[EM] Strategy-free criterion

[Chris Benham]

Kevin,

> 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 that's bad because that list is so boringly short.

> ...and we aren't necessarily getting anything of value except that fewer people can call the method absurd.

So to you nothing actually *is* absurd, and if other people mistakenly 
think otherwise then that is just a marketing problem. Got it.

> What I call inherently of value would be things like sincere Condorcet efficiency or reduced strategic incentives.

I can understand voted Smith-set fundamentalism, and that is expensive 
enough. But if there is a top cycle I don't share the mind-set "Probably 
there is a sincere CW (concealed by strategic truncation or 
order-reversal) and our top priority should be to infer or guess who 
that is and elect him/her."  There may well be no sincere CW or a higher 
SU candidate. So quite nice, but mainly just a marketing benefit.

Of course I agree with the value of "reduced strategic incentives".

> 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.
They "won't" because it isn't even possible to imagine any "other 
considerations".

In reference to my example showing MDDA 2 failing Mono-add-Plump:

> The voters' behavior had a side effect of strengthening B.
No, it just had the "side effect" of exposing the method's perverse 
stupidity.

> All sorts of monotonicity failures take such an appearance.
None anything like as starkly. And without some excuse we avoid them. 
IRV used to be ridiculed for failing mono-raise (then just called 
"Monotonicity"), but we know that it isn't possible to fix that without 
losing other criterion compliances that some people like.
But again, I can't believe that we have to put up with failure of 
Mono-add-Plump in order to get anything desirable.

>> 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?
>
Not really.  The criterion can have nothing to say against candidate X 
in some ballot profile but then if we modify that profile by just adding 
ballots the plump for X it can decide that X is no longer acceptable. 
That is what I meant by the "concept". The two criteria are compatible 
because there are other candidates and GMC doesn't say that X has to win 
in the original profile.   Purely strengthening X (by stuffing extra 
X-plumping ballots into the ballot box) can, according to the criterion. 
change X from a candidate that is not disqualified into one that is.  
That makes the criterion silly and unacceptable.

Because of mutual criteria incompatibilities, we can sometimes make a 
case for a (at least in some way) silly method.  But there is no need or 
excuse for a silly criterion.

>> 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.
>
I see. Then substitute the Strong Defensive Strategy Criterion for SFC.

https://electowiki.org/wiki/Strategy-free_criterion

> If a Condorcet candidate exists, and if a majority prefers this 
> candidate to another candidate, then the other candidate should not 
> win if that majority votes sincerely and no other voter falsifies any 
> preferences.

I think that is very similar to the Generalised Majority Criterion, 
enough for me to reject it on the same grounds. And even if I didn't 
have that criticism, I don't see why it's something we should care much 
about. It looks like something contrived just to serve as ammunition 
against Hare and Margins. (And possibly the similar GMC was contrived 
just to help promote the Schulze method.)

Putting back my  "celebrated" example from December 2008:

25: A>B
26: B>C
23: C>A
04: C

78 ballots (majority threshold = 40)

B>C 51-27,   C>A 53-25,   A>B 48-26.  Implicit Approval scores: C 53,  B 51, A 48.

All the candidates have a majority-strength defeat, so none are eliminated and the most approved candidate, C, wins.

Say we now add 22 ballots that all plump (i.e. bullet vote) for C:

25: A>B
26: B>C
23: C>A
26: C

100 ballots (majority threshold = 51)

B>C 51-49,   C>A 75-25,   A>B 48-26.  Implicit Approval scores: C 75,  B 51, A 48.

Now only B is without a "majority-strength defeat", so the winner changes from C to B.

Of course the method also fails Irrelevant Ballots Independence. If we now add 3 ballots that plump for X, the majority threshold rises to 52 and so C's majority-strength defeat goes away and C wins again by being the most approved candidate.

As I also wrote then:

> As I hope some may have guessed from the spectacular failure of Mono-add-Plump, the GMC
> concept is grossly unfair to truncators.  And Winning Votes  (as a GMC complying method) is
> unfair to truncators.
>
> Say the 26C "we're just here to elect C and don't care about any other candidate" voters use a
> random-fill strategy, each tossing a fair coin to decide between voting C>B or C>A; then even if as
> few as 4 of them vote C>A they will elect C. Their chance making C the decisive winner is  99.9956%
> (according to an online calculator).
>
> I have some sympathy with the idea of giving up something so as to counter order-reversing buriers,
> but not with the idea that electing a CW is obviously so wonderful that when there is no voted CW
> we must guess that there is a "sincere CW" and if we can infer that that can only (assuming no voters
> are order-reversing) be X then we must elect X.
All that also applies to MDDA 2 and SFC. Take the case where of the original 26 C plumbers, 4 vote C>A and the rest vote C>B.

25: A>B
26: B>C
27: C>A
22: C>B

100 ballots (majority threshold = 51)

B>C 51-49,   C>A 75-25,   A>B 52-48.  Implicit Approval scores: C 75,  B 51, A 52.

No candidate has sub-majority approval and no candidate has a majority-strength defeat so the MDDA 2 winner is the most approved candidate, C.

Chris B.


On 21/06/2024 9:32 pm, Kevin Venzke wrote:
> 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
> votingmethods.net
>
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