[EM] Some thoughts on Condorcet and Burial

[Michael Ossipoff]

So that suggests that, for SP, agenda-ordered by Borda or implicit
approval, would, in the strategic top-cycle, start by comparing CW & BF.

BF wins that comparison, & goes against Bus.

Bus wins.

The burial is penalized.

The familiar, widely used & precedented SP is autodeterrent.

On Sat, Nov 4, 2023 at 10:20 Michael Ossipoff <email9648742 at gmail.com>
wrote:

> Referring to what I was saying about the order of the 3 too-cycle
> candidates’ Borda or implicit approval:
>
> I told why I claim that BF is the most likely one to be middle.
>
> So what’s the most likely order for the top & bottom of that ordering?
>
> Well, top & bottom are the most extreme difference in the ordering “. So,
> isn’t that difference more likely to not contradict a pairwise defeat?
>
> Together, those two facts suggest that the most likely order for the 3
> candidates’ Borda or implicit approval is:
>
> Bus>BF>CW.
>
>
> On Fri, Nov 3, 2023 at 06:35 Forest Simmons <forest.simmons21 at gmail.com>
> 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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