[EM] Some thoughts on Condorcet and Burial

[Michael Ossipoff]

I should add that of course my check regarding the compatibility between
one particular order for the 3 candidates’ values of one of two measures of
overall high-ranking, with one of the 3 pairwise-defeats…is just one of 36
such compatibilities that should be checked.

…for the purpose of determining which orders for the candidates’ scores,
which measures, are compatible with the pairwise defeats

…for use in determining which candidate in a top-cycle is most likely to be
a Bus, & therefore the candidate to elect.

But the identification of the candidate with median Borda, or maybe median
implicit approval, among the top-cycle, as the most likely BF seems
convincing.

…making the candidate s/he pairbeats the most likely Bus.



On Fri, Nov 3, 2023 at 14:36 Michael Ossipoff <email9648742 at gmail.com>
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 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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