[EM] Some thoughts on Condorcet and Burial

Fri Nov 3 14:36:20 PDT 2023

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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