[EM] Some thoughts on Condorcet and Burial

[Michael Ossipoff]

Or maybe it would be safer to say “…the member of the top-cycle who is
pairwise-defeated by the candidate whose Borda [or implicit approval] is at
or nearest to the middle.

…even though it would sound counter-intuitive.

On Fri, Nov 3, 2023 at 16:30 Michael Ossipoff <email9648742 at gmail.com>
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 at gmail.com>
> wrote:
>
>> 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 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
>>>
>>> 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.
>>>
>>> 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."
>>>
>>> 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"?
>>>
>>> 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
>>>
>>> Electing B here is completely unacceptable.  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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