[EM] Some thoughts on Condorcet and Burial

[Forest Simmons]

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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