[EM] Strategy-free criterion

[Michael Ossipoff]

On Fri, Jun 21, 2024 at 17:22 Chris Benham <cbenhamau at yahoo.com.au> .

>
> I can understand voted Smith-set fundamentalism, and that is expensive
> enough.
>

It a avoids the possible embarrassment of electing a Condorcet loser, with
the likely resulting repeal. Maybe some additional desired criteria are
gained too.

RP(wv) & Schulze do even better, with their clone-independence, & probably
various other criterion-gains.

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.
>

No. Available evidence, including thousands of CIVS polls, indicates that
sincerely-voted top-cycles are rare. It isn’t speculation. It’s experience.

 Because any top-cycle is almost surely strategic, & because allowing
offensive strategy to defeat a sincere CW (with the consequent
defensive-strategy-need) results in big problematic defensive-strategy-need…

…& because it doesn’t make a whole hell of a lot of difference who wins in
a sincerely-voted circular-tie…

…then yes, what matters is, as well as possible, preventing
offensive-strategy from talking the win away from a sincere-CW.

The wv Condorcet methods excellently achieve that….resulting in a fully
strategy-free method

…by which I mean, a method with which no defensive-strategy is needed.

…the achievement of the Condorcet ideal.

…&, in general, the ideal goal of voting system reform.

The best wv Condorcet methods that I’ve heard of are:

RP(wv)
Schulze
MinMax(wv)
Smith//MinMax(wv)

RP(wv) Schulze meet the most criteria.

Those methods achieve the ideal by two properties.

1. Minimal-Defence Criterion compliance

2. Autodeterence





>
> 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.
>
> Kevinvotingmethods.net
>
>
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