[EM] Some thoughts on Condorcet and Burial

[C.Benham]

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 
> <mailto: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?
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20231031/a853dc87/attachment.htm>