods like Majority Judgment some mild public relations grief]. At this juncture a graphic from Andy's dissertation would be worth a thousand words. Who else has a suggestion to share? -Forest El lun., 2 de may. de 2022 12:47 p. m., Forest Simmons < forest.simmons21@gmail.com> escribió: > While people are playing with election methods based on three level > ballots, I would like to suggest another way to generate these three level > ballots to reinforce my main contention... that three levels are easier to > generate than two. > > This method transforms standard sets of Universal Domain style, ranked > preference, ordinal ballots into 3 level ballots, which you may consider as > cardinal, grade, or judgment category ballots as you so desire. A creative, > accepting, brainstorming environment is what this thread is all about! > > First generate a table of pairwise defeats and ties to consult while > making a second (final) pass through the input ballots. > > Then for each candidate k and each ballot B, decided whether B increments > the Top, Bottom, or Mid level count of candidate k as follows: > > If on ballot B candidate k outranks some candidate j that is not defeated > by any candidate ranked above k, then increment the Top level count of > candidate k. > > ElseIf some candidate j ranked above k is not defeated by any candidate > that is outranked by k, then increment the Bottom level count of candidate > k. > > Else increment the Mid level count of candidate k. > > Isn't that much simpler than any (two level) approval DSV method that > you've ever heard of? > > Of course, for three levels, Implicit Three Level would be even simpler: > just count the ranked ballot Tops, Bottoms, and Middles without the > possibility of dipping down or reaching up into the middle ranks for > additional approvals or disapprovals. But where's the fun in that? > > Now keep grokking a good election method (besides simple Score and > "Explicit Approval" ... the low hanging fruit already grabbed up my Rob > Lanphier) based on three level ballots. > > Thanks. > > -Forest > > > > > El dom., 1 de may. de 2022 8:00 p. m., Forest Simmons < > forest.simmons21@gmail.com> escribió: > >> >> >> El sáb., 30 de abr. de 2022 8:58 p. m., Rob Lanphier <roblan@gmail.com> >> escribió: >> >>> Hi Forest, >>> >>> Thanks for the food for thought (really.... I took a long time >>> composing this email). My hunch is that you're proposing something >>> awfully similar to "explicit approval" as devised by the folks in the >>> Wikimedia community, but more inline below: >>> >>> On Sat, Apr 30, 2022 at 12:42 PM Forest Simmons >>> <forest.simmons21@gmail.com> wrote: >>> > On paper Approval has the best standard criteria compliances of any >>> > method. On top of that it has all around simplicity going for it. Yet >>> > nobody likes it, >>> >>> That's a peculiar definition of "nobody": >>> >>> https://electionscience.org/commentary-analysis/approval-voting-americas-favorite-voting-reform/ >>> >>> > and the most common complaint from experts and lay >>> > citizens alike is that the definition of "approval" is so vague that >>> > it could drive an indecisive person to distraction: There is no clear >>> > guideline for partitioning the candidates into two distinct categories >>> > with a crisp boundary between them. >>> >>> I agree with this complaint, and stated it as my objection for many >>> years, but I've gotten over it. I'll restate a couple heuristics that >>> I posted in a reddit comment recently: >>> >>> https://www.reddit.com/r/EndFPTP/comments/u1qguy/recordsetting_15_candidates_vie_for_fargo_city/i4eb3sw/ >>> >>> HEURISTIC A: >>> 1. Find the candidate which seems likely to get elected, and that the >>> voter is afraid will win. That's the "fear anchor" candidate. >>> 2. For each candidate on the ballot, decide: >>> 2a. if the candidate is better than the "fear anchor", then vote for them >>> 2b. if the candidate is NOT better than the "fear anchor", then DO NOT >>> vote for them >>> >>> HEURISTIC B: >>> If the "frontrunner" is a good candidate, then vote for them. If not, >>> then don't. Then decide on whether to vote for a candidate based on >>> how they compare to the frontrunner (if better, then "YES"; if not >>> better, then "NO"). >>> >> >> Michael Ossipoff had a couple of other good ones: 1. Approve whomever you >> would vote for in a FPTP Plurality election election as well as everyone >> you like better. 2. Approve every candidate that you prefer over another >> trip to the polls. >> >> Joe Weinstein: approve or disapprove X depending on whether you the >> winner is more likely to be worse than X or better than X. >> >> Rob Legrand: Approve down to the most likely winner ... inclusive only if >> the runner-up is worse. >> >> I don't to tip my hand yet ... I want people to grapple with it >> themselves. >> >> >>> > In close second is the related complaint about lack of expressive power >>> > ... in particular the inability to distinguish favorite, compromise, >>> > and anti-favorite with three separate levels of ballot support. >>> >>> I think this is what the appeal of STAR voting is. But it's also what >>> I liked about the form of explicit approval that Wikimedia Foundation >>> used to use for many of its elections: >>> https://electowiki.org/wiki/Explicit_approval_voting >>> >>> My hunch is that the Wikimedia folks got it right with their >>> tabulation method. They had three levels for each candidate (Support >>> / Abstain / Oppose) and then used the formula below to tabulate: >>> >>> Support / (Support + Oppose) >>> >>> ...and then relying on a per-candidate. Default was "abstain", and >>> the quota was recalculated for each candidate. The system was biased >>> against candidates that didn't elicit either strong support or strong >>> opposition (since those candidates would have a difficult time meeting >>> quota, since abstentions didn't count), but it seemed like a >>> reasonable level of work to place on voters (to research candidates) >>> and on candidates (to campaign, and increase their name recognition) >>> >>> Weirdly, English Wikipedia doesn't have an article for "Explicit >>> approval voting", but it has "Combined approval voting": >>> https://en.wikipedia.org/wiki/Combined_approval_voting >>> >>> ...which appears to select equivalent winners to Score voting with +0, >>> +1, and +2 (integers) as the only options.. >>> >>> Regardless, are you proposing a fourth tabulation method? >>> >>> > "Definite Dis/Approval" (DD/A) addresses head on the basis for >>> > these complaints with judgment style ballot instructions... "mark as >>> > definitely approved (DA) only the candidates that you are absolutely >>> > sure that you want to support" ... "mark as definitely disapproved >>> > (DD) only the candidates that you very strongly feel to be unsuitable >>> > for the position." Otherwise, mark the remaining candidates as >>> > either ... "somewhere in the middle (Mid) between strongly suitable >>> > and strongly unsuitable" or "No basis (NB) for an opinion." A blank >>> > (i.e.abstemtion/undecided) is counted with the NB's. >>> > >>> > What if I'm not sure? Then most definitely it would be dishonest to >>> > mark DA or DD. If you cannot decide between NB and Mid, then leave it >>> > blank ... the ultimate expression of "Undecided". >>> > >>> > Now suppose that for each candidate k, you have the total counts DA(k), >>> > DD(k), Mid(k), and NB(k), and no other information. >>> > >>> > 1. How would you use those totals to decide the single winner? >>> > >>> > 2. How would you construct a finish order if need be? >>> > >>> > 3. How would you resolve ties? >>> >>> Why come up with a new name and a new set of complicated jargon if you >>> haven't answered these questions yet (especially since "Mid(k)" and >>> "NB(k)" seem to be equivalent, and "NB" in my mind means "nota bene")? >>> Explicit Approval, Combined Approval, and STAR voting answer your >>> questions in three different ways, and all three of them have worthy >>> cases for them (and against them). Perhaps a good starting point is >>> to come up with your own answers to each of those questions, and then >>> express your case using the language already used to describe one (or >>> more) of those election methods. >>> >>> Sorry if the tone of my email seems negative. It just seems to me >>> that much of the discussion on this mailing list is between people who >>> want to invent their own jargon and their own election methods. I've >>> been guilty of it myself (e.g. when several of us devised MATT and MAF >>> in discussions on this mailing list back in 2018)[1][2][3]. Back in >>> 2018 (after having spent many weekends the prior summer in California >>> knocking on doors outside my district), and then one weekend tabling >>> for the Center for Election Science, I came to realize that approval >>> voting could solve problems in the California primaries, and tried to >>> come up with a system that was simple enough, and didn't have the >>> appearance of a difficult algebra problem photocopied from a linear >>> algebra textbook. Can you (or someone on this list) come up with a >>> system that's suitable for replacing the "blanket primary"[4] we have >>> here in California? >>> >>> Rob >>> [1]: >>> http://lists.electorama.com/pipermail/election-methods-electorama.com//2018-November/thread.html >>> [2]: >>> http://lists.electorama.com/pipermail/election-methods-electorama.com//2018-December/thread.html >>> [3]: https://electowiki.org/wiki/Approval-based_primary_election_methods >>> [4]: https://electowiki.org/wiki/Blanket_primary >>> >>

KM

Kristofer Munsterhjelm

Fri, May 6, 2022 10:02 AM

On 06.05.2022 06:19, Forest Simmons wrote:

There were several 3-slot methods I was considering when I started this
thread, but the main one was a version of median judgment first proposed
by Andy Jennings in his dissertstion more than a decade ago. A few years
ago Adrien Fabre independently published the method as "Usual
Judgment." And last month I discovered the method independently in the
case of three judgment categories.

As soon as I made a graphic available showing the helical ramp
interpolation that characterizes the method, the versions of Jennings
and Fabre were brought to my attention. Both of them contemplated more
than three categories.

A Wikipedia article (Highest Median Voting Rules) comparing various
median judgment methods (rightly) affirms that among the known median
judgment methods, Usual Judgment dominates the others in criteria
compliances ... resolving nagging imperfections (lack of Reverse
Symmetry and Participation compliances) of Majority Judgment, for example.

However, the article pointed out that the perfection of Usual Judgment,
especially in the intricacies of its general case tie breaking
procedure, might put too high a demand on the attention span of the
average voter.

This kind of "problem" is a public relations problem only for methods
whose proponents make too big a deal of the elegance of the arcane
intricacies that do not concern the lay citizen.

When someone picks up a proposal like MAM, for example, from this EM
list and tries to sell it to the public without filtering out the
technical discussions designed to persuade the other EM experts ... Big
Mistake!

For MAM, I think I would put it like this: Candidates are arranged into
one-on-one match-ups like runoffs where the candidate who would win a
runoff with only the two wins. If there is a candidate who wins every
runoff he's part of, he is elected. Otherwise, landslides count more
than close runoffs in determining the winner.

It would probably be a good idea to also mention that there's been a
beats-all candidate in every ranked election known so far. (Except
possibly one actual runoff election in Romania, maybe? -- but that
wasn't a ranked election.)

I'm a theoretician, not a public activist, so I imagine my description
could be polished further :-)

The truly tough methods to describe would be things like fpA-fpC where
the rules seem to be just pulled out of the air with no rhyme or reason,
unless you happen to know that it makes the method satisfy some
desirable criterion. Or Sinkhorn or Keener, which are incomprehensible
without a lot of linear algebra.

-km

On 06.05.2022 06:19, Forest Simmons wrote: > There were several 3-slot methods I was considering when I started this > thread, but the main one was a version of median judgment first proposed > by Andy Jennings in his dissertstion more than a decade ago. A few years > ago Adrien Fabre independently published the method as "Usual > Judgment." And last month I discovered the method independently in the > case of three judgment categories. > > As soon as I made a graphic available showing the helical ramp > interpolation that characterizes the method, the versions of Jennings > and Fabre were brought to my attention. Both of them contemplated more > than three categories. > > A Wikipedia article (Highest Median Voting Rules) comparing various > median judgment methods (rightly) affirms that among the known median > judgment methods, Usual Judgment dominates the others in criteria > compliances ... resolving nagging imperfections (lack of Reverse > Symmetry and Participation compliances) of Majority Judgment, for example. > > However, the article pointed out that the perfection of Usual Judgment, > especially in the intricacies of its general case tie breaking > procedure, might put too high a demand on the attention span of the > average voter. > > This kind of "problem" is a public relations problem only for methods > whose proponents make too big a deal of the elegance of the arcane > intricacies that do not concern the lay citizen. > > When someone picks up a proposal like MAM, for example, from this EM > list and tries to sell it to the public without filtering out the > technical discussions designed to persuade the other EM experts ... Big > Mistake! For MAM, I think I would put it like this: Candidates are arranged into one-on-one match-ups like runoffs where the candidate who would win a runoff with only the two wins. If there is a candidate who wins every runoff he's part of, he is elected. Otherwise, landslides count more than close runoffs in determining the winner. It would probably be a good idea to also mention that there's been a beats-all candidate in every ranked election known so far. (Except possibly one actual runoff election in Romania, maybe? -- but that wasn't a ranked election.) I'm a theoretician, not a public activist, so I imagine my description could be polished further :-) The truly tough methods to describe would be things like fpA-fpC where the rules seem to be just pulled out of the air with no rhyme or reason, unless you happen to know that it makes the method satisfy some desirable criterion. Or Sinkhorn or Keener, which are incomprehensible without a lot of linear algebra. -km

FS

Forest Simmons

Sat, May 7, 2022 5:20 AM

That's a good template for all of us to imitate in our outreach to the
proletariat!

Let me see how well I can imitate it for my latest attempt in the fpA-gpC
vein:

Candidates are arranged into
one-on-one match-ups like runoffs where the candidate who would win a
runoff with only the two wins. If there is a candidate who wins every
runoff he's part of, he is elected.

Otherwise candidates get reward value for every matchup they win or tie,
but lose value for every matchup they lose.

The candidate with the greatest net reward value is elected.

Specifically, a candidate's prize/reward value is proportional to its
estimated formidability as an opponent in these matchups. You get your
opponent's prize value when you defeat or tie him in a matchup. Otherwise,
you pay out that value.

The formidability of a candidate is gauged as a function of its respective
first and last place showings on the ballots.

El vie., 6 de may. de 2022 3:02 a. m., Kristofer Munsterhjelm <
km_elmet@t-online.de> escribió:

On 06.05.2022 06:19, Forest Simmons wrote:

There were several 3-slot methods I was considering when I started this
thread, but the main one was a version of median judgment first proposed
by Andy Jennings in his dissertstion more than a decade ago. A few years
ago Adrien Fabre independently published the method as "Usual
Judgment." And last month I discovered the method independently in the
case of three judgment categories.

As soon as I made a graphic available showing the helical ramp
interpolation that characterizes the method, the versions of Jennings
and Fabre were brought to my attention. Both of them contemplated more
than three categories.

A Wikipedia article (Highest Median Voting Rules) comparing various
median judgment methods (rightly) affirms that among the known median
judgment methods, Usual Judgment dominates the others in criteria
compliances ... resolving nagging imperfections (lack of Reverse
Symmetry and Participation compliances) of Majority Judgment, for

example.

However, the article pointed out that the perfection of Usual Judgment,
especially in the intricacies of its general case tie breaking
procedure, might put too high a demand on the attention span of the
average voter.

This kind of "problem" is a public relations problem only for methods
whose proponents make too big a deal of the elegance of the arcane
intricacies that do not concern the lay citizen.

When someone picks up a proposal like MAM, for example, from this EM
list and tries to sell it to the public without filtering out the
technical discussions designed to persuade the other EM experts ... Big
Mistake!

For MAM, I think I would put it like this: Candidates are arranged into
one-on-one match-ups like runoffs where the candidate who would win a
runoff with only the two wins. If there is a candidate who wins every
runoff he's part of, he is elected. Otherwise, landslides count more
than close runoffs in determining the winner.

It would probably be a good idea to also mention that there's been a
beats-all candidate in every ranked election known so far. (Except
possibly one actual runoff election in Romania, maybe? -- but that
wasn't a ranked election.)

I'm a theoretician, not a public activist, so I imagine my description
could be polished further :-)

The truly tough methods to describe would be things like fpA-fpC where
the rules seem to be just pulled out of the air with no rhyme or reason,
unless you happen to know that it makes the method satisfy some
desirable criterion. Or Sinkhorn or Keener, which are incomprehensible
without a lot of linear algebra.

-km

That's a good template for all of us to imitate in our outreach to the proletariat! Let me see how well I can imitate it for my latest attempt in the fpA-gpC vein: Candidates are arranged into one-on-one match-ups like runoffs where the candidate who would win a runoff with only the two wins. If there is a candidate who wins every runoff he's part of, he is elected. Otherwise candidates get reward value for every matchup they win or tie, but lose value for every matchup they lose. The candidate with the greatest net reward value is elected. Specifically, a candidate's prize/reward value is proportional to its estimated formidability as an opponent in these matchups. You get your opponent's prize value when you defeat or tie him in a matchup. Otherwise, you pay out that value. The formidability of a candidate is gauged as a function of its respective first and last place showings on the ballots. El vie., 6 de may. de 2022 3:02 a. m., Kristofer Munsterhjelm < km_elmet@t-online.de> escribió: > On 06.05.2022 06:19, Forest Simmons wrote: > > There were several 3-slot methods I was considering when I started this > > thread, but the main one was a version of median judgment first proposed > > by Andy Jennings in his dissertstion more than a decade ago. A few years > > ago Adrien Fabre independently published the method as "Usual > > Judgment." And last month I discovered the method independently in the > > case of three judgment categories. > > > > As soon as I made a graphic available showing the helical ramp > > interpolation that characterizes the method, the versions of Jennings > > and Fabre were brought to my attention. Both of them contemplated more > > than three categories. > > > > A Wikipedia article (Highest Median Voting Rules) comparing various > > median judgment methods (rightly) affirms that among the known median > > judgment methods, Usual Judgment dominates the others in criteria > > compliances ... resolving nagging imperfections (lack of Reverse > > Symmetry and Participation compliances) of Majority Judgment, for > example. > > > > However, the article pointed out that the perfection of Usual Judgment, > > especially in the intricacies of its general case tie breaking > > procedure, might put too high a demand on the attention span of the > > average voter. > > > > This kind of "problem" is a public relations problem only for methods > > whose proponents make too big a deal of the elegance of the arcane > > intricacies that do not concern the lay citizen. > > > > When someone picks up a proposal like MAM, for example, from this EM > > list and tries to sell it to the public without filtering out the > > technical discussions designed to persuade the other EM experts ... Big > > Mistake! > > For MAM, I think I would put it like this: Candidates are arranged into > one-on-one match-ups like runoffs where the candidate who would win a > runoff with only the two wins. If there is a candidate who wins every > runoff he's part of, he is elected. Otherwise, landslides count more > than close runoffs in determining the winner. > > It would probably be a good idea to also mention that there's been a > beats-all candidate in every ranked election known so far. (Except > possibly one actual runoff election in Romania, maybe? -- but that > wasn't a ranked election.) > > I'm a theoretician, not a public activist, so I imagine my description > could be polished further :-) > > The truly tough methods to describe would be things like fpA-fpC where > the rules seem to be just pulled out of the air with no rhyme or reason, > unless you happen to know that it makes the method satisfy some > desirable criterion. Or Sinkhorn or Keener, which are incomprehensible > without a lot of linear algebra. > > -km > >

KM

Kristofer Munsterhjelm

Sat, May 7, 2022 9:41 AM

On 07.05.2022 07:20, Forest Simmons wrote:

That's a good template for all of us to imitate in our outreach to the
proletariat!

"Arise ye workers from your slumbers", eh? :-)

Let me see how well I can imitate it for my latest attempt in the
fpA-gpC vein:

Candidates are arranged into
one-on-one match-ups like runoffs where the candidate who would win a
runoff with only the two wins. If there is a candidate who wins every
runoff he's part of, he is elected.

Otherwise candidates get reward value for every matchup they win or tie,
but lose value for every matchup they lose.

The candidate with the greatest net reward value is elected.

Specifically, a candidate's prize/reward value is proportional to its
estimated formidability as an opponent in these matchups. You get your
opponent's prize value when you defeat or tie him in a matchup.
Otherwise, you pay out that value.

The formidability of a candidate is gauged as a function of its
respective first and last place showings on the ballots.

Yeah, it would have to be something like that. For fpA - sum fpC:

A candidate starts out being as strong as his first preference votes,
but he loses strength by being beaten by other candidates, according to
their first preference votes. The strongest candidate wins.

On an aside, your definition makes me think of an interesting recursive
primitive for Condorcet-compliant methods. Suppose X's score is f(X) and
let f(X) be some monotone nondecreasing function of f of all the
candidates X beat (or the strongest such candidate). Then there exist
very broad subsets of monotone nondecreasing functions so that the CW
always wins by f score (e.g. sum or max, possibly any p-norm for p>=1 as
long as f(X) >= 0 for all X). Similar broad proofs can probably be had
for the case where f(X) is some monotone nonincreasing function of f of
the candidates who beat X pairwise. However, cycles would require
finding equilibrium points, which can be pretty hard to explain.

-km

On 07.05.2022 07:20, Forest Simmons wrote: > That's a good template for all of us to imitate in our outreach to the > proletariat! "Arise ye workers from your slumbers", eh? :-) > Let me see how well I can imitate it for my latest attempt in the > fpA-gpC vein: > > Candidates are arranged into > one-on-one match-ups like runoffs where the candidate who would win a > runoff with only the two wins. If there is a candidate who wins every > runoff he's part of, he is elected. > > Otherwise candidates get reward value for every matchup they win or tie, > but lose value for every matchup they lose. > > The candidate with the greatest net reward value is elected. > > Specifically, a candidate's prize/reward value is proportional to its > estimated formidability as an opponent in these matchups. You get your > opponent's prize value when you defeat or tie him in a matchup. > Otherwise, you pay out that value. > > The formidability of a candidate is gauged as a function of its > respective first and last place showings on the ballots. Yeah, it would have to be something like that. For fpA - sum fpC: A candidate starts out being as strong as his first preference votes, but he loses strength by being beaten by other candidates, according to *their* first preference votes. The strongest candidate wins. On an aside, your definition makes me think of an interesting recursive primitive for Condorcet-compliant methods. Suppose X's score is f(X) and let f(X) be some monotone nondecreasing function of f of all the candidates X beat (or the strongest such candidate). Then there exist very broad subsets of monotone nondecreasing functions so that the CW always wins by f score (e.g. sum or max, possibly any p-norm for p>=1 as long as f(X) >= 0 for all X). Similar broad proofs can probably be had for the case where f(X) is some monotone nonincreasing function of f of the candidates who beat X pairwise. However, cycles would require finding equilibrium points, which can be pretty hard to explain. -km

RL

Richard Lung

Sat, May 7, 2022 4:26 PM

Kristofer,

Werner Heisenberg said that if in the end you cannot say what you have found, then all your finding is worthless.
Fortunately, voters only need to know how to do the vote. Those who expect the count also to be understandable by everyone - typically claimed by anti-reformers - talk as if elections were an exception to the division of labor.
("Complicated, that word of fear," as HG Wells described a refrain to STV.)
My system is an example. I doubt anyone understands FAB STV (I don't understand it, or even the much simpler hand count, because it hasn't been tested and modified in the light of experience.)
But all voters need to know is that: You have a preference vote equal to the number of candidates. The first preference counts as much to elect a candidate, as the last preference counts to exclude a candidate. A blank paper ( "white paper" as they call it in France, same as NOTA) is one vote towards a seat remaining vacant. Individual preferences left blank also contribute, in their degree, to a vacancy.

For example, 10 candidates contest 5 seats. The first five preferences count more or less to 5 seat elections. The last 5 preferences count less or more, to the exclusion of the other 5 candidates.

Note that the election counts and exclusion counts need not count against each other. An exclusion quota consolidates an election quota. In other words, a candidate is helped both by popularity and lack of unpopularity.

Regards,
Richard Lung.

On 7 May 2022, at 6:20 am, Forest Simmons forest.simmons21@gmail.com wrote:

That's a good template for all of us to imitate in our outreach to the proletariat!

Let me see how well I can imitate it for my latest attempt in the fpA-gpC vein:

Candidates are arranged into
one-on-one match-ups like runoffs where the candidate who would win a
runoff with only the two wins. If there is a candidate who wins every
runoff he's part of, he is elected.

Otherwise candidates get reward value for every matchup they win or tie, but lose value for every matchup they lose.

The candidate with the greatest net reward value is elected.

Specifically, a candidate's prize/reward value is proportional to its estimated formidability as an opponent in these matchups. You get your opponent's prize value when you defeat or tie him in a matchup. Otherwise, you pay out that value.

The formidability of a candidate is gauged as a function of its respective first and last place showings on the ballots.

El vie., 6 de may. de 2022 3:02 a. m., Kristofer Munsterhjelm km_elmet@t-online.de escribió: