Saturday, 25 November 2023

John Allen Paulos's potty party game theory

15 years ago, 3 Quarks published a post titled

From Dreams And Delusions To Wars And Wiretapping
POSTED ON WEDNESDAY, AUG 6, 2008 4:46AM BY S. ABBAS RAZA

John Allen Paulos in his excellent Who’s Counting column at ABC News
It appears Paulos thought that the recent amendment to the FISA act permitting more wiretapping of people abroad would have bad consequences.

Earlier this week 3 Quarks published another post from the same author which once again claims that we can understand the world better by paying attention to a 'party game' thought-experiment. 
This post is titled-

Dreams, Stories, And Self-Revelation

POSTED ON MONDAY, NOV 20, 2023 1:15AM BY JOHN ALLEN PAULOS

I'm not sure what prompted this particular, nearly identical piece. Still, it is worth drawing attention to what may be a popular misconceptions regarding game theory which some mathematicians might subscribe to. To begin, I need to explain that, in Econ, a 'money pump' is a thought experiment designed to show it is irrational to hold intransitive preferences- i.e. to prefer a over b and b over c but then choose c over a. Sadly, such preferences are rational because, where Knightian Uncertainty exists, it is regret minimizing to do 'discovery'.  Moreover, where there is information asymmetry it is irrational to think there will be only one extended game form or (equivalently) that all information can be captured in the pay-off matrix (because of impredicativity, intensional fallacy etc.) This means you have to be very scrupulous in how you use game theory or, indeed, any type of inductive reason.

Turning from 'money pumps' to 'intuition pumps' or 'persuasion machines' which are, in the words of their inventor 

'A popular strategy in philosophy (involving the construction of) a certain sort of thought experiment. (They) are cunningly designed to focus the reader's attention on "the important" features, and to deflect the reader from bogging down in hard-to-follow details. There is nothing wrong with this in principle.'

Nor is it wrong for a magician to 'force a card' on a member of the audience. But it is merely a trick done for the purpose of entertainment.

 'Indeed one of philosophy's highest callings is finding ways of helping people see the forest=

the forest is useful, sciencey, stuff or else things which improve our decision making in economics and politics. 

 and not just the trees. 

Only philosophy bothers with Smullyan truth trees. 

'But intuition pumps are often abused, though seldom deliberately.'

So, philosophers are so stupid they don't know they are abusing things they invent. Still, if they aren't raping their students, perhaps we should just let them get on with such shenanigans. 

Paulos's current article begins thus-

Philosopher Daniel Dennett’s new book, I’ve Been Thinking, just came out, and I was reminded of a party game he’s written about. A variant of the child’s game of twenty questions, it is relevant to an increasingly pressing question: How do different social bubbles, media subcultures, or cults develop.

This is something we know a great deal about. To simplify matters, we begin with certain 'uncorrelated asymmetries'- i.e. arbitrary differences, e.g. that of race or gender or age- and consider what 'coordination' and 'discoordination' games they give rise to. These correspond to 'cheap talk' pooling equilibria and 'costly signal' based separating equilibria. There is arbitrage- involving hedging and income effects between coordination and discoordination games and this can affect what is or isn't in the 'core' (or contract curve) of the relevant Political Economy. 

Some game theoretic concepts- e.g. 'Shapley Values'- can be useful but they may not be robust. There can be 'topological holes' in the decision space. Things can change in the blink of an eye.  Math can be misleading even if it appears to be 'paying for itself'.  

Let me start with the game, generalized versions of which are ubiquitous. It’s probably one of Dennett’s most compelling intuition pumps; that is, thought experiments with made-up, but plausible outcomes.

Will Paulos supply a game theoretic account of the game? My contention is that if he did so he would soon see the thing is misconceived. It would end abruptly after a couple of iterations. The guy who suggested it would be looked upon as a fool.  

Imagine a group of people at a party who choose one person and ask him (throughout, or her) to leave the room. The “victim” is told that while he is out of the room one of the other partygoers will relate a recent dream to the group. He is also told that on his return to the party, he must try, asking Yes or No questions only, to do two things: describe the dream and possibly figure out whose dream it was.

His first question is 'is there really any dream that was described? Yes or No.'  If the answer is No, the game terminates immediately. If it is 'Yes', it must terminate on the next round if rational expectations obtain- i.e. the correct economic theory (which is game theoretic) is held by all participants. 

The big reveal is that no one relates any dream.

The thing is a 'gotcha'. You tried to be super-smart and Freudian but you ended up looking a shmuck.  

The party-goers decide to respond either Yes or No to the victim’s questions according to chance or, perhaps, according to some arbitrary rule.

In which there is a 50 percent chance the game terminates immediately. Even otherwise, the guy is at liberty to say he doesn't believe there was any dream unless for his own reasons he wants to embarrass guests by asking whether the dreamer enjoyed having sex with her granny while her Daddy jizzed on her face.  

Any rule will do and may be supplemented by a non‑contradiction requirement so that no answer directly contradicts an earlier one.

But the guy asking the questions can use any rule he likes- e.g. ask the most embarrassing possible question- or, if he can't be bothered, adamantly insist that there was no dream. The other guests just wanted him out of the room so as to display their puny genitals to each other. 

What might happen is that the victim, impelled by his own obsessions, constructs a phantasmagoric, or at least a, weird dream in response to the random answers he elicits.

Which is only interesting because we think dreams might themselves be weird 'narratives' imposed on some sort of brain activity to do with memory updating and conservation during sleep. In a sense, the 'victim' is like a Freudian analyst imposing his own psychic pathology on the sub-consciousness of the supposed dreamer. It doesn't matter if there was no dream. By refusing to recognize you fucked your granny in your dream you are displaying 'resistance' which proves you do nothing but lust after granny save when you take a break to imagine decapitating Dad and shitting down his neck. You need therapy. Lots of therapy- unless you are poor in which case you can just fuck off.  

He may even think he knows whose dream it was, but then the trick is revealed to him. The dream, of course, has no author, but in a sense the victim himself is.

There was a time when Freud was considered a great healer, not a charlatan. It was in that context that this gedanken had salience. 

His preoccupations dictate his questions, which even if answered negatively at first, frequently receive a positive response when slightly reformulated. These positive responses are then pursued.

We are familiar with situations where the interlocutor is trying to steer you to a pre-determined outcome- e.g admitting guilt to the detective or agreeing with the salesman that buying a Time Share in Atlantis will definitely make you the envy of your neighbouring fishes. 

We can relax the rules of the party game. It’s not hard to develop more realistic generalizations that can be presented informally, say as a quiz on a slyly programmed website.

This sounds like 'click-bait' unless you are paying people to play. But, if it is 'click-bait' surely it will be used for some more remunerative purpose? There may be ways to buy votes using such techniques but the techniques themselves don't matter because those with lots of cash, or time on their hands, could use that technique to advance their own agenda. But this type of competition 'cancels out'. Maybe there is a little more 'noise-to-signal' but nothing really changes.  

Instead of inducing the victim to describe a dream, for example, he can be tasked to elaborate on a generic story or parable (for example, boy meets girl, or person overcomes obstacles, or man tricks his boss) he’s given. Let’s also assume that the party-goers are somewhat more uniform, say university students, or race car fans, or pediatric nurses, a collection of bots, or whatever, and that they are told that their answers should be generally random, but coherent and loosely relevant to the generic story. The story elicited by the victim’s questions in this case might be likely to reflect a worldview similar to the party-goers, albeit perhaps more self-revelatory and extreme.

It is likely to be less so. This is because we think of dreams as less structured and more bizarre than narratives we construct. 

Or we can go much further and assume that the victim himself chooses the party-goers. Assume these people belong to a loose association of more or less like-minded people, either online or in real life, and that they subscribe to a party line that jibes roughly with his outlook on many matters.

This is irrelevant. The fact is, the guy looks a fool if he doesn't first establish there really was a dream. Assuming asking questions is costly (it uses up valuable drinking time), the way to go is to ask 'was there really a dream?' and then say 'I don't believe you' if the answer is 'yes'. 

There is a kind of 'a priori' reason why there can be no dream. This has to do with the difficulty of describing a dream or even a personal experience with such high accuracy that other people can answer more and more detailed 'yes/no' questions about it. In physics there is a 'constructor theory of information'. What is the 'constructor' such that a dream can be accurately described? Surely it doesn't exist. You remember things about your dream (though they may be confabulations) the more you talk about it.  But even a person who spent hours listening to you gassing on about the dream can't add details you did not mention because it wasn't their dream, it was yours. You can't answer 'Yes/No' honestly. You have to say 'I don't know. Please ask the person who had that dream.' True, you can tell random lies, but there are statistical ways to test for inconsistency though, in this case, there would be no point to going down that laborious road. Just trust to the maximal uncertainty principle and declare there was no dream.

The group (or even an app or a collection of bots) is also told (programmed) to give answers that are somewhat random,

by Razbarov-Rudich we can't distinguish pseudo-random from random 

but coherent and generally relevant to their take on the generic story given to the victim. Because of the victim’s existing but perhaps nascent predilections and his similarity to the party-goers he has chosen, the group’s simple Yes-or-No answers to his questions are more likely to lead him down a political, psychological, or even hallucinatory rabbit hole.

But, from the sound of things, he was already away with the fairies. The rational response is to say there can't be a dream because no description can reproduce its every detail and thus some members of the party will have to answer 'I don't know' to a finer-grained question. True, they may tell random lies but it would be little fun to catch them out by some laborious process of statistical analysis.

 There are some games which look 'symmetric' but can't possibly be so because of an uncorrelated asymmetry of an arbitrary type- e.g. who actually had the dream. Consider the Monty Hall problem. The Game Show host will only open the door behind which there is nothing. He has knowledge the contestant does not. Thus the contestant's expected distribution changes and so it is rational for her to change her choice.  In this case, there is no rational reason not to go with the 'pure strategy' of saying there was no dream. The thing was a 'gotcha'. 

Again the author of the resultant story is the victim, whose obsessive questions guide its development, but here the party-goers obviously have a much stronger supporting role.

Not if the victim is rational. He explains to them why the game was fundamentally flawed. Suppose the party goers agree on a fabricated dream as a 'back up' just in case the guy raises the obvious objection to it. He can then grill the party-goers and detect their deceit because there is a suspicious unanimity in some responses, but random fluctuations on others. Fraud investigators look for such patterns all the time. The trouble with lying is that the list of things you can affirm is much smaller than it is for the truth teller who can always come up with additional information consistent with his basic story. 

Moreover, in this latter case when the victim chooses his party-goers, matters can easily become incestuous enough to further shape the group as well as the victim.

So, we are now speaking of a maniac who has carefully chosen a bunch of similarly crazy collaborators. They are all wearing tin-foil hats and whispering about the Jewish Lesbians who have taken over the Papacy.  

Over time, their inchoate inclinations can be mutually cultivated, repeated, and exaggerated to allow them to settle on those they endow with halos and those they endow with horns. The distinction between victim and party-goers dissolves and a cult is born.

No. Cults require a charismatic leader. There has to be a 'buck stopping' mechanism even for paranoid nonsense. The Pope, it is true, is a Jewish Lesbian, but this doesn't mean we can't get milkshakes from McDonald's because my cousin works there and, anyway, it is actually a front for the Muslim Brotherhood.  

These extensions of the party game are not such unrealistic scenarios as common critiques of the algorithms governing various platforms show.

3Quarks very quickly bans comments from people like me. Do they bother with an algorithm? Who cares?  

Not just parties, but many everyday interactions in close-knit social groups easily give rise to similar situations as well. Tweaking the game in these and other ways can lead a victim to a lockstep submission to groupthink.

This guy is a Professor at Temple University which appears to be deeply divided on Hamas's atrocities. There certainly does seem to be a lot of 'lockstep' submission to 'groupthink' on campuses. But campuses may be ceasing to matter. China may already have overtaken the US in certain strategic STEM subjects. By the end of the decade, the West may have no say in what happens not just in the MENA but also Mexico and Latin America.  

His hypothesis-generating ability can remain intact even if the ability to test or falsify hypotheses is undermined by misinformation, sensory deprivation, societal unrest, or interpersonal stress.

Not to mention being sodomized by the Lesbian Pope.  

He rejects nuance and uncertainty and unencumbered by any critical reality checks, spews out dreams, absurdities, and extreme political views.

What is this Math Professor spewing here? Dennett's 'intuition pump' is obviously shit. Why? Either this is an interesting game because there is something like a 'Harsanyi Transformation' (if everybody is rational) or else there is a 'gotcha' element to it. In the former case, there is some convoluted mathematical method to extract noise from signal. But that isn't really very amusing- is it? Thus the thing has to be a 'gotcha' situation. 

The principle of maximum uncertainty dictates a pure strategy of terminating the game after one or two iterations  because it is not rational to think that a dream can have an accurate description. (This does not mean Statistical analysis can't be helpful in weeding out non-dreamers but you would need additional assumptions).

I suppose what the Professor is getting at is the notion that right-wing people are crazy and evil and they get together and start ranting and raving. But this may be even more true of left-wing academics. 

Similar remarks may help clarify why silly I Ching sayings,

Chinese literary culture solves many coordination and discoordination problems for very smart people spread across the globe. The same is true of traditional Hindu astrology. There are screening and signalling aspects to such civilizational artefacts. Moreover, they create ontologically dysphoric goods and services of a positional or prudential kind. 

astrological predictions, ethnic and religious differences,

which are the basis of nationality in many parts of the world. They are 'uncorrelated asymmetries' which dictate eusocial 'bourgeoise strategies' though, sadly, some ethnicities or religious sects may currently be unable to create viable states.   

or even QAnon conspiracies seem to so many to be so apt.

3Quarks has its own political slant. So what? We understand that different people have different affiliative needs. Pakistanis are bound to have sympathy for Palestinian Muslims. Sadly, they are currently having to deport a lot of Afghan refugees. Affiliation is all very well, but the Economy comes first. 

Their aptness is self‑provided and often bolstered by the group with whom they gradually choose to align ourselves.

Some people at Temple University are aligning themselves with Hamas. How long before some guy runs amok with a knife?  

To one degree or another we’re all prone to the party game of life.

Not if we know game theory. Scratch that. You need common sense to get what you want out of cocktail parties and political parties and other affiliative mechanisms.  

As F. Scott Fitzgerald famously wrote, “The test of a first-rate intelligence is the ability to hold two opposing ideas in mind at the same time and still retain the ability to function.”

Socrates said this was the mark of a philosopher. But a 'lover of wisdom' isn't necessarily wise and a lover of super-models, like myself, remains a sad and lonely virgin.  

Difficult as it may be, we have to forswear simple questions and answers,

No. We should stick to simple questions like 'how does this benefit me?' and settle for  answers which are 'good-enough' approximations or 'buck stopped' solutions to concurrency problems.  

be wary of the people with whom we associate,

be wary of certain types of associations. The trouble with cheering for 'pay for slay' terrorists is that they may want you to do a bit of knifing yourself. If you refuse, they laugh very loudly after they frame you for their own crimes and watch you rot in prison.  

and restrain our tendency to be seduced by just-so stories,

Jews did not immigrate to Palestine and buy land there. They invaded the place with their mighty air-force and colonized it. Then they instituted 'apartheid'. It became illegal for a Jew to marry an Arab. This is a 'just-so' story. Is this Professor going to come out against it? Not if he wants to continue to publish in 3Quarks. The people who run it may be pretty humane and liberal (the founder, who is Pakistani, personally re-posted an article showing UNRWA as complicit in Hamas's atrocities)  but they don't want to go the way of Salman Taseer, not to mention Salman Rushdie.  

our own and those of others. Voltaire was dead-on: believing absurdities can lead to committing atrocities.

Absurdly, he believed that a Jesuit text was actually an ancient Hindu text. But he committed no atrocities. Hamas has done so because it wants unconditional support from the get-go. So far, it has achieved its aim. Sadly, this may mean more misery for the Palestinians while Shia' Iran dominates the Fertile Crescent. What matters is that billionaires in Doha and TV stations in Erdogan's Turkey, not to mention the Ikhwan's position in the Iraqi administration, are secured for at least the next couple of years. 

Still, it is brave of this Math Professor to suggest that crazy 'pay for slay' nutters believe in an absurd creed. 

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