[EM] Strategy-free criterion

[Chris Benham]

Kevin,

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".

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?

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. 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.

> 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?  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.

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.

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 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.*

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?   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.

Chris B.


On 16/06/2024 6:56 am, Kevin Venzke wrote:
> Hi Chris,
>
>> Kevin,
>>   
>>> I don't like the CD criterion because of the three incentives it creates, only
>>> one of them is positive.
>> What are they?
> The disunited majority has three options to avoid the criterion's wrath:
> 1. The "defecting" faction can add another preference, if they have it or are
> willing to lie that they have it.
> 2. The "defected-against" faction can compromise and try to give the other
> candidate a majority of first preferences.
> 3. One of the candidates can simply drop out of the race, as it will be apparent
> that the method poses such risks.
>
> On an additional note, it's strange to me that CD crit allows one faction to defect
> but not the other. If both factions optimistically think they are the larger one,
> they will all assume CD applies to the other voters and not themselves. It seems to
> me that a "real" CD criterion would take no nonsense from anyone.
>
>>> I'm not sure I follow, that a winner barred by Plurality has more credibility than
>>> a winner who won under the rules but is challenged by a second candidate who
>>> regrets how his supporters filled out their ballots.
>>   
>> I didn't mean to make it a big competition, because I don't accept
>> failure of either.  "Plumpers" for X didn't exactly "fill out" their
>> ballots, they had no interest in any other candidate, so they showed up
>> and plumped for X.
>>   
>> It would be readily apparent from the post-election ballot profile that
>> if some or all of them had stayed home then X would have won.  It's the
>> simplest and most egregious version of Participation failure. There is
>> no excuse for any algorithm to be confused by such pure and simple
>> information.
> Yes but almost all proposals fail Participation, so we will be in a lot of trouble
> if we insist on this kind of thinking. I understand that you see a difference in
> severity, but for myself I don't see where to draw the line.
>
>> Sometimes methods that fail Plurality meet Later-no-Harm and may have a
>> (at least zero-info) random-fill incentive.  So then failures of
>> Plurality would be very rare, and the occasional complaint would usually
>> be answerable by the retort:
>>   
>> "Well suckers, you didn't make your (full) contribution to GIGO!" :)
>>   
>> I am intolerant of methods that fail Irrelevant Ballot Independence
>> (although I recognise that putting up with its failure might be able to
>> buy something) so I'm suspicious of methods that have arbitrary
>> thresholds (relating to some fraction of the "total votes") as an
>> essential part of their definitions.
> Well, in an environment where the concept of "median voter" is likely to be
> meaningful, pairwise majorities are basically the only suggestion you can get about
> what side the median voter is on. I don't think the premise of IIB is necessarily
> sound, because introducing IBs can remove information we previously thought we had
> about the median voter.
>
>>> I start this reply by introducing MDDA 2. Yes, after 19 years! We just add a
>>> rule at the start:
>>> 1. Disqualify all candidates with sub-majority approval if possible.
>>> 2. Disqualify all candidates with a majority pairwise defeat if possible.
>>> 3. Elect the most approved remaining candidate.
>>   
>> Given that you are using implicit approval (ranking), I struggle to see
>> how rule 1 can make any difference. Can the most approved candidate
>> without a "majority pairwise defeat" really have sub-majority approval
>> while some other candidate doesn't?
> Yes, actually Woodall showed it in 2005:
>
> 20 a>b
> 5 b>a
> 24 b>c
> 24 c>a
> 9 d>a>b
> 9 d>b>c
> 9 d>c>a
>
> D wins in original MDDA. The new version is an A-B tie.
>
>>>    As a Condorcet method, MinMax(margins) doesn't satisfy LNHarm.
>>   
>> Yes, my mistake.  I forget what name Woodall used for MMM.   I think he
>> said it meets Condorcet, Mono-add-Top and "Symmetric Completion" (which
>> happily means in the zero-info case there is neither truncation or
>> random-fill incentive).
>>   
>> I know that MMM is equivalent to "elect the X who needs the fewest extra
>> X-plumping ballots to become the CW."   Obviously that meets
>> Mono-add-Top, which strikes me as almost implying LNHarm.
> That's an interesting comparison, but note that DAC satisfies Participation
> (implying Mono-add-top), and DAC is definitely not good according to Later-no-harm.
>
>>> I wouldn't want to say a method is "good" just because no one can call it absurd.
>>   
>> I think it is a promising start, especially if we are aware of (and
>> honest about) which criteria are  compatible with others.
>>   
>> I think a "votes only" definition of SFC is
>>   
>> * If  X has a majority strength pairwise win over Y, and it is possible
>> to complete the truncated ballots in a way that makes X the CW, then Y
>> can't win.*
>>   
>> Do you agree?
> That sounds about right.
>
>> A version that goes without the "majority" bit:
>>   
>> *If X pairwise beats Y, and it is possible to complete the truncated
>> ballots in a way that makes X (but not Y) the CW, then Y can't win.*
>>   
>> I prefer the second.
> They're both hard to test because they are asking us to search for ways of actually
> completing the presented ballots. And it's not totally clear why it's helpful for
> there to be a sort of loophole here.
>
> This is probably clear to you, but if it's possible to complete the ballots so that
> X is the CW, but it's not possible to do the same for Y, then the normal intuition
> is that Y probably does have a majority loss to somebody. But it might not be to X.
>
> An interesting idea. I'm not really sure how to look into it, or find scenarios
> where we can see a contrast.
>
> Kevin
> votingmethods.net