[EM] Some thoughts on Condorcet and Burial

[Forest Simmons]

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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