On Mon, Oct 30, 2023, 6:21 PM C.Benham cbenham@adam.com.au wrote:

 Why do we support the Condorcet criterion?  For me there are three
 reasons:

 (1) Failure to elect a voted CW can give the voters who voted the
 CW over the actual winner
 a potentially very strong, difficult (if not impossible ) to
 answer complaint.

 And those voters could be more than half the total.

 (2) Always electing a voted CW is (among methods that fail
 Favorite Betrayal) is the best way to minimise
 Compromise incentive.

 (3) Limited to the information we can glean for pure ranked
 ballots (especially if we decide to only refer
 to the pairwise matrix), the voted CW is the most likely utility
 maximiser.

 If there is no voted CW , then the winner should come from the
 Smith set.  Condorcet is just the logical
 consequence of Smith and Clone Independence (specifically
 Clone-Winner).

 Some methods are able to meet Condorcet but not Smith, but
 hopefully they get something in return.
 (For example I think Min Max Margins  gets Mono-add-Top and maybe
 something else).

 So coming to the question of which individual member of the Smith
 set should we elect, I don't see that a
 supposed, guessed-at "sincere CW" has an especially strong claim,
 certainly nothing compared to an actual
 voted CW.

 Suppose sincere looks like:

 49 A>>>C>B
 48 B>>>C>A
 03 C>A>>>B

My favorite burial proof  method is to elect the nemesis of the
nemesis of the (repeated) Submidway Approval Elimination winner.

Max Approval is 52
Min Approval is 3
Midway is 27.5

So we eliminate C.

Updating approvals we have 52 for A and 48 for B. Midway is 50. B is
the only Sub Midway candidate so A is the SubMidway Approval winner.

The nemesis of A is C, and C has no nemesis because it not pairbeaten.
We respect the Condorcet Criterion and elect C, a very weak CW.

There is no way out of it if we want a Condorcet Criterion Compliant
method.

 Suppose that all voters get about the same utility from electing
 their favourites.  In that case A is the big utility
 maximiser.

 Now suppose that this is say the first post-FPP election, and the
 voters are all exhorted to express their full
 rankings, no matter how weak or uncertain some of their
 preferences may be, because we don't want anything
 that looks like the (shudder) "minority rule" we had under FPP.

This reminds me of the practice omanipulative judges in the US warning
jurors to ignore their sacred right of "Jury Nullification" (inherited
from English Common Law).

Those lying (by intimidation) judges are a disgrace to their office
... and should be stripped of their holy robes ...  imho.

 So they vote:

 49 A>C
 48 B>C
 03 C>A

 C is the voted CW. For some pro-Condorcet zealots, this is ideal.
 No sincere preferences were reversed or
 "concealed", resulting in the election of the "sincere CW".

 (In passing I note that in most places if the non-Condorcet method
 IRV/RCV were used, A would be uncontroversially
 elected probably without anyone even noticing that C is the CW.)

 Backing up a bit, suppose that instead of the voters being
 exhorted to fully rank no-matter-what, they are given the
 message "this election is for a serious powerful office, so we
 don't want anything like GIGO ("garbage in, garbage out")
 so if some of your preferences are weak or uncertain it is quite
 ok to keep them to yourself via truncation or equal-ranking."

That warning should be mandatory ... as should an honest effort to
"fully inform" a jury of their most sacred rights predatimg even the
Magna Carta.

 So they vote:

 49 A
 48 B
 03 C>A

 Now the voted CW is A.     Should anyone be seriously concerned
 that, due to so many voters truncating, that some other
 candidate might actually be the "sincere CW"?

Your example shows the wisdom of electing the ballot CW when there is one.

In fact, all of our burial resistant methods elect the voted CW when
one exists. But when one does not exist we suspiciously suspect that
its absence was most likely  caused by subversion of a CW, since that
is by far the easiest way to create a beat cycle ... whether
innocently or with "malice aforethought."

 For me, if voters have the freedom to fully rank but for whatever
 reason choose to truncate (and/or equal-rank, assuming that
 is allowed) a lot of that is fine and the voting method should
 prefer not to know about weak and uncertain preferences.

 The type of insincere voting that most concerns me is that which
 produces outrageous failure of Later-no-Help, achieving by
 order-reversal
 Burial what could not have been done by simple truncation.

 46 A
 44 B>C (sincere is B or B>A)
 10 C

Let's see what our Sub Midway Approval Elimination burial resistant
method does here:

The respective max and min implicit approval scores are 54 for C and
44 for B. So Midway is 49. Both A and B have Sub Midway Approval
leaving C as the candidate whose nemesis's nemesis we should elect.

C's nemesis is B, and B's nemesis is A.

So A is the winner of our burial resistant method.

How does this work?

Well, Nanson is very good at fingering the Burial Faction Favorite,
but Poor man's Nanson aka SubMidApproval Elimination is even better at
electing the BFF than ordinary Nanson or RP wv, although they are both
pretty good at it as this example shows.

Once you have the likely BFF you can follow the cycle forward one or
backward two candidates to the "bus" under which the buried candidate
was buried.

[Electing this "bus" is what makes the method backfire on the burying
faction ... so electing the strongest bus (their could be a clone set
of them) is the proper aim of a good burial proof method designer ...
to completely deter potential subverters from even flirting with the
idea.]

Like I said you can go in either direction around the cycle to get to
a "bus" from the BFF candidate .... but it's better psychologically to
elect the syrongest wv defeater of the strongest wv defeater of the
Nanson winner .... as opposed to saying "Elect the candidate with the
most losing votes against the Nanson winner" .. they are almost always
the same candidate even when Smith has more than three members.

Like I say, SubMidAolroval Elimination is more reliable than even
ordinary Nanson or RP wv at finding the BFF candidate.  But for the
curjous, you can always do a sincere runoff between the likely
strongest Bus (the nemesis of the nemesis of the likely BFF), and the
Smith candidate with the fewest losing votes against it (i.e.against
the bus) the same as the weakest Smith  weakest Smith candidate to
defeat the BFF.

[It is easy to show that a subverted CW always defeats the BFF, which
beats the bus that beat the buried candidate that precipitated the
insincere cycle resulting from the burial.]

In this example the sincere runoff (were that option to be taken)
would be between the Bus A and the Smith candidate B with the fewest
losing votes to it A.

For the sincere winner of this runoff we have to go clear back to the
original scenario. And it turns out that A is the sincere winner of
the runoff, because C, the sincere CW was acting more like a BFF ...
so not a finalist in the runoff!

 Electing B here is completely unacceptable.

Right, and now we have a method designed to automatically avoid that
kind of mistake.

 Regardless of whether or not the B>C voters are sincere, there
 isn't any case that B has a stronger
 claim than A.

 I don't like (but it can sometimes be justified) a larger faction
 being stung by a successful  truncation Defection strategy of a
 smaller one, but apart
 from that I consider a lot of truncation to be normal, natural and
 mostly desirable.

 More later.

 Chris Benham

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

On Mon, Oct 30, 2023, 6:21 PM C.Benham cbenham@adam.com.au wrote:

 Why do we support the Condorcet criterion?  For me there are three
 reasons:

 (1) Failure to elect a voted CW can give the voters who voted the
 CW over the actual winner
 a potentially very strong, difficult (if not impossible ) to
 answer complaint.

 And those voters could be more than half the total.

 (2) Always electing a voted CW is (among methods that fail
 Favorite Betrayal) is the best way to minimise
 Compromise incentive.

 (3) Limited to the information we can glean for pure ranked
 ballots (especially if we decide to only refer
 to the pairwise matrix), the voted CW is the most likely utility
 maximiser.

 If there is no voted CW , then the winner should come from the
 Smith set.  Condorcet is just the logical
 consequence of Smith and Clone Independence (specifically
 Clone-Winner).

 Some methods are able to meet Condorcet but not Smith, but
 hopefully they get something in return.
 (For example I think Min Max Margins  gets Mono-add-Top and maybe
 something else).

 So coming to the question of which individual member of the Smith
 set should we elect, I don't see that a
 supposed, guessed-at "sincere CW" has an especially strong claim,
 certainly nothing compared to an actual
 voted CW.

 Suppose sincere looks like:

 49 A>>>C>B
 48 B>>>C>A
 03 C>A>>>B

My favorite burial proof  method is to elect the nemesis of the
nemesis of the (repeated) Submidway Approval Elimination winner.

Max Approval is 52
Min Approval is 3
Midway is 27.5

So we eliminate C.

Updating approvals we have 52 for A and 48 for B. Midway is 50. B is
the only Sub Midway candidate so A is the SubMidway Approval winner.

The nemesis of A is C, and C has no nemesis because it not pairbeaten.
We respect the Condorcet Criterion and elect C, a very weak CW.

There is no way out of it if we want a Condorcet Criterion Compliant
method.

 Suppose that all voters get about the same utility from electing
 their favourites.  In that case A is the big utility
 maximiser.

 Now suppose that this is say the first post-FPP election, and the
 voters are all exhorted to express their full
 rankings, no matter how weak or uncertain some of their
 preferences may be, because we don't want anything
 that looks like the (shudder) "minority rule" we had under FPP.

This reminds me of the practice omanipulative judges in the US warning
jurors to ignore their sacred right of "Jury Nullification" (inherited
from English Common Law).

Those lying (by intimidation) judges are a disgrace to their office
... and should be stripped of their holy robes ...  imho.

 So they vote:

 49 A>C
 48 B>C
 03 C>A

 C is the voted CW. For some pro-Condorcet zealots, this is ideal.
 No sincere preferences were reversed or
 "concealed", resulting in the election of the "sincere CW".

 (In passing I note that in most places if the non-Condorcet method
 IRV/RCV were used, A would be uncontroversially
 elected probably without anyone even noticing that C is the CW.)

 Backing up a bit, suppose that instead of the voters being
 exhorted to fully rank no-matter-what, they are given the
 message "this election is for a serious powerful office, so we
 don't want anything like GIGO ("garbage in, garbage out")
 so if some of your preferences are weak or uncertain it is quite
 ok to keep them to yourself via truncation or equal-ranking."

That warning should be mandatory ... as should an honest effort to
"fully inform" a jury of their most sacred rights predatimg even the
Magna Carta.

 So they vote:

 49 A
 48 B
 03 C>A

 Now the voted CW is A.     Should anyone be seriously concerned
 that, due to so many voters truncating, that some other
 candidate might actually be the "sincere CW"?

Your example shows the wisdom of electing the ballot CW when there is one.

In fact, all of our burial resistant methods elect the voted CW when
one exists. But when one does not exist we suspiciously suspect that
its absence was most likely  caused by subversion of a CW, since that
is by far the easiest way to create a beat cycle ... whether
innocently or with "malice aforethought."

 For me, if voters have the freedom to fully rank but for whatever
 reason choose to truncate (and/or equal-rank, assuming that
 is allowed) a lot of that is fine and the voting method should
 prefer not to know about weak and uncertain preferences.

 The type of insincere voting that most concerns me is that which
 produces outrageous failure of Later-no-Help, achieving by
 order-reversal
 Burial what could not have been done by simple truncation.

 46 A
 44 B>C (sincere is B or B>A)
 10 C

Let's see what our Sub Midway Approval Elimination burial resistant
method does here:

The respective max and min implicit approval scores are 54 for C and
44 for B. So Midway is 49. Both A and B have Sub Midway Approval
leaving C as the candidate whose nemesis's nemesis we should elect.

C's nemesis is B, and B's nemesis is A.

So A is the winner of our burial resistant method.

How does this work?

Well, Nanson is very good at fingering the Burial Faction Favorite,
but Poor man's Nanson aka SubMidApproval Elimination is even better at
electing the BFF than ordinary Nanson or RP wv, although they are both
pretty good at it as this example shows.

Once you have the likely BFF you can follow the cycle forward one or
backward two candidates to the "bus" under which the buried candidate
was buried.

[Electing this "bus" is what makes the method backfire on the burying
faction ... so electing the strongest bus (their could be a clone set
of them) is the proper aim of a good burial proof method designer ...
to completely deter potential subverters from even flirting with the
idea.]

Like I said you can go in either direction around the cycle to get to
a "bus" from the BFF candidate .... but it's better psychologically to
elect the syrongest wv defeater of the strongest wv defeater of the
Nanson winner .... as opposed to saying "Elect the candidate with the
most losing votes against the Nanson winner" .. they are almost always
the same candidate even when Smith has more than three members.

Like I say, SubMidAolroval Elimination is more reliable than even
ordinary Nanson or RP wv at finding the BFF candidate.  But for the
curjous, you can always do a sincere runoff between the likely
strongest Bus (the nemesis of the nemesis of the likely BFF), and the
Smith candidate with the fewest losing votes against it (i.e.against
the bus) the same as the weakest Smith  weakest Smith candidate to
defeat the BFF.

[It is easy to show that a subverted CW always defeats the BFF, which
beats the bus that beat the buried candidate that precipitated the
insincere cycle resulting from the burial.]

In this example the sincere runoff (were that option to be taken)
would be between the Bus A and the Smith candidate B with the fewest
losing votes to it A.

For the sincere winner of this runoff we have to go clear back to the
original scenario. And it turns out that A is the sincere winner of
the runoff, because C, the sincere CW was acting more like a BFF ...
so not a finalist in the runoff!

 Electing B here is completely unacceptable.

Right, and now we have a method designed to automatically avoid that
kind of mistake.

 Regardless of whether or not the B>C voters are sincere, there
 isn't any case that B has a stronger
 claim than A.

 I don't like (but it can sometimes be justified) a larger faction
 being stung by a successful  truncation Defection strategy of a
 smaller one, but apart
 from that I consider a lot of truncation to be normal, natural and
 mostly desirable.

 More later.

 Chris Benham

I strongly agree with everything you said in this message ... including
the importance of judicious use of truncations ... especially when approval
cutoffs are not allowed.

And most of the time no sincerity check is needed ... best policy is to
elect the Smith candidate  most likely to be the "bus" under whom the
buriers threw the buried candidate to cause the cycle .... assuming that
the most common cause of cycles is insincere order reversals.

That's a controversial assumption, but I now believe that these insincere
order reversals are much more common than inconsistent sincere preferences
as a cause of these ballot cycles.

Over the years I have contrived my share or scenarios that result in
sincere Paper Rock Scissors cycles ...  Paper sincerely covers Rock which
sincerely smashes Scissors which cuts Paper ... and perfectly plausible
issue space examples.

But the insincere burials are easier to engineer ... even by accident ...
just innocently pushing your second choice to the bottom of your ballot to
give your favorite an edge ... perhaps assuming that as many people do that
the same Borda Count used in Sports competitions had something to do with
the tally of Condorcet methods like ... Black, Baldwin, and Nanson.

Sincere pairwise beat cycles are not impossible .... but I believe that
they are relatively much less likely .... based on the difficultly of them
arising naturally as opposed to innocent opportunistic order reversals.

It turns out that Condorcet wv is almost as easy to fool as Norda based
Nanson ... two methods that almost always elect the Burier faction
candidate as in your example below.

We have devised methods that make burial backfire on the burial faction.

That's good enough for me and you, but some people need more evidence ...
and education ....including influential people like Foley and Maskin, who
are proposing burial prone Baldwin in place of burial resistant  IRV.

I'm simply proposing a way of distinguishing statistically between the
relative prevalence of sincere and imsincere pairbeaten cycles.

Here's one test:

As often as possible when an RP Condorcet rules election has no ballot CW
...

Let W be the RP winner. And let X be the Smith candidate with the most
losing votes against W.  Finally, let Y be the Smith candidate with the
fewest losing votes against X.

Suppose the voters have agreed to a two stage runoff for Scientific purpose

The first stage of the runoff is to decidenif there will be a second stage.

If not W retainsbthe win .... and that's that. Otherwise, the final choice
is between X and Y.

If the ballots were sincere, then since they say X beats Y, the voters
would expect X to win the secomd stage if it were held ... So if the ballot
votes were sincere they would prefer not to have the second stage ... so W
would retain her wim.

But if X or Y were sincerely preferred over the other two participants in
this new tangled runoffbthen the moderately well informed voters will be
aware of that .... and the supporters of this "local CW" will willingly
support having a second stage knowing that they can win it ... and thereby
winvthe election.

So in the long run if more of these RP winners are retained than not ..the
null hypothesis of sincere cycle preponderance will be supported.

fws

On Mon, Oct 30, 2023, 6:21 PM C.Benham cbenham@adam.com.au wrote:

Forest & Chris—

…

With wv Condorcet, defense against burial, as  you said, requires
defensive truncation:

…

If your candidate might be CW, & you don’t want burial to take the win
from hir & give it to someone you don’t approve, then you & others who
agree with you should refuse to rank anyone you don’t approve.

…

But it’s best to not make a strategic demand on voters. Maybe I
defensively truncate but others in my faction don’t. So, because I regard
our current elections as completely dichotomous, I’d rank all of the
Acceptables together in 1st place, & refuse to rank anyone else.  …so
that I’m not helping anyone’s burial of one of my Acceptables under another
of my Acceptables.

…

So I’d be voting Approval-like.  But it would be much better to avoid
depending on others to defensively-truncate.

…

Hence the desirability of autodeterrent methods.

…

I like Forest’s improvement on CTE by making it into SP with takedown,
where the SP is agenda-ordered by Borda or implicit Approval.

…

For one thing, SP, when there are lots of candidates, is autodeterrent
already, & moreso with takedown. it seems to me. SP with (primary &
secondary) takedown could be called SPT, for SP with Takedown.

…

SP & SPT both seem autodeterrent when there are lots of candidates.  …especially
SPT, because there then are likely more than 1 Bus, which greatly decreases
the likelihood of electing anyone other than a Bus.  …& even moreso when
there are still more buses, as is likely in burial with lots of candidates.

…

But when there are only 3 candidates, SP & SPT, or any autodeterrent
method, depends on predicting which of the 3 candidates is the Bus (whom
it’s desired to elect).

…

That’s the core of the problem, it seems to me.

…

Say there are 3 candidates, & all of one candidate’s preferrers  strategically
bury the CW.

…

What can be said about the pairwise defeats & victories, the wins & loses,
of CW, BF & Bus?

…

BF is in the unique position of having only natural defeats & victories.

…

BF has 1 natural victory & 1 natural defeat.

…

CW has two natural defeats & 1 strategic lowering.

…

Bus has two natural defeats & 1 strategic raising.

…

Do 2 natural defeats or victories affect someone’s Borda or implicit
Approval more, or less, than 1strategic raising or lowering?

…

The natural defeats & victories result from a majority of the electorate
ranking someone low or high.  A strategic lowering or raising results
from just one faction strategically raising or lowering someone.

…

Don’t the two natural victorys or defeats, then ,sound stronger than the
one strategtic lowering or raising?

…

…& so, doesn’t that suggest that implicit-Approval & Borda would be
expected to be in the following order?  :

…

CW>BF>Bus

…

I wanted to check that out, for implicit-Approval & for Borda.

…

I started with implicit-Approval.

…

There are 6 ways that 3 candidates can be ordered. We can assume that all
of the BF-preferrers rank BF>Bus>CW, since the ones who prefer CW to Bus
will bury.

…

So that’s 5 kinds of rankings. Write the rankings in a row, & label them
at the top from A to E.

…

Write the inequality, relating the numbers of voters for A thru E, that
must be satisfied in order for Bus to pairwise-beat CW.

…

Write the inequalities that must be satisfied in order for the implicit
approvals to be in the order:

…

CW>BF>Bus.

…

Check for whether any of those inequalities, together, imply a
contradiction.

…

Unless I made an error, they imply several contradictions.

…

Oh well.  Hopefully I’ll have better luck with Borda.

On Fri, Nov 3, 2023 at 2:50 AM Forest Simmons forest.simmons21@gmail.com
wrote:

Forest,

Douglas Woodall in a 1996 article demonstrated that Condorcet is
incompatible with Later-no-Help.

By simple logic we know that any method that fails Later-no-Help must be
vulnerable to Burial strategy.

Therefore your quest to invent a completely burial-proof Condorcet method
is futile.

https://www.sciencedirect.com/science/article/pii/S0166218X9600100X

Theorem 2. (a) Even if truncated preference listings are not allowed,
CONDORCET is incompatible with
PARTICIPATION, MONO-RAISE-RANDOM and MONO-SUB-TOP.

(b) In general, CONDORCET is incompatible with LATER-NO-HELP,
LATER-NO-HARM, MONO-RAISE-DELETE, MONO-SUB-PLUMP and,
in the presence of PLURALITY, MONO-ADD-TOP.

(c) There is no election rule that sutisfies LATER-NO-HELP and
LATER-NO-HARM,
and that also satisfies CONDORCET whenever there are no truncated
preference listings.

Election 3. (1 seat)
3 A>B>C
3 B>C>A
3 C>A>B
2 A>C>B
2 B>A>C
2 C>B>A

Consider Election 3. By symmetry, the result must be a 3-way tie; but, by
the axiom of discrimination, there must be a profile P
arbitrarily close to this (in the proportions of ballots of each type)
that does not yield a tie. Without loss of generality, suppose a is elected
in P.

But c becomes the Condorcet winner, and so must be elected by CONDORCET,
...if all the abc ballots are replaced by a (contrary to LATER-NO-HELP),
or if all the bac ballots are replaced by a (contrary to MONO-RAISE-DELETE
and MONO-SUB-PLUMP), or if all the abc ballots are replaced by acb
(contrary to LATER-NO-HELP and LATER-NO-HARM together).

This proves (a), (c) and three parts of (b).

The three relatively burial-resistant Condorcet methods that meet
mono-raise and don't ask or allow voters to enter an explicit approval
cutoff that I like are
Smith//Approval (ranking),  Margins-Sorted Approval (ranking), and

Smith//Descending Acquiescing Coalitions.

Not allowing voters to rank among unapproved candidates increase the risk
for Burial strategists that they will simply elect their "bus".

By itself DAC (one of Woodall's inventions) meets Later-no-Help and
Participation (both incompatible with Condorcet) but can behave very oddly
and badly in the presence
of one or two weak should-be-irrelevant candidates (which is why I'm wary
of Smith,DAC).

So defining it thus: Voters rank from the top, equal ranking and
truncation is fine.  Eliminate and drop from the ballots all the candidates
not in
the Smith set.

Ballots "acquiesce" to a candidate or set or subset of candidates (a
"coalition") if they vote no other (outside the set or subset) candidate
strictly above any of them.

Number all the possible coalitions according to how may ballots acquiesce
to them. Start with the highest-numbered and disqualify all the candidate
not in it.
Proceed to the next-highest numbered that contains any not-yet
disqualified candidates and disqualify those not in it, and so on until one
candidate is left undisqualified.

46 A
44 B>C (sincere might be B or B>A)
10 C

In this example all candidates are in the Smith set.  The acquiescing
coalitions are  AC 56,  BC 54,  AB 46,  A 46,  B 44,  C 10.

AC disqualifies B,  BC disqualifies A so  C wins.

That would be great for fans of  the Minimal Defense criterion, but would
be sad if the B>C voters are sincere and the C voters are
truncating against B.

Chris B.

On 4/11/2023 12:05 am, Forest Simmons wrote:

On Mon, Oct 30, 2023, 6:21 PM C.Benham cbenham@adam.com.au wrote:

My favorite burial proof  method is to elect the nemesis of the nemesis of
the (repeated) Submidway Approval Elimination winner.

Max Approval is 52
Min Approval is 3
Midway is 27.5

So we eliminate C.

Updating approvals we have 52 for A and 48 for B. Midway is 50. B is the
only Sub Midway candidate so A is the SubMidway Approval winner.

The nemesis of A is C, and C has no nemesis because it not pairbeaten. We
respect the Condorcet Criterion and elect C, a very weak CW.

There is no way out of it if we want a Condorcet Criterion Compliant
method.

This reminds me of the practice omanipulative judges in the US warning
jurors to ignore their sacred right of "Jury Nullification" (inherited from
English Common Law).

Those lying (by intimidation) judges are a disgrace to their office ...
and should be stripped of their holy robes ...  imho.

That warning should be mandatory ... as should an honest effort to "fully
inform" a jury of their most sacred rights predatimg even the Magna Carta.

Your example shows the wisdom of electing the ballot CW when there is one.

In fact, all of our burial resistant methods elect the voted CW when one
exists. But when one does not exist we suspiciously suspect that its
absence was most likely  caused by subversion of a CW, since that is by far
the easiest way to create a beat cycle ... whether innocently or with
"malice aforethought."

Let's see what our Sub Midway Approval Elimination burial resistant method
does here:

The respective max and min implicit approval scores are 54 for C and 44
for B. So Midway is 49. Both A and B have Sub Midway Approval leaving C as
the candidate whose nemesis's nemesis we should elect.

C's nemesis is B, and B's nemesis is A.

So A is the winner of our burial resistant method.

How does this work?

Well, Nanson is very good at fingering the Burial Faction Favorite, but
Poor man's Nanson aka SubMidApproval Elimination is even better at electing
the BFF than ordinary Nanson or RP wv, although they are both pretty good
at it as this example shows.

Once you have the likely BFF you can follow the cycle forward one or
backward two candidates to the "bus" under which the buried candidate was
buried.

[Electing this "bus" is what makes the method backfire on the burying
faction ... so electing the strongest bus (their could be a clone set of
them) is the proper aim of a good burial proof method designer ... to
completely deter potential subverters from even flirting with the idea.]

Like I said you can go in either direction  around the cycle to get to a
"bus" from the BFF candidate .... but it's better psychologically to elect
the syrongest wv defeater of the strongest wv defeater of the Nanson winner
.... as opposed to saying "Elect the candidate with the most losing votes
against the Nanson winner" .. they are almost always the same candidate
even when Smith has more than three members.

Like I say, SubMidAolroval Elimination is more reliable than even ordinary
Nanson or RP wv at finding the BFF candidate.  But for the curjous, you can
always do a sincere runoff between the likely strongest Bus (the nemesis of
the nemesis of the likely BFF), and the Smith candidate with the fewest
losing votes against it (i.e.against the bus) the same as the weakest
Smith  weakest Smith candidate to defeat the BFF.

[It is easy to show that a subverted CW always defeats the BFF, which
beats the bus that beat the buried candidate that precipitated the
insincere cycle resulting from the burial.]

In this example the sincere runoff (were that option to be taken) would be
between the Bus A and the Smith candidate B with the fewest losing votes to
it A.

For the sincere winner of this runoff we have to go clear back to the
original scenario. And it turns out that A is the sincere winner of the
runoff, because C, the sincere CW was acting more like a BFF ... so not a
finalist in the runoff!

Right, and now we have a method designed to automatically avoid that kind
of mistake.

I strongly agree with everything you said in this message ... including
the importance of judicious use of truncations ... especially when approval
cutoffs are not allowed.

And most of the time no sincerity check is needed ... best policy is to
elect the Smith candidate  most likely to be the "bus" under whom the
buriers threw the buried candidate to cause the cycle .... assuming that
the most common cause of cycles is insincere order reversals.

That's a controversial assumption, but I now believe that these insincere
order reversals are much more common than inconsistent sincere preferences
as a cause of these ballot cycles.

Over the years I have contrived my share or scenarios that result in
sincere Paper Rock Scissors cycles ...  Paper sincerely covers Rock which
sincerely smashes Scissors which cuts Paper ... and perfectly plausible
issue space examples.

But the insincere burials are easier to engineer ... even by accident ...
just innocently pushing your second choice to the bottom of your ballot to
give your favorite an edge ... perhaps assuming that as many people do that
the same Borda Count used in Sports competitions had something to do with
the tally of Condorcet methods like ... Black, Baldwin, and Nanson.

Sincere pairwise beat cycles are not impossible .... but I believe that
they are relatively much less likely .... based on the difficultly of them
arising naturally as opposed to innocent opportunistic order reversals.

It turns out that Condorcet wv is almost as easy to fool as Norda based
Nanson ... two methods that almost always elect the Burier faction
candidate as in your example below.

We have devised methods that make burial backfire on the burial faction.

That's good enough for me and you, but some people need more evidence ...
and education ....including influential people like Foley and Maskin, who
are proposing burial prone Baldwin in place of burial resistant  IRV.

I'm simply proposing a way of distinguishing statistically between the
relative prevalence of sincere and imsincere pairbeaten cycles.

Here's one test:

As often as possible when an RP Condorcet rules election has no ballot CW
...

Let W be the RP winner. And let X be the Smith candidate with the most
losing votes against W.  Finally, let Y be the Smith candidate with the
fewest losing votes against X.

Suppose the voters have agreed to a two stage runoff for Scientific purpose

The first stage of the runoff is to decidenif there will be a second stage.

If not W retainsbthe win .... and that's that. Otherwise, the final choice
is between X and Y.

If the ballots were sincere, then since they say X beats Y, the voters
would expect X to win the secomd stage if it were held ... So if the ballot
votes were sincere they would prefer not to have the second stage ... so W
would retain her wim.

But if X or Y were sincerely preferred over the other two participants in
this new tangled runoffbthen the moderately well informed voters will be
aware of that .... and the supporters of this "local CW" will willingly
support having a second stage knowing that they can win it ... and thereby
winvthe election.

So in the long run if more of these RP winners are retained than not ..the
null hypothesis of sincere cycle preponderance will be supported.

fws

On Mon, Oct 30, 2023, 6:21 PM C.Benham cbenham@adam.com.au wrote:

Because BF has one natural defeat & one natural victory.  …& CW has two
natural victories & one strategic lowering…& Bus has two natural defeats &
one strategic raising…

… then regardless of how we compare natural defeat or victory to strategic
raising or lowering…

…doesn’t that mean that BF is at the middle?

Then say:

Among the top-cycle, elect the nemesis of the nemesis is the candidate
whose Borda [or implicit approval] is at or nearest to the middle
[midrange, median or mean] ?

On Thu, Nov 2, 2023 at 23:50 Forest Simmons forest.simmons21@gmail.com
wrote: