[EM] Some thoughts on Condorcet and Burial

[Michael Ossipoff]

In SP, if there are many candidates instead of only 3, causing Bus to
pairbeat CW, just replaces a possible CW win with a Bus win.

So, with only 3 candidates, or with many, SP is autodeterrent.

SP could be used as the Condorcet completion method, applied to the
top-cycle, for autodeterrence.

But plain SP, by itself, is autodeterrent too.

On Sat, Nov 4, 2023 at 10:40 Michael Ossipoff <email9648742 at gmail.com>
wrote:

>
>
> ---------- Forwarded message ---------
> From: Michael Ossipoff <email9648742 at gmail.com>
> Date: Sat, Nov 4, 2023 at 10:33
> Subject: Re: Some thoughts on Condorcet and Burial
> To: Forest Simmons <forest.simmons21 at gmail.com>
>
>
> Sorry—I meant that CW wins that 1st comparison, against BF, & so CW then
> goes against Bus. Bus wins.
>
> SP is autodeterrent.
>
> On Sat, Nov 4, 2023 at 10:29 Michael Ossipoff <email9648742 at gmail.com>
> wrote:
>
>> 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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