Empathy List Archives

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Technical discussion of election methods

28 years of progress and a wakeup call

Closed Limelike Curves

Tue, May 21, 2024 7:49 PM

This list started in 1996. I was born 3 years later, in 1999.

Six years before I was born, and 3 years before this list was started,
Myerson and Weber proved that approval (and score, highest medians, or )
will elect the Condorcet winner. This is true as long as voters use a
strategy even a brain-dead turnip could work out: set your approval
threshold between the frontrunners.

This infuriates me. This should not be my problem. The problem of
electing Condorcet winners in spite of strategic voting was solved a full
generation ago. I should be waking up every election day to news that a
new state has adopted score/STAR/Bucklin/[insert your Condorcet variant
that manages to satisfy nonelection of turkeys here, assuming one exists. I
think maximal lotteries fit the bill].

A brief digression now to thank some of the people who have done their best
to fix this problem and thank them for their hard work. Most notably, Rob
Lanphier and all the people who have gone on to work for Equal Vote, the
Center for Election Science, etc. have done so, so much to popularize
better voting methods.

On the other hand, I'd like to offer a response I got from someone after I
wrote my simple description of Schulze.

Thank you for your recasting in Plain English, from a former technical
editor of a policy manual.

I really appreciate finally understanding the election techspeak about

beatpaths that's permeated this list for about 28 years.

Twenty-eight years! It took *twenty-eight years *for someone on this list
to clearly explain Schulze to the technical editor of a policy manual! No
wonder we've had our asses handed to us by FairVote. We refuse to give up
our pedantry at the altar of using normal words!

This list has had a massive impact on popular discussions of voting
systems, mostly through its influence on Wikipedia. Articles like IRV,
Schulze method, Arrow's theorem, etc. get hundreds of hits *per day, *and
are the main source for most people's information on electoral systems.
Before my edits over the past few months, my guess is almost every one of
them came away with the exact same impression I (a young teenager) had when
I first stumbled on these in 2014: "Huh? OK, I guess I'll support IRV then.
I heard CGPGrey say it solves the spoiler effect or something. I guess
every voting system is basically the same because of Gibbard's theorem and
Arrow's theorem, or something."

The effect of this communication strategy, which emphasizes minor
mathematical detail, technical language, and comparing systems based on
long lists of criteria rather than memorable scenarios or social utility
efficiency, has been to entrench IRV as the only alternative to FPP,
because nobody understands any other alternative.

The feedback I've gotten since starting to make these fixes to Wikipedia
has so far been mixed in this list, but unanimous in conversations with
everyday people. From Wiki editors and this email list, the response has
often involved nitpicking phrasing based on 12-dimensional mathematics,
philosophy, or a strict interpretation of Wikipedia guidelines. The
response from normal people, every time I link them to the newly-improved
version of the article, has been "Oh! I get it now, that finally makes
sense. Why didn't anyone explain it like that before?!"

Please:

Be polite and helpful.
Use smaller words. No LaTeX or single-letter variable names.
Avoid minor details like handling ties.
Emphasize what's important. Don't get sidetracked in discussing minor
problems like strategy. What matters is each method's Condorcet efficiency
and social utility efficiency, and whether it's better than IRV's.
Put material where people will read it. That means Wikipedia. If you
can't put it there, put it on Arxiv, then put it on Wikipedia. If you put
it on Arxiv first, it's not original research anymore. :)
Put the important material in the lede. Only about 3% of Wiki users read
past the lede.
Tell the truth. Don't lie or exaggerate or mislead about your favorite
method. Don't say stuff like "Condorcet methods only have strategy if
there's a cycle", because people will just google that and immediately
learn not to trust you.
Focus on what matters, and what we can all agree on: we need to beat the
everloving shit out of IRV. Even if you hate every other voting method
that's been proposed on this list, that doesn't matter. FairVote is the
biggest obstacle standing between us and meaningful election reform.

In 10 years or so, the knowledge will have fully percolated down into the
electorate (much like how FairVote's edits to the IRV article have become
gospel faith for every liberal commentator over the past 10 years).

If you disagree with everything I've said and hate my guts, please let me
know at my other email, which is robrichie@fairvote.org

This list started in 1996. I was born 3 years later, in 1999. Six years before I was born, and 3 years before this list was started, Myerson and Weber proved that approval (and score, highest medians, or ) will elect the Condorcet winner. This is true as long as voters use a strategy even a brain-dead turnip could work out: set your approval threshold between the frontrunners. This infuriates me. *This* *should not be my problem*. The problem of electing Condorcet winners in spite of strategic voting was solved *a full generation ago*. I should be waking up every election day to news that a new state has adopted score/STAR/Bucklin/[insert your Condorcet variant that manages to satisfy nonelection of turkeys here, assuming one exists. I think maximal lotteries fit the bill]. A brief digression now to thank some of the people who have done their best to fix this problem and thank them for their hard work. Most notably, Rob Lanphier and all the people who have gone on to work for Equal Vote, the Center for Election Science, etc. have done so, so much to popularize better voting methods. On the other hand, I'd like to offer a response I got from someone after I wrote my simple description of Schulze. > Thank you for your recasting in Plain English, from a former technical > editor of a policy manual. I really appreciate finally understanding the election techspeak about > beatpaths that's permeated this list for about 28 years. *Twenty-eight years!* It took *twenty-eight years *for someone on this list to clearly explain Schulze to the *technical editor of a policy manual!* No *wonder* we've had our asses handed to us by FairVote. We refuse to give up our pedantry at the altar of *using* *normal words!* This list has had a massive impact on popular discussions of voting systems, mostly through its influence on Wikipedia. Articles like IRV, Schulze method, Arrow's theorem, etc. get hundreds of hits *per day, *and are the main source for most people's information on electoral systems. Before my edits over the past few months, my guess is almost every one of them came away with the exact same impression I (a young teenager) had when I first stumbled on these in 2014: "Huh? OK, I guess I'll support IRV then. I heard CGPGrey say it solves the spoiler effect or something. I guess every voting system is basically the same because of Gibbard's theorem and Arrow's theorem, or something." The effect of this communication strategy, which emphasizes minor mathematical detail, technical language, and comparing systems based on long lists of criteria rather than memorable scenarios or social utility efficiency, has been to entrench IRV as the only alternative to FPP, because nobody understands any other alternative. The feedback I've gotten since starting to make these fixes to Wikipedia has so far been mixed in this list, but unanimous in conversations with everyday people. From Wiki editors and this email list, the response has often involved nitpicking phrasing based on 12-dimensional mathematics, philosophy, or a strict interpretation of Wikipedia guidelines. The response from normal people, every time I link them to the newly-improved version of the article, has been "Oh! I get it now, that finally makes sense. Why didn't anyone explain it like that before?!" Please: 1. Be polite and helpful. 2. Use smaller words. No LaTeX or single-letter variable names. 3. Avoid minor details like handling ties. 4. Emphasize what's important. Don't get sidetracked in discussing minor problems like strategy. What matters is each method's Condorcet efficiency and social utility efficiency, and whether it's better than IRV's. 5. Put material where people will read it. That means *Wikipedia.* If you can't put it there, put it on Arxiv, *then* put it on Wikipedia. If you put it on Arxiv first, it's not original research anymore. :) 6. Put the important material in the lede. Only about 3% of Wiki users read past the lede. 7. Tell the truth. Don't lie or exaggerate or mislead about your favorite method. Don't say stuff like "Condorcet methods only have strategy if there's a cycle", because people will just google that and immediately learn not to trust you. 8. Focus on what matters, and what we can all agree on: we need to beat the everloving shit out of IRV. Even if you hate every other voting method that's been proposed on this list, that doesn't matter. FairVote is the biggest obstacle standing between us and meaningful election reform. In 10 years or so, the knowledge will have fully percolated down into the electorate (much like how FairVote's edits to the IRV article have become gospel faith for every liberal commentator over the past 10 years). If you disagree with everything I've said and hate my guts, please let me know at my other email, which is robrichie@fairvote.org

robert bristow-johnson

Tue, May 21, 2024 8:30 PM

On 05/21/2024 3:49 PM EDT Closed Limelike Curves closed.limelike.curves@gmail.com wrote:

This list started in 1996. I was born 3 years later, in 1999.

Six years before I was born, and 3 years before this list was started, Myerson and Weber proved that approval (and score, highest medians, or ) will elect the Condorcet winner.

I'm sorry. This "proof" cannot be true. It is certainly possible not to elect the Condorcet winner using either Approval or Score. This "proof" can be successfully refuted with a counter example. I posted one a few days ago regarding STAR (but it also says the same about Score and wouldn't be hard to modify to show that for Approval). A single counter-example is sufficient to disprove that conclusion that Approval and Score will (always) elect the Condorcet winner.

This is true as long as voters use a strategy even a brain-dead turnip could work out: set your approval threshold between the frontrunners.

But what are frontrunners? How do you know who these candidates are under different ballot conditions? Do you mean FPTP frontrunners?

Lastly, I consider it disadvantageous to require any tactical thinking or to incentivize any strategic thinking from voters. Any more than what Arrow of Gibbard or Satterthwaite say we cannot get away from. This is why I am for strictly an ordinal ballot, where voters are not required to rank any candidate they don't want to rank, and where possible equal rankings are allowed (this is one reason I have sorta soured regarding BTR-IRV), and the Condorcet winner should always be elected whenever such candidate exists. I am still not committed about which Condorcet method, but, besides disincentivizing strategic or tactical voting, I am also concerned about the quality and conciseness of the legislative language to describe the method (that was the sole reason I had previously considered BTR-IRV).

r b-j . _ . _ . _ . _ rbj@audioimagination.com

"Imagination is more important than knowledge."

.
.
.

> On 05/21/2024 3:49 PM EDT Closed Limelike Curves <closed.limelike.curves@gmail.com> wrote: > > > This list started in 1996. I was born 3 years later, in 1999. > > Six years before I was born, and 3 years before this list was started, Myerson and Weber proved that approval (and score, highest medians, or ) will elect the Condorcet winner. I'm sorry. This "proof" cannot be true. It is certainly possible *not* to elect the Condorcet winner using either Approval or Score. This "proof" can be successfully refuted with a counter example. I posted one a few days ago regarding STAR (but it also says the same about Score and wouldn't be hard to modify to show that for Approval). A single counter-example is sufficient to disprove that conclusion that Approval and Score will (always) elect the Condorcet winner. > This is true as long as voters use a strategy even a brain-dead turnip could work out: set your approval threshold between the frontrunners. But what are frontrunners? How do you know who these candidates are under different ballot conditions? Do you mean FPTP frontrunners? Lastly, I consider it disadvantageous to require any tactical thinking or to incentivize any strategic thinking from voters. Any more than what Arrow of Gibbard or Satterthwaite say we cannot get away from. This is why I am for strictly an ordinal ballot, where voters are not required to rank any candidate they don't want to rank, and where possible equal rankings are allowed (this is one reason I have sorta soured regarding BTR-IRV), and the Condorcet winner should always be elected whenever such candidate exists. I am still not committed about which Condorcet method, but, besides disincentivizing strategic or tactical voting, I am also concerned about the quality and conciseness of the legislative language to describe the method (that was the sole reason I had previously considered BTR-IRV). -- r b-j . _ . _ . _ . _ rbj@audioimagination.com "Imagination is more important than knowledge." . . .

Closed Limelike Curves

Tue, May 21, 2024 8:38 PM

I'm sorry. This "proof" cannot be true. It is certainly possible not

to elect the Condorcet winner using either Approval or Score. This "proof"
can be successfully refuted with a counter example. I posted one a few
days ago regarding STAR (but it also says the same about Score and wouldn't
be hard to modify to show that for Approval). A single counter-example is
sufficient to disprove that conclusion that Approval and Score will
(always) elect the Condorcet winner.

Like I said, this holds true if voters are strategic. They pick an approval
threshold between the frontrunners (more strictly, set it at the expected
value of the election result).

This is the minimal amount of strategy possible: just say you like a
candidate if you think they’re above-average. I’m not aware of any system
that requires less strategizing to get the same result, except maybe
MDD//Score.

I don’t know if the result extends to STAR, but I suspect no, and that any
use of pairwise comparisons breaks this property. Monroe (2000) showed that
every well-known Condorcet method (including Minimax and all of its
variants, like Schulze and RP, as well as Nanson-Baldwin) will fail to
elect the Condorcet winner if voters are strategic.

On Tue, May 21, 2024 at 1:30 PM robert bristow-johnson <
rbj@audioimagination.com> wrote:

On 05/21/2024 3:49 PM EDT Closed Limelike Curves <

closed.limelike.curves@gmail.com> wrote:

This list started in 1996. I was born 3 years later, in 1999.

Six years before I was born, and 3 years before this list was started,

Myerson and Weber proved that approval (and score, highest medians, or )
will elect the Condorcet winner.

I'm sorry. This "proof" cannot be true. It is certainly possible not
to elect the Condorcet winner using either Approval or Score. This "proof"
can be successfully refuted with a counter example. I posted one a few
days ago regarding STAR (but it also says the same about Score and wouldn't
be hard to modify to show that for Approval). A single counter-example is
sufficient to disprove that conclusion that Approval and Score will
(always) elect the Condorcet winner.

This is true as long as voters use a strategy even a brain-dead turnip

could work out: set your approval threshold between the frontrunners.

But what are frontrunners? How do you know who these candidates are under
different ballot conditions? Do you mean FPTP frontrunners?

Lastly, I consider it disadvantageous to require any tactical thinking or
to incentivize any strategic thinking from voters. Any more than what
Arrow of Gibbard or Satterthwaite say we cannot get away from. This is why
I am for strictly an ordinal ballot, where voters are not required to rank
any candidate they don't want to rank, and where possible equal rankings
are allowed (this is one reason I have sorta soured regarding BTR-IRV), and
the Condorcet winner should always be elected whenever such candidate
exists. I am still not committed about which Condorcet method, but,
besides disincentivizing strategic or tactical voting, I am also concerned
about the quality and conciseness of the legislative language to describe
the method (that was the sole reason I had previously considered BTR-IRV).

r b-j . _ . _ . _ . _ rbj@audioimagination.com

"Imagination is more important than knowledge."

.
.
.

> I'm sorry. This "proof" cannot be true. It is certainly possible *not* to elect the Condorcet winner using either Approval or Score. This "proof" can be successfully refuted with a counter example. I posted one a few days ago regarding STAR (but it also says the same about Score and wouldn't be hard to modify to show that for Approval). A single counter-example is sufficient to disprove that conclusion that Approval and Score will (always) elect the Condorcet winner. Like I said, this holds true if voters are strategic. They pick an approval threshold between the frontrunners (more strictly, set it at the expected value of the election result). This is the minimal amount of strategy possible: just say you like a candidate if you think they’re above-average. I’m not aware of any system that requires less strategizing to get the same result, except *maybe* MDD//Score. I don’t know if the result extends to STAR, but I suspect no, and that any use of pairwise comparisons breaks this property. Monroe (2000) showed that every well-known Condorcet method (including Minimax and all of its variants, like Schulze and RP, as well as Nanson-Baldwin) will fail to elect the Condorcet winner if voters are strategic. On Tue, May 21, 2024 at 1:30 PM robert bristow-johnson < rbj@audioimagination.com> wrote: > > > > On 05/21/2024 3:49 PM EDT Closed Limelike Curves < > closed.limelike.curves@gmail.com> wrote: > > > > > > This list started in 1996. I was born 3 years later, in 1999. > > > > Six years before I was born, and 3 years before this list was started, > Myerson and Weber proved that approval (and score, highest medians, or ) > will elect the Condorcet winner. > > I'm sorry. This "proof" cannot be true. It is certainly possible *not* > to elect the Condorcet winner using either Approval or Score. This "proof" > can be successfully refuted with a counter example. I posted one a few > days ago regarding STAR (but it also says the same about Score and wouldn't > be hard to modify to show that for Approval). A single counter-example is > sufficient to disprove that conclusion that Approval and Score will > (always) elect the Condorcet winner. > > > This is true as long as voters use a strategy even a brain-dead turnip > could work out: set your approval threshold between the frontrunners. > > But what are frontrunners? How do you know who these candidates are under > different ballot conditions? Do you mean FPTP frontrunners? > > Lastly, I consider it disadvantageous to require any tactical thinking or > to incentivize any strategic thinking from voters. Any more than what > Arrow of Gibbard or Satterthwaite say we cannot get away from. This is why > I am for strictly an ordinal ballot, where voters are not required to rank > any candidate they don't want to rank, and where possible equal rankings > are allowed (this is one reason I have sorta soured regarding BTR-IRV), and > the Condorcet winner should always be elected whenever such candidate > exists. I am still not committed about which Condorcet method, but, > besides disincentivizing strategic or tactical voting, I am also concerned > about the quality and conciseness of the legislative language to describe > the method (that was the sole reason I had previously considered BTR-IRV). > > -- > > r b-j . _ . _ . _ . _ rbj@audioimagination.com > > "Imagination is more important than knowledge." > > . > . > . >

robert bristow-johnson

Tue, May 21, 2024 8:49 PM

On 05/21/2024 4:38 PM EDT Closed Limelike Curves closed.limelike.curves@gmail.com wrote:

Like I said, this holds true if voters are strategic. They pick an approval threshold between the frontrunners (more strictly, set it at the expected value of the election result).

This is the minimal amount of strategy possible: just say you like a candidate if you think they’re above-average. I’m not aware of any system that requires less strategizing to get the same result, except maybe MDD//Score.

I posted this here before, just last April.

L => Left candidate
C => Center candidate
R => Right candidate

100 voters:

34 Left supporters:
--- 23 ballots: L:5 C:1 R:0
--- 4 ballots: L:5 C:0 R:1
--- 7 ballots: L:5 C:0 R:0
29 Center supporters:
--- 15 ballots: L:1 C:5 R:0
--- 9 ballots: L:0 C:5 R:1
--- 5 ballots: L:0 C:5 R:0
37 Right supporters:
--- 17 ballots: L:0 C:1 R:5
--- 5 ballots: L:1 C:0 R:5
--- 15 ballots: L:0 C:0 R:5

Now, in the STAR final runoff, the Center candidate will defeat either candidate on the Left or Right, head-to-head.

Score totals:

Left = 34x5 + 15 + 5 = 190
Center = 29x5 + 23 + 17 = 185
Right = 37x5 + 9 + 4 = 198

So who wins?
With Score or FPTP, Right wins.
With STAR or IRV, Left wins.
With Condorcet, Center wins.

Now, if you put the approval threshold somewhere between 1 and 5, then Approval comes out the same as FPTP.

r b-j . _ . _ . _ . _ rbj@audioimagination.com

"Imagination is more important than knowledge."

.
.
.

> On 05/21/2024 4:38 PM EDT Closed Limelike Curves <closed.limelike.curves@gmail.com> wrote: > > > > I'm sorry. This "proof" cannot be true. It is certainly possible *not* to elect the Condorcet winner using either Approval or Score. This "proof" can be successfully refuted with a counter example. I posted one a few days ago regarding STAR (but it also says the same about Score and wouldn't be hard to modify to show that for Approval). A single counter-example is sufficient to disprove that conclusion that Approval and Score will (always) elect the Condorcet winner. > > Like I said, this holds true if voters are strategic. They pick an approval threshold between the frontrunners (more strictly, set it at the expected value of the election result). > > This is the minimal amount of strategy possible: just say you like a candidate if you think they’re above-average. I’m not aware of any system that requires less strategizing to get the same result, except *maybe* MDD//Score. I posted this here before, just last April. L => Left candidate C => Center candidate R => Right candidate 100 voters: - 34 Left supporters: --- 23 ballots: L:5 C:1 R:0 --- 4 ballots: L:5 C:0 R:1 --- 7 ballots: L:5 C:0 R:0 - 29 Center supporters: --- 15 ballots: L:1 C:5 R:0 --- 9 ballots: L:0 C:5 R:1 --- 5 ballots: L:0 C:5 R:0 - 37 Right supporters: --- 17 ballots: L:0 C:1 R:5 --- 5 ballots: L:1 C:0 R:5 --- 15 ballots: L:0 C:0 R:5 Now, in the STAR final runoff, the Center candidate will defeat either candidate on the Left or Right, head-to-head. Score totals: Left = 34x5 + 15 + 5 = 190 Center = 29x5 + 23 + 17 = 185 Right = 37x5 + 9 + 4 = 198 So who wins? With Score or FPTP, Right wins. With STAR or IRV, Left wins. With Condorcet, Center wins. Now, if you put the approval threshold somewhere between 1 and 5, then Approval comes out the same as FPTP. -- r b-j . _ . _ . _ . _ rbj@audioimagination.com "Imagination is more important than knowledge." . . .

Closed Limelike Curves

Tue, May 21, 2024 8:51 PM

These are not strategically-viable ballots under Score (they don’t min-max).

On Tue, May 21, 2024 at 1:49 PM robert bristow-johnson <
rbj@audioimagination.com> wrote:

On 05/21/2024 4:38 PM EDT Closed Limelike Curves <

closed.limelike.curves@gmail.com> wrote:

I'm sorry. This "proof" cannot be true. It is certainly possible not

to elect the Condorcet winner using either Approval or Score. This "proof"
can be successfully refuted with a counter example. I posted one a few days
ago regarding STAR (but it also says the same about Score and wouldn't be
hard to modify to show that for Approval). A single counter-example is
sufficient to disprove that conclusion that Approval and Score will
(always) elect the Condorcet winner.

Like I said, this holds true if voters are strategic. They pick an

approval threshold between the frontrunners (more strictly, set it at the
expected value of the election result).

This is the minimal amount of strategy possible: just say you like a

candidate if you think they’re above-average. I’m not aware of any system
that requires less strategizing to get the same result, except maybe
MDD//Score.

I posted this here before, just last April.

L => Left candidate
C => Center candidate
R => Right candidate

100 voters:

- 34 Left supporters:
--- 23 ballots: L:5 C:1 R:0
---  4 ballots: L:5 C:0 R:1
---  7 ballots: L:5 C:0 R:0

- 29 Center supporters:
--- 15 ballots: L:1 C:5 R:0
---  9 ballots: L:0 C:5 R:1
---  5 ballots: L:0 C:5 R:0

- 37 Right supporters:
--- 17 ballots: L:0 C:1 R:5
---  5 ballots: L:1 C:0 R:5
--- 15 ballots: L:0 C:0 R:5

Now, in the STAR final runoff, the Center candidate will defeat either
candidate on the Left or Right, head-to-head.

Score totals:

Left = 34x5 + 15 + 5 = 190
Center = 29x5 + 23 + 17 = 185
Right = 37x5 + 9 + 4 = 198

So who wins?
With Score or FPTP, Right wins.
With STAR or IRV, Left wins.
With Condorcet, Center wins.

Now, if you put the approval threshold somewhere between 1 and 5, then
Approval comes out the same as FPTP.

r b-j . _ . _ . _ . _ rbj@audioimagination.com

"Imagination is more important than knowledge."

.
.
.

Election-Methods mailing list - see https://electorama.com/em for list
info

These are not strategically-viable ballots under Score (they don’t min-max). On Tue, May 21, 2024 at 1:49 PM robert bristow-johnson < rbj@audioimagination.com> wrote: > > > > On 05/21/2024 4:38 PM EDT Closed Limelike Curves < > closed.limelike.curves@gmail.com> wrote: > > > > > > > I'm sorry. This "proof" cannot be true. It is certainly possible *not* > to elect the Condorcet winner using either Approval or Score. This "proof" > can be successfully refuted with a counter example. I posted one a few days > ago regarding STAR (but it also says the same about Score and wouldn't be > hard to modify to show that for Approval). A single counter-example is > sufficient to disprove that conclusion that Approval and Score will > (always) elect the Condorcet winner. > > > > Like I said, this holds true if voters are strategic. They pick an > approval threshold between the frontrunners (more strictly, set it at the > expected value of the election result). > > > > This is the minimal amount of strategy possible: just say you like a > candidate if you think they’re above-average. I’m not aware of any system > that requires less strategizing to get the same result, except *maybe* > MDD//Score. > > I posted this here before, just last April. > > > L => Left candidate > C => Center candidate > R => Right candidate > > 100 voters: > > - 34 Left supporters: > --- 23 ballots: L:5 C:1 R:0 > --- 4 ballots: L:5 C:0 R:1 > --- 7 ballots: L:5 C:0 R:0 > > - 29 Center supporters: > --- 15 ballots: L:1 C:5 R:0 > --- 9 ballots: L:0 C:5 R:1 > --- 5 ballots: L:0 C:5 R:0 > > - 37 Right supporters: > --- 17 ballots: L:0 C:1 R:5 > --- 5 ballots: L:1 C:0 R:5 > --- 15 ballots: L:0 C:0 R:5 > > Now, in the STAR final runoff, the Center candidate will defeat either > candidate on the Left or Right, head-to-head. > > Score totals: > > Left = 34x5 + 15 + 5 = 190 > Center = 29x5 + 23 + 17 = 185 > Right = 37x5 + 9 + 4 = 198 > > So who wins? > With Score or FPTP, Right wins. > With STAR or IRV, Left wins. > With Condorcet, Center wins. > > Now, if you put the approval threshold somewhere between 1 and 5, then > Approval comes out the same as FPTP. > > -- > > r b-j . _ . _ . _ . _ rbj@audioimagination.com > > "Imagination is more important than knowledge." > > . > . > . > ---- > Election-Methods mailing list - see https://electorama.com/em for list > info >

Closed Limelike Curves

Tue, May 21, 2024 8:57 PM

if you put the approval threshold between 1 and 5

Yes, so voters would not pick that approval threshold in strategic
equilibrium. Myerson and Weber calculate the approval threshold strategic
voters will use, and find it elects the Condorcet winner.

On Tue, May 21, 2024 at 1:51 PM Closed Limelike Curves <
closed.limelike.curves@gmail.com> wrote:

These are not strategically-viable ballots under Score (they don’t
min-max).

On Tue, May 21, 2024 at 1:49 PM robert bristow-johnson <
rbj@audioimagination.com> wrote:

On 05/21/2024 4:38 PM EDT Closed Limelike Curves <

closed.limelike.curves@gmail.com> wrote:

I'm sorry. This "proof" cannot be true. It is certainly possible

not to elect the Condorcet winner using either Approval or Score. This
"proof" can be successfully refuted with a counter example. I posted one a
few days ago regarding STAR (but it also says the same about Score and
wouldn't be hard to modify to show that for Approval). A single
counter-example is sufficient to disprove that conclusion that Approval and
Score will (always) elect the Condorcet winner.

Like I said, this holds true if voters are strategic. They pick an

approval threshold between the frontrunners (more strictly, set it at the
expected value of the election result).

This is the minimal amount of strategy possible: just say you like a

candidate if you think they’re above-average. I’m not aware of any system
that requires less strategizing to get the same result, except maybe
MDD//Score.

I posted this here before, just last April.

L => Left candidate
C => Center candidate
R => Right candidate

100 voters:

- 34 Left supporters:
--- 23 ballots: L:5 C:1 R:0
---  4 ballots: L:5 C:0 R:1
---  7 ballots: L:5 C:0 R:0

- 29 Center supporters:
--- 15 ballots: L:1 C:5 R:0
---  9 ballots: L:0 C:5 R:1
---  5 ballots: L:0 C:5 R:0

- 37 Right supporters:
--- 17 ballots: L:0 C:1 R:5
---  5 ballots: L:1 C:0 R:5
--- 15 ballots: L:0 C:0 R:5

Now, in the STAR final runoff, the Center candidate will defeat either
candidate on the Left or Right, head-to-head.

Score totals:

Left = 34x5 + 15 + 5 = 190
Center = 29x5 + 23 + 17 = 185
Right = 37x5 + 9 + 4 = 198

So who wins?
With Score or FPTP, Right wins.
With STAR or IRV, Left wins.
With Condorcet, Center wins.

Now, if you put the approval threshold somewhere between 1 and 5, then
Approval comes out the same as FPTP.

r b-j . _ . _ . _ . _ rbj@audioimagination.com

"Imagination is more important than knowledge."

.
.
.

Election-Methods mailing list - see https://electorama.com/em for list
info

>if you put the approval threshold between 1 and 5 Yes, so voters would not pick that approval threshold in strategic equilibrium. Myerson and Weber calculate the approval threshold strategic voters will use, and find it elects the Condorcet winner. On Tue, May 21, 2024 at 1:51 PM Closed Limelike Curves < closed.limelike.curves@gmail.com> wrote: > These are not strategically-viable ballots under Score (they don’t > min-max). > > On Tue, May 21, 2024 at 1:49 PM robert bristow-johnson < > rbj@audioimagination.com> wrote: > >> >> >> > On 05/21/2024 4:38 PM EDT Closed Limelike Curves < >> closed.limelike.curves@gmail.com> wrote: >> > >> > >> > > I'm sorry. This "proof" cannot be true. It is certainly possible >> *not* to elect the Condorcet winner using either Approval or Score. This >> "proof" can be successfully refuted with a counter example. I posted one a >> few days ago regarding STAR (but it also says the same about Score and >> wouldn't be hard to modify to show that for Approval). A single >> counter-example is sufficient to disprove that conclusion that Approval and >> Score will (always) elect the Condorcet winner. >> > >> > Like I said, this holds true if voters are strategic. They pick an >> approval threshold between the frontrunners (more strictly, set it at the >> expected value of the election result). >> > >> > This is the minimal amount of strategy possible: just say you like a >> candidate if you think they’re above-average. I’m not aware of any system >> that requires less strategizing to get the same result, except *maybe* >> MDD//Score. >> >> I posted this here before, just last April. >> >> >> L => Left candidate >> C => Center candidate >> R => Right candidate >> >> 100 voters: >> >> - 34 Left supporters: >> --- 23 ballots: L:5 C:1 R:0 >> --- 4 ballots: L:5 C:0 R:1 >> --- 7 ballots: L:5 C:0 R:0 >> >> - 29 Center supporters: >> --- 15 ballots: L:1 C:5 R:0 >> --- 9 ballots: L:0 C:5 R:1 >> --- 5 ballots: L:0 C:5 R:0 >> >> - 37 Right supporters: >> --- 17 ballots: L:0 C:1 R:5 >> --- 5 ballots: L:1 C:0 R:5 >> --- 15 ballots: L:0 C:0 R:5 >> >> Now, in the STAR final runoff, the Center candidate will defeat either >> candidate on the Left or Right, head-to-head. >> >> Score totals: >> >> Left = 34x5 + 15 + 5 = 190 >> Center = 29x5 + 23 + 17 = 185 >> Right = 37x5 + 9 + 4 = 198 >> >> So who wins? >> With Score or FPTP, Right wins. >> With STAR or IRV, Left wins. >> With Condorcet, Center wins. >> >> Now, if you put the approval threshold somewhere between 1 and 5, then >> Approval comes out the same as FPTP. >> >> -- >> >> r b-j . _ . _ . _ . _ rbj@audioimagination.com >> >> "Imagination is more important than knowledge." >> >> . >> . >> . >> ---- >> Election-Methods mailing list - see https://electorama.com/em for list >> info >> >

Michael Ossipoff

Tue, May 21, 2024 9:00 PM

What Meyerson & Weber demonstrated was that Approval’s Meyerson-Weber
equilibrium is at the voter-median. i.e. Approval homes in on where the CW
is.

But, additionally, it seems to me that Approval has chosen the CW on every
EM poll.

Other than wv Condorcet, Condorcet’s won’t always elect the sincere CW,
because of strategic-cycles.

My & W also demonstrated that Plurality can keep on electing any pair of
parties forever at MW-equilibrium.

…which of course is what it’s doing now. (with a bit of help from
mass-media promotion, & evidently at least occasional count-fraud.

wv Condorcet will, because of how well it deters offensive-strategy.

On Tue, May 21, 2024 at 13:30 robert bristow-johnson <
rbj@audioimagination.com> wrote: