[EM] Fwd: Some thoughts on Condorcet and Burial

[Michael Ossipoff]

---------- Forwarded message ---------
From: Michael Ossipoff <email9648742 at gmail.com>
Date: Sun, Nov 5, 2023 at 11:23
Subject: Re: Some thoughts on Condorcet and Burial
To: Forest Simmons <forest.simmons21 at gmail.com>


Two other methods that seem to me to be autodeterrent are:

Smith//SP

Apply SP(Borda)to the Smith-set.

(…though plain SP(Borda) by itself seems autodeterrent too.)

Smith//Approval:

Elect the Smith member with highest implicit Approval.

On Sun, Nov 5, 2023 at 11:10 Michael Ossipoff <email9648742 at gmail.com>
wrote:

> Forest—
>
> But the incentive for the potential buriers is the matter of whether
> burial’s expectation is positive or negative.
>
> You can have a procedure that probably elects the CW, but that doesn’t
> figure in the expectation. What matters for the burial’s expectation is the
> relative-probabilities of electing Bus vs BF, & their utilities for the
> burier.
>
> We can’t affect the utilities of those two outcomes for the potential
> buriers. We can only increase the factor by which the probability of
> electing a Bus is greater than the probability of electing BF.
>
>  Black (with Borda applied to the Smith-set) & SP, it seems to me, are
> more likely to elect Bus than BF.
>
> Likewise, it seems to me, so is your suggestion to elect the candidate wit
> the largest wv against the candidate who has the most wv against hir in a
> defeat. I call that Greatest Win Against Greatest Loser (GWAGL).
>
> But, for the greatest likelihood of electing a Bus in a many-candidate
> election, doe anything else equal your suggestion to apply takedown
> (primary & secondary) to SP (agenda-ordered by Borda)?
>
> I call that method TSP.
>
> …partly to stand for Takedown-SP…
>
> …& partly because TSP is also the name for the powerful cleaning alkali,
> Trisodium Phosphate.
>
> TSP cleans it up !!!
>
> What’s that? We aren’t allowed to use Trisodium Phosphate?
>
> That’s okay, we aren’t allowed to use an adequate voting-system either.
>
>
>
> On Sun, Nov 5, 2023 at 01:14 Forest Simmons <forest.simmons21 at gmail.com>
> wrote:
>
>> Woodall has been a great EM pioneer .... and has done us a great favor by
>> making clear some of the limitations of the UD box, as well has showing us
>> by his Solid Coalitions methods some of the previously unknown
>> possibilities of working within that box.
>>
>> I have suggested some of the "pockets of predictability" within the UD
>> domain that have not been fully exploited for burial resistant methods ...
>> at the same time coloring outside the UD lines as you have (eg with
>> approval cutoffs) to surpass some of the UD limitations.
>>
>> I'm glad that you did not give up In helpless futility .... nut have
>> pragmatically pressed on.
>>
>> In general, impossibility proofs are valuable by making clear the
>> assumptions that entail impossibility ... so we know which lines we have to
>> color outside of if we want to avoid dead endends.
>>
>> The three candidate two stage fresh ballot runoff is one non UD tool
>> tailor made for finishing elections that surpass the boundaries of UD
>> possibilities.
>>
>> Sometimes with manipulated ballot sets we can narrow down to two
>> candidates that form a satisfactory basis for a two candidate fresh ballot
>> runoff.
>>
>> But when you push the boundaries further, a two candidate runoff isn't
>> good enough.
>>
>> But in the case of a three candidate Landau set ... the right kind of
>> fresh ballots runoff is adequate for recovering the buried candidate.
>>
>> I doubt there has ever been (or ever will be) a real public election
>> ballot set with more than three uncovered candidates.
>>
>> It is easy to show that when a CW is buried, it will still be a member of
>> (not only the Smith set), but also a member of Landau.
>>
>> Smith may have a large clone set of "buses", but (with statistical
>> certainty) one of these buses  will cover all of the others.
>>
>> These tools are outside the scope of Woodall ... who would surely
>> appreciate their usefulness were he still in the loop.
>>
>> fws
>>
>>
>>
>>
>> On Fri, Nov 3, 2023, 1:32 PM C.Benham <cbenham at adam.com.au> 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 at 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
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> *Forest Simmons* forest.simmons21 at gmail.com
>>>> <election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20Benefit%20of%20a%20doubt%20runoff%20challenge&In-Reply-To=%3CCANUDvfru_xs%2BEE6kd7Xbb4p%2Bsh3Zijqy-yCmBwNPOdwLP1emgQ%40mail.gmail.com%3E>
>>>> *Sun Oct 29 21:30:58 PDT 2023*
>>>> ------------------------------
>>>>
>>>> Are the beatcycles that sometimes arise from expressed ballot preferences
>>>> ... are these cycles more likely to arise from occasional inevitable
>>>> inconsistencies inherent in sincerely voted ballots? ... or from ballots
>>>> that reflect exaggerated preferences from attempts to improve the election
>>>> outcome over the one likely to result from honest, unexagerated ballots (?)
>>>>
>>>> Should Condorcet methods be designed on the assumption that most ballot
>>>> cycles are sincere? .... or on the assumption that most are the result of
>>>> insincere ballots (?)
>>>>
>>>> Some people think that the question is irrelevant ... that no matter the
>>>> answer, the  best result will be obtained by assuming the sincerity of the
>>>> voted ballots. Others think healthy skepticism is necessary for optimal
>>>> results. What do you think?
>>>>
>>>>
>>>>
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