DH3 and honest Condorcet winners
In the classical DH3 scenario, the dark horse is universally loathed by
the voters. This suggests a smart-aleck way of making almost every
method DH3-proof: just eliminate every candidate that don't have at
least one first preference. Since the dark horse is eliminated outright,
there's no point in attempting a burial - it simply won't work.
DH3 resistance thus shares with clone independence the feature that it's
easy to make a brittle method that technically complies with the
criterion. But add some very slight amount of noise (a few voters who
rank other candidates between the clones, or a few voters who rank the
dark horse first) and the hack fails.
Now suppose that we have an election after every faction has gone on its
burial spree, and there were initially some voters who ranked the dark
horse first. It would look something like this:
34: A>X>B>C
33: B>X>C>A
32: C>X>A>B
5: X
But this is just a three candidate version of the Left, Center, Right
scenario. If X is a genuine consensus candidate, then X should be
elected and a failure to do so is an instance of center squeeze. But if
this is the aftermath of a DH3 scenario, then X must absolutely not be
elected.
If the method's strategy is to eliminate candidates who are ranked first
by too few voters, then it has to have some kind of threshold -- how
many X voters distinguish a DH3 scenario from one with a centrist
candidate. In addition, it'll fail the Condorcet criterion because you
can have a CW that has zero first preference votes.
So this means that a Condorcet method can't defend against the worst DH3
outcome by simply rejecting the dark horse - because it can't tell the
dark horse apart from a true centrist winner once the buriers have all
done their damage.
Thus, the way a Condorcet method resists DH3 must be by making it either
pointless or harmful to the faction to try to engineer a cycle to begin
with. If A wins, and a faction who prefers B buries A under X, then if
the winner changes, it mustn't be to B.
Just how to do that is not an easy feat - but at least the argument
above shows what doesn't work. (Not if you want to pass Condorcet, at
least.)
On 07/17/2021 1:31 PM Kristofer Munsterhjelm km_elmet@t-online.de wrote:
In the classical DH3 scenario, the dark horse is universally loathed by
the voters. This suggests a smart-aleck way of making almost every
method DH3-proof: just eliminate every candidate that don't have at
least one first preference.
which, if you have 10,000 voters will never happen. try flipping a coin and get heads 50 times in a row. that's more likely to happen.
Now suppose that we have an election after every faction has gone on its
burial spree,
so voters are upping the Dark Horse that they loathe in an attempt to gain advantage over the other candidates they fear will beat their favorite?
and there were initially some voters who ranked the dark
horse first. It would look something like this:
34: A>X>B>C
33: B>X>C>A
32: C>X>A>B
5: X
But this is just a three candidate version of the Left, Center, Right
scenario. If X is a genuine consensus candidate, then X should be
elected
and i cannot see how you can differentiate this scenario from the ostensible Dark Horse insincerely bumped up.
and a failure to do so is an instance of center squeeze. But if
this is the aftermath of a DH3 scenario, then X must absolutely not be
elected.
listen, if we cannot differentiate a sincere mark on a ballot from an insincere mark, we should not try to. but we should have systems and rules that do not predictable incentivize insincere marking.
Arrow or Gibbard or Satterthwaite aside, we should examine what are common or likely scenarios that would incentivize strategic voting and not use contrived and highly unlikely specific scenarios in policy making to evaluate voting systems.
it's the most threatening hazards that we should try to avoid.
outside of a cycle, and valuing equal voter influence in elections, what is a realistic hazard that would challenge the main election ethic of elections, that is to determine the majority will of the electorate and elect a candidate so that the minority voters' votes do not count more than the majority voters' votes?
I think, to be honest, we should accept the marked ballots as sincere and count X as the genuine consensus candidate and the only Consistent Majority Candidate (which is what the CW is) there is.
If more voters mark their ballots preferring Candidate A over Candidate B than the number of voters marking their ballots to the contrary, then there is no consistently good reason why Candidate B should be elected (again, assuming we're nowhere near a cycle).
I cannot think of a good reason ever to not elect the Condorcet Winner when the ballot data clearly indicates that some candidate is the CW. When a cycle happens, then perhaps there is some subtlety in electing a candidate without rewarding bad strategic voting behavior. But I really think that a cycle will never happen in a governmental election and, while we should have law that will elect someone even without a CW in the outcome. It's just that I would weight that problem scenario with a very small probability of occurrence.
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
On 7/18/21 6:03 AM, robert bristow-johnson wrote:
On 07/17/2021 1:31 PM Kristofer Munsterhjelm km_elmet@t-online.de wrote:
In the classical DH3 scenario, the dark horse is universally loathed by
the voters. This suggests a smart-aleck way of making almost every
method DH3-proof: just eliminate every candidate that don't have at
least one first preference.
which, if you have 10,000 voters will never happen. try flipping a
coin and get heads 50 times in a row. that's more likely to happen.
Now suppose that we have an election after every faction has gone on its
burial spree,
so voters are upping the Dark Horse that they loathe in an attempt
to gain advantage over the other candidates they fear will beat their
favorite?
and there were initially some voters who ranked the dark
horse first. It would look something like this:
34: A>X>B>C
33: B>X>C>A
32: C>X>A>B
5: X
But this is just a three candidate version of the Left, Center, Right
scenario. If X is a genuine consensus candidate, then X should be
elected
and i cannot see how you can differentiate this scenario from the
ostensible Dark Horse insincerely bumped up.
That was my point. If you want Condorcet, you can't just exclude
candidates with few first preferences. So the only remaining option to
resist DH3 is to make the burial not pay.
Arrow or Gibbard or Satterthwaite aside, we should examine what are
common or likely scenarios that would incentivize strategic voting and
not use contrived and highly unlikely specific scenarios in policy
making to evaluate voting systems.
it's the most threatening hazards that we should try to avoid.
outside of a cycle, and valuing equal voter influence in elections,
what is a realistic hazard that would challenge the main election
ethic of elections, that is to determine the majority will of the
electorate and elect a candidate so that the minority voters' votes do
not count more than the majority voters' votes?
The thing is, we don't know, because Condorcet methods have been used so
little. On the one hand, when Wikimedia used Schulze, they had no
problems with strategy, and they chose to replace it with Approval for
complexity reasons alone. So if they're anything to go by, any advanced
(Smith, strategic entry/exit resistant) Condorcet method will do.
On the other hand, people worry that e.g. mass burial will happen. The
whole DH3 scenario is based on Warren's experience with Borda, which is
inordinately susceptible to Burial. On the face of it, it might seem
absurd that two thirds of the voters would preemptively bury opposition
candidates under someone nobody likes. I don't think it would happen in
Condorcet, but some people do.
So e.g. DH3 resistance or DMTBR is then less about resisting strategy we
know will happen, and more as insurance: to say to the people who think
that the voters would mass bury, that there's no incentive to do it
under this method.
Then the people can choose: do they want excellent results with honesty?
Then Ranked Pairs. Or do they want to be insured against strategy? Then
Smith-IRV, Pb, whatever.
But in practice, if you're aiming for a particular Condorcet method...
any Condorcet is better than no Condorcet! (Well, pathological methods
notwithstanding.)
-km
On Sun, Jul 18, 2021 at 3:59 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:
But in practice, if you're aiming for a particular Condorcet method...
any Condorcet is better than no Condorcet! (Well, pathological methods
notwithstanding.)
I'm learning a lot from this discussion. Here's my question: do you count
Copeland as a pathological method? I quite liked Copeland when I first
learned about it but I quickly realized that it frequently produces times,
and then later I learned about the clones issue. I think Copeland
(especially if there's a runoff to resolve ties) is probably superior to
any non-Condorcet method I've heard of including STAR and approval, but I'd
like to to hear from someone that understands voting methods better than I
do.
Cheers,
Daniel
On 18.07.2021 18:05, Daniel Carrera wrote:
On Sun, Jul 18, 2021 at 3:59 AM Kristofer Munsterhjelm
<km_elmet@t-online.de mailto:km_elmet@t-online.de> wrote:
But in practice, if you're aiming for a particular Condorcet method...
any Condorcet is better than no Condorcet! (Well, pathological methods
notwithstanding.)
I'm learning a lot from this discussion. Here's my question: do you
count Copeland as a pathological method? I quite liked Copeland when I
first learned about it but I quickly realized that it frequently
produces times, and then later I learned about the clones issue. I think
Copeland (especially if there's a runoff to resolve ties) is probably
superior to any non-Condorcet method I've heard of including STAR and
approval, but I'd like to to hear from someone that understands voting
methods better than I do.
Because it produces ties so often, I consider it more a set than a
method. Thus it needs a tiebreaker, or a method that elects from the
Copeland set according to some unified logic.
The Copeland set has some nice game theory properties, as it's an easy
to compute subset of the uncovered set. But any method that elects from
it will inherit its clone problems. My numerical experiments with
Copland also shows that it's not particularly robust to worst-case strategy.
So, yes, if the choice is between something that elects from the
Copeland set and something that doesn't satisfy Condorcet at all, I'll
pick the former.
But if I were proposing a method, I would instead choose either
something like Ranked Pairs (to make it absolutely clear there's no
clone problem) or Smith-IRV (to be directly robust to strategy instead
of having to rely on possible game theory arguments).
(By not being particularly robust to worst-case strategy I mean that if
A wins, there often exists a strategy for voters who prefer some B to A
can use to make B win instead. It might well be that the strategy is
unstable in the sense that voters who prefer A can defensively employ
strategy so that any attempted strategy by B-voters make C win instead.
My analysis can't detect that kind of defense - it assumes the first
election is honest. But when arguing that a method is robust to
strategy, it's easier to just say "under impartial culture, B voters can
only make B win 10% of the time" than to argue that there exist moves
and countermoves that neutralize the strategy in an equilibrium.)
-km