[EM] Strategy-free criterion

[Kevin Venzke]

Hi Chris,

> On Mono-add-Plump as a weak version of Participation:
> 
> > Yes but almost all proposals fail Participation, so we will be in a lot of trouble
> > if we insist on this kind of thinking.
> 
> What sort of "trouble"?  I don't see how your conclusion follows from
> your premise. Why do "almost all proposals fail Participation"?  It
> isn't because there is anything inherently wrong with "that kind of
> thinking". It is because it just happens that Participation is very
> expensive (in terms of other desirable criterion compliances, such as
> Condorcet).  But in that way Mono-add-Plump is very very cheap (if not
> free), and some of us are currently "in trouble" due to disregarding
> "this kind of thinking".

What I'm saying is that if we pursue criteria in the vein of Participation (or
monotonicity), we cut down the list of methods we can consider, and we aren't
necessarily getting anything of value except that fewer people can call the method
absurd. What I call inherently of value would be things like sincere Condorcet
efficiency or reduced strategic incentives.

> Suppose a mini-bus with a driver is contracted to pick up a group of
> people and take then on a trip to one of  X, Y or Z  after polling the
> passengers on their ranking-preferences among these alternative
> destinations. After the bus is nearly full it is mistakenly assumed that
> there will be no more passengers and the driver applies some algorithm
> to the rankings of those present and announces that winning alternative
> is X.
> 
> Then it is learned that there are two more passengers to come to fill up
> the bus.  They do so and the driver says to them  "I've polled all the
> other passengers and at the moment the winning destination is X. Where
> would you like to go?" and they reply "X is our first preference and Y
> wouldn't be too bad and we are very glad we aren't gong to Z".
> 
> The driver replies "You prefer Y to Z?  In that case the new winning
> alternative is Y".   Now if these two voters (and perhaps others whose
> first preference was X) were enlightened election-method experts, they
> might think "Obviously this fellow's election-method algorithm fails
> Participation (and presumably Later-no-Harm).  Perhaps it meets
> Condorcet, which we know is incompatible with both Participation and
> Later-no-Harm. Perhaps before we showed up there was a top cycle and our
> Y>Z preferences turned Y into the Condorcet winner.
> But we know that Condorcet is also incompatible with Later-no-Help so us
> revealing our second preferences could have just as likely helped us, so
> I suppose we were just unlucky."
> 
> Or if they were not experts but charitably minded they might think "I
> suppose it is possible that this fellow made an honest mistake due to
> him being thick and us confusing him with too much information".
> 
> Now replay this scenario except this time the new passengers just say
> "Great!  We just really want to go to X and we don't know or care about
> any other destination."  And then the driver says "In that case the
> winning alternative changes from X to Y".
> 
> The response could only be that the destination-decider (supposedly
> purely based on the passengers' stated preferences) is insane (or
> malevolent, in any case illegitimate)  and that Y is obviously an
> illegitimate winner.
> 
> Did you notice a very different vibe from the first case, which was a
> failure of Participation and  Mono-add-Top but not Mono-add-Plump?

The difference in vibe is quite similar to your own difference in vibe when you
compare these situations.

In one case, some voters are willing to say "I guess there were other considerations
in play; we were unlucky" but in the other case they won't go there. And that's
fine, that is their right.

> In December 2008 on EM I argued that Schulze's Generalised Majority
> Criterion is a mistaken standard because the concept is vulnerable to
> Mono-add-Plump.

But given their compatibility, isn't that a strange thing to say?

> Your new MDDA 2 method fails the example I gave:
> 
> 25 A>B
> 26 B>C
> 23 C>A
> 04 C
> (78 ballots, majority threshold = 40)
> 
> Implicit approval scores:  C 53,   B 51,  A 48.   No candidate is
> disqualified due to sub-majority approval.
> 
> B>C 51-27,   C>A 53-25,   A>B 48-26.     All candidates have a
> "majority" strength defeat, so it "isn't possible" to disqualify any
> candidate on that basis.  So, according to the rules of MDDA 2, we elect
> the most approved candidate, C.
> 
> Now say we add 22 ballots that plump for C to give:
> 
> 25 A>B
> 26 B>C
> 23 C>A
> 26 C
> (100 ballots, majority threshold = 51)
> 
> Implicit approval scores:  C 75,   B 51,  A 48.   Now A has sub-majority
> approval and so is disqualified.
> 
> B>C 51-49,   C>A 75-25,   A>B 48-26.    Now C and A have
> majority-strength defeats and B doesn't, so (according to the rules of
> MDDA 2),  A (again) and C are disqualified leaving B as the new winner.
> 
> The contention that C is the right winner when there were just 78
> ballots but when we add 22 ballots that plump (bullet vote) for C the
> right winner is no longer C is .... completely crazy.

The voters' behavior had a side effect of strengthening B. All sorts of monotonicity
failures take such an appearance.

And again, there could be differences in severity, e.g. what percent of voters think
a given phenomenon is absurd. But I don't find that very interesting because it
doesn't tell us about the merits of the method. It's basically marketability.

> > Well, in an environment where the concept of "median voter" is likely
> > to be meaningful,...
> 
> What "environment" is that?  And why is that the environment the one we
> should primarily focus on?

One where voter and candidate preferences can be explained by an underlying issue
space. In this case if you could project everyone onto a plane or spectrum it would
be a bit easy to find the median voter and their preferred candidate.

I think this usually describes public elections, but it probably wouldn't cover a
vote on what color is the best, or a vote on what cuisine to have delivered. So I
think we should probably have IIB for those cases.

> I think that is the sort of thinking that
> leads some people to support Median Ratings methods, which we know are
> garbage because they fail Dominant Candidate and Irrelevant Ballots
> Independence, and the voters have a strong incentive to just submit
> approval ballots (giving the same result as Approval). And it has led
> you to the absurdity of suggesting a method that fails Mono-add-Plump.

Not at all, median rating methods aren't motivated by the notion of a single median
voter. There are multiple median voters on different posed questions, and that's
true on a pairwise matrix as well.

> I think for the purposes of properly analysing single-winner election
> methods and inspiring the invention of  new ones, we can and should do
> without criteria that refer  to irrelevant ballots dependent "majority"
> thresholds or pairwise defeats.  Those have almost no positive point
> aside from marketing.

You're saying that criteria directly specifying "majority" and not something else
is what lacks positive points aside from marketing? That could be true.

> My suggestion for something as close as possible to Minimal Defense: 
> *If the number of ballots that vote X above bottom and Y no higher than
> equal-bottom is greater than Y's maximum pairwise support, then Y can't
> win.*

I don't hate that. I don't know what you gain from using "max pairwise support"
instead of "votes in total."

> I propose Double Defeat (Implicit) as something that can substitute for
> the votes-only versions of Minimal Defense and SFC and also Plurality.
> 
> *Interpreting ranking (or ranking above equal bottom) as approval, no
> candidate that is pairwise-beaten by a more approved candidate is
> allowed to win.*

It's interesting but it doesn't cover SFC. In an SFC failure scenario the
disqualified candidate might very well have more approval than the candidate who
disqualifies them. The concern is that supporters of the latter gave the election
away.

> That already inspires a simple method suggestion:  DDI,MMM: *Elect the
> candidate  not disqualified by Double-Defeat (Implicit) that is highest
> ordered by MinMax(Margins).*
> 
> What do you think of that?

I don't like it but it might be fine.

> And what is wrong with your "Improved
> Condorcet Approval" method ?  I think it would be good using
> unrestricted ranking ballots with an explicit approval cutoff.

ICA or C//A (implicit) are not bad. They don't satisfy SFC. In my recent simulations
on frontrunner truncation strategy, C//A is among the best Condorcet methods. In
random elections I am disturbed that ICA and C//A are worse than WV methods at
strong FBC (i.e. what I call compromise incentive).

You've asked me many times about C//A(explicit) and I still think it's bad. The
entire notion of C//A(implicit) being good at deterring burial is based on the
fact that if you use burial to prevent there from being a Condorcet winner, then in
the "cycle resolution" you cannot prefer any candidate to the one you raised
insincerely.

In C//A(explicit), burial only backfires if it actually creates a fake CW. Creating
a fake cycle is never bad for your favorite.

Kevin
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