# Lawful Uncertainty

In Ra­tional Choice in an Uncer­tain World, Robyn Dawes de­scribes an ex­per­i­ment by Tver­sky:1

Many psy­cholog­i­cal ex­per­i­ments were con­ducted in the late 1950s and early 1960s in which sub­jects were asked to pre­dict the out­come of an event that had a ran­dom com­po­nent but yet had base-rate pre­dictabil­ity—for ex­am­ple, sub­jects were asked to pre­dict whether the next card the ex­per­i­menter turned over would be red or blue in a con­text in which 70% of the cards were blue, but in which the se­quence of red and blue cards was to­tally ran­dom.

In such a situ­a­tion, the strat­egy that will yield the high­est pro­por­tion of suc­cess is to pre­dict the more com­mon event. For ex­am­ple, if 70% of the cards are blue, then pre­dict­ing blue on ev­ery trial yields a 70% suc­cess rate.

What sub­jects tended to do in­stead, how­ever, was match prob­a­bil­ities—that is, pre­dict the more prob­a­ble event with the rel­a­tive fre­quency with which it oc­curred. For ex­am­ple, sub­jects tended to pre­dict 70% of the time that the blue card would oc­cur and 30% of the time that the red card would oc­cur. Such a strat­egy yields a 58% suc­cess rate, be­cause the sub­jects are cor­rect 70% of the time when the blue card oc­curs (which hap­pens with prob­a­bil­ity .70) and 30% of the time when the red card oc­curs (which hap­pens with prob­a­bil­ity .30); (.70×.70) + (.30×.30) = .58.

In fact, sub­jects pre­dict the more fre­quent event with a slightly higher prob­a­bil­ity than that with which it oc­curs, but do not come close to pre­dict­ing its oc­cur­rence 100% of the time, even when they are paid for the ac­cu­racy of their pre­dic­tions . . . For ex­am­ple, sub­jects who were paid a nickel for each cor­rect pre­dic­tion over a thou­sand tri­als . . . pre­dicted [the more com­mon event] 76% of the time.

Do not think that this ex­per­i­ment is about a minor flaw in gam­bling strate­gies. It com­pactly illus­trates the most im­por­tant idea in all of ra­tio­nal­ity.

Sub­jects just keep guess­ing red, as if they think they have some way of pre­dict­ing the ran­dom se­quence. Of this ex­per­i­ment Dawes goes on to say, “De­spite feed­back through a thou­sand tri­als, sub­jects can­not bring them­selves to be­lieve that the situ­a­tion is one in which they can­not pre­dict.”

But the er­ror must go deeper than that. Even if sub­jects think they’ve come up with a hy­poth­e­sis, they don’t have to ac­tu­ally bet on that pre­dic­tion in or­der to test their hy­poth­e­sis. They can say, “Now if this hy­poth­e­sis is cor­rect, the next card will be red”—and then just bet on blue. They can pick blue each time, ac­cu­mu­lat­ing as many nick­els as they can, while men­tally not­ing their pri­vate guesses for any pat­terns they thought they spot­ted. If their pre­dic­tions come out right, then they can switch to the newly dis­cov­ered se­quence.

I wouldn’t fault a sub­ject for con­tin­u­ing to in­vent hy­pothe­ses—how could they know the se­quence is truly be­yond their abil­ity to pre­dict? But I would fault a sub­ject for bet­ting on the guesses, when this wasn’t nec­es­sary to gather in­for­ma­tion, and liter­ally hun­dreds of ear­lier guesses had been dis­con­firmed.

Can even a hu­man be that over­con­fi­dent?

I would sus­pect that some­thing sim­pler is go­ing on—that the all-blue strat­egy just didn’t oc­cur to the sub­jects.

Peo­ple see a mix of mostly blue cards with some red, and sup­pose that the op­ti­mal bet­ting strat­egy must be a mix of mostly blue cards with some red.

It is a coun­ter­in­tu­itive idea that, given in­com­plete in­for­ma­tion, the op­ti­mal bet­ting strat­egy does not re­sem­ble a typ­i­cal se­quence of cards.

It is a coun­ter­in­tu­itive idea that the op­ti­mal strat­egy is to be­have lawfully, even in an en­vi­ron­ment that has ran­dom el­e­ments.

It seems like your be­hav­ior ought to be un­pre­dictable, just like the en­vi­ron­ment—but no! A ran­dom key does not open a ran­dom lock just be­cause they are “both ran­dom.”

You don’t fight fire with fire; you fight fire with wa­ter. But this thought in­volves an ex­tra step, a new con­cept not di­rectly ac­ti­vated by the prob­lem state­ment, and so it’s not the first idea that comes to mind.

In the dilemma of the blue and red cards, our par­tial knowl­edge tells us—on each and ev­ery round—that the best bet is blue. This ad­vice of our par­tial knowl­edge is the same on ev­ery sin­gle round. If 30% of the time we go against our par­tial knowl­edge and bet on red in­stead, then we will do worse thereby—be­cause now we’re be­ing out­right stupid, bet­ting on what we know is the less prob­a­ble out­come.

If you bet on red ev­ery round, you would do as badly as you could pos­si­bly do; you would be 100% stupid. If you bet on red 30% of the time, faced with 30% red cards, then you’re mak­ing your­self 30% stupid.

When your knowl­edge is in­com­plete—mean­ing that the world will seem to you to have an el­e­ment of ran­dom­ness—ran­dom­iz­ing your ac­tions doesn’t solve the prob­lem. Ran­dom­iz­ing your ac­tions takes you fur­ther from the tar­get, not closer. In a world already foggy, throw­ing away your in­tel­li­gence just makes things worse.

It is a coun­ter­in­tu­itive idea that the op­ti­mal strat­egy can be to think lawfully, even un­der con­di­tions of un­cer­tainty .

And so there are not many ra­tio­nal­ists, for most who per­ceive a chaotic world will try to fight chaos with chaos. You have to take an ex­tra step, and think of some­thing that doesn’t pop right into your mind, in or­der to imag­ine fight­ing fire with some­thing that is not it­self fire.

You have heard the un­en­light­ened ones say, “Ra­tion­al­ity works fine for deal­ing with ra­tio­nal peo­ple, but the world isn’t ra­tio­nal.” But faced with an ir­ra­tional op­po­nent, throw­ing away your own rea­son is not go­ing to help you . There are lawful forms of thought that still gen­er­ate the best re­sponse, even when faced with an op­po­nent who breaks those laws. De­ci­sion the­ory does not burst into flames and die when faced with an op­po­nent who di­s­obeys de­ci­sion the­ory.

This is no more ob­vi­ous than the idea of bet­ting all blue, faced with a se­quence of both blue and red cards. But each bet that you make on red is an ex­pected loss, and so too with ev­ery de­par­ture from the Way in your own think­ing.

How many Star Trek epi­sodes are thus re­futed? How many the­o­ries of AI?

1 Amos Tver­sky and Ward Ed­wards, “In­for­ma­tion ver­sus Re­ward in Bi­nary Choices,” Jour­nal of Ex­per­i­men­tal Psy­chol­ogy 71, no. 5 (1966): 680–683. See also Yaa­cov Schul and Ruth Mayo, “Search­ing for Cer­tainty in an Uncer­tain World: The Difficulty of Giv­ing Up the Ex­pe­ri­en­tial for the Ra­tional Mode of Think­ing,” Jour­nal of Be­hav­ioral De­ci­sion Mak­ing 16, no. 2 (2003): 93–106.

• For­ag­ing an­i­mals make the same ‘mis­take’: given two ter­ri­to­ries in which to for­age, one of which has a much more plen­tiful re­source and is far more likely to re­ward an in­vest­ment of effort and time with a pay­off, the ob­vi­ous strat­egy is to only for­age in the richer ter­ri­tory; how­ever, an­i­mals in­stead split their time be­tween the two spaces as the rel­a­tive prob­a­bil­ity of a suc­cess­ful re­turn.

In other words, if one ter­ri­tory is twice as likely to pro­duce food through for­ag­ing as the other, an­i­mals spend twice as much time there: 2/​3rds of their time in the richer ter­ri­tory, 1/​3rd of their time in the poorer. Similar pat­terns hold when there are more than two for­ag­ing ter­ri­to­ries in­volved.

Although this re­sults in a short-term re­duc­tion in food ac­qui­si­tion, it’s been shown that this strat­egy min­i­mizes the chances of ex­ploit­ing the re­source to lo­cal ex­tinc­tion, and en­sures that the sud­den loss of one ter­ri­tory for some rea­son (blight of the re­source, nat­u­ral di­aster, pre­da­tion threats, etc.) doesn’t re­sult in a to­tal in­abil­ity to find food.

The strat­egy is highly adap­tive in its origi­nal con­text. The prob­lem with hu­mans that we re­tain our evolved, adap­tive be­hav­iors long af­ter the con­text changes to make them non- or even mal-adap­tive.

• Surely if you told the sub­jects that 90% or 95% of the cards were blue, they might hy­poth­e­size or stum­ble upon the op­ti­mal solu­tion. So I won­der how high that num­ber needs to be. Or would they still guess red 1 out of 20 times?

• So, in short: “Ran­dom­ness is like poi­son: Yes, it can benefit you, but only if you feed it to peo­ple you don’t like.”

• IIRC, there ex­ist min­i­max strate­gies in some games that are stochas­tic. There are some games in which it is in fact best to fight ran­dom­ness with ran­dom­ness.

• Only when the op­po­nent has a brain.

• Go­ing into game the­ory, if an op­po­nent makes a truly ran­dom de­ci­sion be­tween two num­bers, and you win if you guess which num­ber they guessed, that would be a time that you should fight ran­dom­ness with ran­dom­ness. There aren’t a lot of other situ­a­tions where ran­dom­ness should be fought with ran­dom­ness but in situ­a­tions similar to that situ­a­tion that is the right move.

• If the other player is choos­ing ran­domly be­tween two num­bers, you will have a 50% chance of guess­ing his choice cor­rectly with any strat­egy what­so­ever. It doesn’t mat­ter whether your strat­egy is ran­dom or not; you can choose the first num­ber ev­ery time and you will still have ex­actly a 50% chance of get­ting it.

• But you want to be purely un­pre­dictable or the op­po­nent( if they are a su­per ai) would grad­u­ally figure out your strat­egy and have a slightly bet­ter chance. A hu­man(with­out tools) can’t ac­tully gen­er­ate a ran­dom num­ber. If your op­po­nent was guess­ing a non-com­pletely ran­dom num­ber/​ a “ran­dom” num­ber in their head, then you want your choice to be ran­dom. I should have said if the op­po­nent chooses a non-com­pletely ran­dom num­ber then you should ran­domly de­ter­mine your num­ber.

• You can gen­er­ate a ran­dom num­ber in your head by gen­er­at­ing sev­eral num­bers un­re­li­ably and tak­ing the sum mod X.

• That works for some pur­poses but it is not truly ran­dom so it would be bet­ter to use a dice or other more ran­dom num­ber if available. Of course, be re­al­is­tic with get­ting ran­dom num­bers. If the situ­a­tion calls for a quickly thought de­ci­sion, that works. If you have dice in your pocket go ahead and pull them out.

• Nomin­ull: By adding ran­dom­ness to your al­gorithm, you spread its be­hav­iors out over a par­tic­u­lar dis­tri­bu­tion, and there must be at least one point in that dis­tri­bu­tion whose ex­pected value is at least as high as the av­er­age ex­pected value of the dis­tri­bu­tion.

Well said! This is an ob­vi­ous point, but I’ve never heard it put quite so sharply be­fore.

• Alexei, they pre­dicted blue, that’s not the same as cor­rectly pre­dict­ing blue.

De­nis, that leapt out at me as well—who­ever wrote that sen­tence isn’t defin­ing “ra­tio­nal” the same way I do.

Cyan, that’ll be cov­ered in a fu­ture post. Cer­tainly in situ­a­tions of op­po­si­tion you will want to take ac­tions that are not pre­dictable to your op­po­nent, and so you’ll want to sam­ple some­thing as un­pre­dictable as pos­si­ble ac­cord­ing to a known, game-the­o­ret­i­cally de­ter­mined prob­a­bil­ity dis­tri­bu­tion. A quan­tum de­vice is fine for this, but re­al­is­ti­cally, so is ther­mal un­cer­tainty and strong cryp­to­graphic ran­dom-num­ber gen­er­a­tors. To look at it an­other way, what you’re do­ing in this situ­a­tion is not so much be­ing clever your­self, but rather re­duc­ing the op­ti­miza­tion power of your op­po­nent—cer­tainly chaos and noise can act as an an­ti­dote to in­tel­li­gence.

• Put­ting ran­dom­ness in your al­gorithms is only use­ful when there are sec­ond-or­der effects, when some­how re­al­ity changes based on the con­tent of your al­gorithm in some way other than you ex­e­cut­ing your al­gorith. We see this in Rock-Paper-Scis­sors, where you use ran­dom­ness to keep your op­po­nent from pre­dict­ing your moves based on learn­ing your al­gorithm.

Bar­ring these sec­ond or­der effects, it should be plain that ran­dom­ness can’t be the best strat­egy, or at least that there’s a non-ran­dom strat­egy that’s just as good. By adding ran­dom­ness to your al­gorithm, you spread its be­hav­iors out over a par­tic­u­lar dis­tri­bu­tion, and there must be at least one point in that dis­tri­bu­tion whose ex­pected value is at least as high as the av­er­age ex­pected value of the dis­tri­bu­tion.

• A lot of com­ments say­ing var­i­ous forms of “well but for some situ­a­tions it *is* best to be ran­dom.” Fine, maybe so; but the de­ci­sion to ‘act ran­domly’ is ar­rived af­ter a care­ful anal­y­sis of the situ­a­tion. It is the most ra­tio­nal thing to do *in that in­stance.* That doesn’t mean that de­ci­sion the­ory is thus re­futed at all. Reach­ing the the con­clu­sion that you’re play­ing a min­max stochas­tic game in which the best way for­ward is to play at ran­dom is not at all the same as “might as well just be ran­dom all the time in the face of some­thing that seems ir­ra­tional.”

Act­ing ran­domly *all the time* be­cause hey the world is ran­dom is in fact use­less. Yes, some­times you’ll hit the right an­swer (30% of the cards were red af­ter all) but if you’re not en­gag­ing in ‘ran­dom’ be­hav­ior as part of a larger strat­egy or goal then you’re just throw­ing ev­ery­thing at the wall and see­ing what sticks (granted some­times brute-forc­ing an an­swer is also the best way for­ward).

Ar­gu­ing about ‘well in *this one in­stance* it is best to be ran­dom’ is en­tirely beside the point. The point is how do you reach that con­clu­sion and by what thought pro­cesses?

‘If faced with ir­ra­tional­ity, throw­ing your own rea­son away won’t help you’ is ex­actly cor­rect. Con­versely, when faced with ra­tio­nal­ity then act­ing ir­ra­tionally won’t help you ei­ther. Un­like the pop­u­lar me­dia trope, in real life you’re not re­ally go­ing to baf­fle and thus defeat the com­puter op­po­nent by just play­ing at ran­dom. You’re not re­ally go­ing to beat a chess mas­ter in the park by just play­ing ran­domly in or­der to con­fuse them.

• @Mike

I got the point of Eliezer’s post, and I don’t see why I’m wrong. Could you tell me more speci­fi­cally than “for the rea­sons stated” why I’m wrong?

• The as­sump­tion be­hind this post, as An­neC touched on, is that higher scores are lin­early cor­re­lated to what is per­ceived as a good out­come. Guess­ing blue ev­ery time will guaran­tee a worst case and best case out­come of 70%; as such, guess­ing ran­domly be­comes a much bet­ter strat­egy if the player puts a sig­nifi­cant pre­mium on scor­ing, say, 95% or higher. Whether this val­u­a­tion is ra­tio­nally jus­tifi­able is an­other ques­tion en­tirely (though an im­por­tant one).

The same as­sump­tion lies be­hind A Pickup Artist’s post. It all de­pends on your ob­jec­tive: if you want to sleep with as many women as pos­si­ble, rou­tines are prob­a­bly the best bet, though likely it de­pends on your per­son­al­ity. If in­stead you are look­ing for deep, mean­ingful re­la­tion­ships with women, rou­tines may have a place, but nat­u­ral game will take you fur­ther.

• There are caveats though. For in­stance, if the op­po­nent is an ac­tual op­po­nent, ie, some­thing that in some way mod­els the world and so on.

If so, then at times it may be de­sir­able to re­duce the ac­cu­racy of the op­po­nent’s model of the world, or at least that part of it that con­sists of you. So you may want to then have some as­pect of your ac­tions be al­gorith­mi­cally more com­plex than your op­po­nent can com­pu­ta­tion­ally deal with, so some form of ran­dom­ness may be of use.

• I think the be­hav­ior we are see­ing here may be more a case of loss aver­sion rather than any­thing else.

As­sum­ing that red cards must come at some point (true if we are flip­ping over a limited set of cards with a blue-red ra­tio of 7 to 3; not sure if that is the setup), the sub­jects adopt a strat­egy that gives them the high­est like­li­hood of avoid­ing failure com­pletely. Pre­dict­ing blue cards ev­ery time re­quires ac­cept­ing a cer­tain de­gree failure right from the out­set and is thus un­palat­able to the hu­man mind which is loss-averse.

Even if the ex­per­i­ment is de­signed so that red cards are not guaran­teed to come at some point (if, for ex­am­ple, you shuffle af­ter ev­ery flip), the sub­jects may fall prey to gam­bler’s fal­lacy, which, when com­bined with their loss-aver­sion, leads them to adopt the 70-30 strat­egy.

• OK, upon read­ing the ex­per­i­men­tal premise (I blocked out the rest of the text be­low that so it wouldn’t in­fluence me) the very first idea, the idea that seemed most ob­vi­ous to me, was to bet on blue ev­ery time.

I ba­si­cally figured that if I had 10 cards, and 7 of them were blue, and I had to guess the color of all the cards at once (rather than be­ing given them se­quen­tially, which would give me the op­por­tu­nity to take notes and keep track of how many of each had already ap­peared), then the most re­li­able way of achiev­ing the most “hits” would be to pre­dict that each card would be blue. That way I’d be guaran­teed a cor­rect an­swer as to the color of 7 of the 10 cards.

At the same time I’d know I’d be wrong about 3 of the cards go­ing into the ex­per­i­ment, but this wouldn’t con­cern me if my goal was to max­i­mize cor­rect an­swers, and I was given only the in­for­ma­tion that 70% of the cards were blue while 30% were red, and that they were ar­ranged in a ran­dom or­der. Short of mov­ing out­side the con­di­tions of the ex­per­i­ment (and try­ing to, for in­stance, peek at the cards), there sim­ply isn’t any path to in­for­ma­tion about what’s on them.

Now, if it were a mat­ter of, “Guess the col­ors of all the cards ex­actly or we’ll shoot you”, I’d be mo­ti­vated to try and find ways out­side the ex­per­i­men­tal con­straints—as I’m sure most peo­ple would be. It would be in­ter­est­ing, though, to test peo­ple’s con­vic­tion that their self-made al­gorithms were valid by propos­ing that sce­nario. Ob­vi­ously not ac­tu­ally threat­en­ing peo­ple, but ask­ing them to re-eval­u­ate their con­fi­dence in light of the hy­po­thet­i­cal sce­nario. I’d be cu­ri­ous to know if most peo­ple would be look­ing for ways to ob­tain more in­for­ma­tion (i.e., “cheat” per the ex­per­i­ment), or whether they’d stick to their the­o­ries.

• Com­ing back to this post, I don’t un­der­stand what Eliezer means by “ra­tio­nal­ity” here. The game de­scribed isn’t the log-score game, and the in­put se­quence is de­scribed as un­com­putable (“truly ran­dom”), so I guess Solomonoff in­duc­tion will also fare asymp­tot­i­cally worse than a hu­man who always bets on blue. Does any­one have an ideal­ized model of a ra­tio­nal agent that can “bring it­self to be­lieve that the situ­a­tion is one in which it can­not pre­dict”?

• An im­por­tant point to make, but what of the op­ti­mal meta-strat­egy (strat­egy in form­ing strate­gies)?

I recog­nise the enor­mous ad­van­tage that a for­mal (rea­soned) anal­y­sis of a prob­lem pro­vides how­ever is this strat­egy statis­ti­cally op­ti­mal (i.e. likely to lead to a win) in most en­vi­ron­ments?

For ex­am­ple, most challenges are time limited, so ex­ten­sive anal­y­sis is im­prac­ti­cal. In ad­di­tion, the prob­lem (and the solu­tion) may not lend it­self to ra­tio­nal anal­y­sis but in­stead re­quire in­ter­nal men­tal statis­ti­cal mod­el­ling (e.g. how should I throw a rock in or­der to hit a tar­get may be best an­swered by re­peat­edly try­ing).

In the ex­am­ple in the ar­ti­cle the as­sump­tion that the deck of cards is ran­dom may it­self be un­rea­son­able (and when av­er­aged over many challenges may be a sub-op­ti­mal heuris­tic). The strat­egy em­ployed by those play­ing may ap­pear ran­dom but may in fact rep­re­sent an (in­for­ma­tion the­o­ret­i­cally) op­ti­mal hy­poth­e­sis of the likely next re­sult given the pre­vi­ous in­puts ex­ploit­ing a set of mod­el­ling heuris­tics that are them­selves op­ti­mal se­lec­tions given the past ex­pe­rience and ge­netic his­tory. This is likely to pro­duce an out­put that had a match­ing dis­tri­bu­tion (be­cause in a situ­a­tion where a cor­rect model could be pro­duced it would have this dis­tri­bu­tion). The ar­gu­ment that some prob­lems ‘are not ra­tio­nal’ may ac­tu­ally be an in­di­ca­tion that the prob­lem solv­ing strat­egy of rea­soned anal­y­sis has not pro­duced pos­i­tive re­sults in their ex­pe­rience and so they are ac­cu­rately com­mu­ni­cat­ing their statis­ti­cal meta-knowl­edge. For them to al­ter their strat­egy in an op­ti­mal way would re­quire that they had a statis­ti­cally valid rea­son for do­ing so, i.e. that they were aware that such ap­proaches had led to su­pe­rior re­sults in the past. Of course they have no means of com­mu­ni­cat­ing this way be­cause their ex­pe­riences have not led them to de­velop the con­scious mod­els that would en­able that kind of self aware­ness.

• I think you’re right that the sub­jects in the ex­per­i­ment sim­ply don’t think of the 100% blue strat­egy, and I won­der if there’s any way to find out why it’s so un­aes­thetic that it doesn’t cross peo­ple’s minds.

My ten­ta­tive the­ory is that con­for­mity is a good strat­egy for deal­ing with peo­ple if you don’t have a definite rea­son for do­ing some­thing else, and that the sub­jects are mod­el­ing the uni­verse (or at least the ran­dom se­quence) as con­scious.

In­tro­spect­ing, I think that choos­ing 100% blue also feels like choos­ing to be wrong some of the time, so some loss aver­sion kicks in, while do­ing a 7030 strat­egy feels like try­ing to be right ev­ery time.

“Even a hu­man” might just be a fair in­sult.

• Chicken is not a good ex­am­ple of a ran­dom game. The best strat­egy is to be a bloody minded SOB, if you can’t con­vince your op­po­nent that you are ac­tu­ally crazy. This is more or less what I got from Schel­ling’s es­says in “Strat­egy of Con­flict”.
And if you both do that, you both crash and die. It is not the best re­sponse to it­self, so can’t be seen to be a Nash equil­ibrium.

• I won­der what the pre­dic­tion per­centages in the ex­per­i­ment were, con­di­tional on the color of the pre­vi­ous card?

• “When your knowl­edge is in­com­plete—mean­ing that the world will seem to you to have an el­e­ment of ran­dom­ness—ran­dom­iz­ing your ac­tions doesn’t solve the problem

“Ants don’t agree. Take away their food. They’ll go in to ran­dom search mode.”

It de­pends on your de­gree of ig­no­rance. When to­tally ig­no­rant try any­thing, at the least you’ll learn some­thing that doesn’t work, and watch­ing how it fails should teach you more. Other­wise, you should use your best knowl­edge, with­out ran­dom in­put. It works for ants, more or less, but for any­thing with more in­tel­li­gence and knowl­edge, us­ing the in­tel­li­gence and knowl­edge will work much bet­ter. Even ants only use ran­dom search when they need to.

Chicken is not a good ex­am­ple of a ran­dom game. The best strat­egy is to be a bloody minded SOB, if you can’t con­vince your op­po­nent that you are ac­tu­ally crazy. This is more or less what I got from Schel­ling’s es­says in “Strat­egy of Con­flict”.

• Even in some cases where you might think that the best game-the­o­retic strat­egy in­volves ran­dom­ness, the ac­tual best strat­egy is to play non-ran­domly—e.g. see Der­ren Brown—Paper, Scis­sors, Stone.

• Great post! I think this an­swers one com­mon de­bate in the Pickup Com­mu­nity: rou­tines vs. no rou­tines game.

In case you don’t know what I’m talk­ing about:

When ap­proach­ing lots of women is it bet­ter to en­gage in spon­ta­neous con­ver­sa­tion with each and ev­ery one or to always use the same, tried and true ma­te­rial(canned rou­tines)? Rou­tines win!

• When your knowl­edge is in­com­plete—mean­ing that the world will seem to you to have an el­e­ment of ran­dom­ness—ran­dom­iz­ing your ac­tions doesn’t solve the problem

Ants don’t agree. Take away their food. They’ll go in to ran­dom search mode.

As far as that ex­per­i­ment is con­cerned, it seems that An­neC hits the point: How was it framed? Were the sub­jects led to be­lieve that they were search­ing for a pat­tern? Or were they told the pat­tern? Wild guess: the former.

• Thanks for this post. I have always thought this way about bets (I always call ‘tails’ in a coin flip, for ex­am­ple), and I had a lot of trou­ble try­ing to ex­plain to my friends why if I was go­ing to play the lot­tery, I’d have a set of num­bers I’d play ev­ery time. I ap­pre­ci­ate see­ing this spel­led out so clearly.

• If you wanted to play the lot­tery, the best strat­egy is to play the “least lucky” and “least ‘ran­dom’” num­bers, ie pick the num­bers that won’t be picked by a bunch of su­per­sti­tious peo­ple. De­crease your odds of hav­ing the split the win­nings with an­other win­ner.

• [The fol­low­ing is just me be­ing slightly in­sane about prob­a­bil­ity and has no bear­ing on the point of the ar­ti­cal]

I have to point out some flaws with the prob­a­bil­ity that you are us­ing here. For the most part bet­ting blue all the time works. How­ever Cards don’t work quite like that. Each draw of the cards re­duces the to­tal num­ber of the card that was drawn. For in­stance if you have 10 cards, 7 blue, 3 red, and af­ter the first 7 draws there have been 6 blue cards drawn, but only one red card drawn then the prob­a­bil­ity now fa­vors draw­ing a red card. In fact, if now you switch to call­ing red for ev­ery card you can achieve an 80% suc­cess rate over all be­cause now there is only 1 blue card left, but two red cards. Just be­cause you have come up with a strat­egy for suc­cess does not mean that you should stop think­ing and re­assess­ing the situ­a­tion as more in­for­ma­tion be­comes known.

• “There are lawful forms of thought that still gen­er­ate the best re­sponse, even when faced with an op­po­nent who breaks those laws”

I’ve only just come to the Bayesian way of thought, so please di­rect me to the cor­rect an­swer if I’m not think­ing about this right:

If I and my op­po­nent are of equal train­ing, ra­tio­nal­ity, abilty, and in­tel­lect, ex­cept that my op­po­nent has a 10% chance of do­ing some­thing com­pletely at odds with ra­tio­nal­ity as we both un­der­stand it due to some men­tal dam­age: how should I plan to face him?

If I have plan A to deal with his plan A, plan B to deal with his plan B, and so on (as close as I am ca­pa­ble of dis­cern­ing them), is there a ra­tio­nal way to deal with this un­pre­dictable el­e­ment, and how do I de­ter­mine how much of my re­sources to spend on this plan?

That is: how do I plan in the face of the un­pre­dictable, es­pe­cially in cases where I do not have the re­sources to cover ev­ery even­tu­al­ity?

• I was as­sum­ing that run­ning, say, 100 tri­als meant go­ing all the way through a 100-card deck with­out shuffling.

I be­lieve this should be the case. There’s no need to reshuffle be­tween each trial be­cause it would un­nec­es­sar­ily com­pli­cate things. I’d as­sume they reshuffled a deck of hun­dred cards af­ter ev­ery 100 tri­als.

Also, if you put the card back and reshuffle, you can­not guaran­tee a %70 suc­cess rate as de­scribed.

• Just to clar­ify the util­ity of ran­dom­ness is­sue, I think what some re­spon­dents are talk­ing about is the benefit of un­pre­dictablility, which is in­stru­men­tal when play­ing a game against a live op­po­nent. This is to­tally differ­ent from ran­dom­iz­ing. I also don’t think that say­ing that ants “ran­domly” search for food is the most ac­cu­rate way to de­scribe their pro­cess. So ran­dom­ness, in its strict in­ter­pre­ta­tion, is never op­ti­mal game strat­egy. Another thought I had is that there are some cir­cum­stances in which it would make sense to change one’s pre­dic­tion to red. If you had a good idea how many to­tal cards were left and had the knowl­edge that blue cards had sig­nifi­cantly over-rep­re­sented them­selves (50 to­tal cards, 30 already flipped, all blue), it would lead to the con­clu­sion that over half of the re­main­ing cards would be red. Such a cir­cum­stance could lead to a higher than 70% suc­cess rate.

• Ran­dom search can be an effec­tive strat­egy due to bounded ra­tio­nal­ity. As pointed el­se­where on this thread, the ex­pected util­ity of a mixed strat­egy is not greater than the max­i­mum util­ity of the pure strate­gies in its sup­port. But de­ter­min­ing the util­ity of the pure strate­gies may not be pos­si­ble. For ex­am­ple, an ant can­not carry the neu­ral ma­chin­ery nec­es­sary to re­mem­ber ev­ery­thing it has seen, or to use such in­for­ma­tion to de­ter­mine with ac­cu­racy the most likely di­rec­tion to food—but it can carry suffi­cient neu­ral ma­chin­ery to perform a ran­dom walk.

• I was won­der­ing whether to make the pedan­tic point that some­times peo­ple do fight fire with fire, by seek­ing to stop a for­est fire by burn­ing a patch in the fire’s path, so that the fire can­not leap over that patch.

I think too much pedantry can paralyse thought, but if our aim is ra­tio­nal­ity we should avoid un­truths.

• @michael e sullivan

You are right, my mis­take. I was as­sum­ing that run­ning, say, 100 tri­als meant go­ing all the way through a 100-card deck with­out shuffling. Go­ing back over the de­scrip­tion of the prob­lem, I don’t see where it ex­plic­itly says that the cards are re­placed and reshuffled, but that’s prob­a­bly a more mean­ingful ex­per­i­ment to run, and I’m sure that’s how they did it.

At least I’m not crazy (nor, hope­fully, stupid, if only 30%). :)

@A Pickup Artist

• We are talk­ing past each other some­what. I’m talk­ing about the the­o­ret­i­cal one shot/​no com­mu­ni­ca­tion game the­ory ver­sion of chicken. This has a mixed strat­egy as an equil­ibrium. You are talk­ing about the testos­terone fueled young lad car ver­sion. Which doesn’t have a nice math­e­mat­i­cal anal­y­sis, or best strat­egy as such.

• “And if you both do that, you both crash and die. It is not the best re­sponse to it­self, so can’t be seen to be a Nash equil­ibrium.”

Of course it’s not. I was mainly ob­ject­ing to the ear­lier com­ment that it was an ex­am­ple of a ran­dom game. The it is is a psy­cholog­i­cal game—ideally, you want to con­vince your op­po­nent be­fore the game starts that you’ll drive right into him if you need to to win.

• @Stu­art Arm­strong: First of all, the strongest in­fluence on fu­ture suc­cess in so­ciety is whether or not one is already suc­cess­ful (most eas­ily ac­com­plished by hav­ing suc­cess­ful par­ents). One would also ex­pect some per­centage of non-ra­tio­nal­ists to suc­ceed any­ways sim­ply through chance. As­sum­ing that non-ra­tio­nal­ists sub­stan­tially out­num­ber ra­tio­nal­ists, it isn’t ter­ribly sur­pris­ing to see more of the former among suc­cess­ful peo­ple. Rather than look­ing at how many suc­cess­ful peo­ple are ra­tio­nal­ists, it would be more in­for­ma­tive to look at ra­tio­nal peo­ple and see how many be­come more suc­cess­ful over their lives com­pared to av­er­age. Or, you could try and es­ti­mate the like­li­hoods of be­ing ra­tio­nal, be­ing suc­cess­ful, and be­ing ra­tio­nal given suc­cess, then ap­ply Bayes’ law...

Also, if ra­tio­nal­ists seem more skil­led at avoid­ing failure than at win­ning, per­haps that merely sug­gests that failure is more pre­dictable than suc­cess?

• It is a coun­ter­in­tu­itive idea that the op­ti­mal strat­egy can be to think lawfully, even un­der con­di­tions of un­cer­tainty.

Nicely put. I can think of ex­am­ples where you should think chaot­i­cally in or­der to solve a chaotic prob­lem—but they’re very con­voluted, unatu­ral ex­am­ples.

One thing still nig­gles me; the fact that ra­tio­nal­ists should win. Look­ing around sucess­ful peo­ple, I see more ra­tio­nal­ists than the av­er­age—but not much more. Our so­ciety is noisy, yes, but ra­tio­nal­ists should still win much more of­ten than they do. Ra­tion­al­ists seem more skil­led at avoid­ing los­ing, than at ac­tu­ally win­ning.

• @A Pickup Artist

I got the point of Eliezer’s post, and I don’t see why I’m wrong. Could you tell me more speci­fi­cally than “for the rea­sons stated” why I’m wrong? And while you’re at it, ex­plain to me your op­ti­mal strat­egy in An­neC’s vari­a­tion of the game (you’re shot if you get one wrong), as­sum­ing you can’t effec­tively cheat.

(In­ci­den­tally, and some­what off-topic, there’s a beau­tiful puz­zle with a similar setup — see “Names in Boxes” on the first page of http://​​math.dart­mouth.edu/​​~pw/​​solu­tions.pdf. The solu­tions are in­cluded, but try to figure it out for your­self. It’s worth it.)

I’ll con­cede the point on rou­tines. Since so much of hu­man in­ter­ac­tion is scripted any­way (where are you from? what do you do? etc.), the differ­ence be­tween us­ing canned ma­te­rial and not is hard to pin down. I’d love to see a study done on the sub­ject, but it would be dev­il­ishly difficult to de­sign a good one.

• A Pickup Artist,

(kind of off topic)

I am also a PUA and have thought about this de­bate for a while. I think that suc­cess­ful rou­tines can ex­pire af­ter some point. If a girl has heard your rou­tine be­fore, she is likely to turn you down. The best rou­tines are ones that abide by the LOAs and where the tar­get doesn’t know the rou­tine. This un­pre­dictable fac­tor in your rou­tine demon­strates ro­mance, in­tel­li­gence, spon­tane­ity and other alpha male qual­ities.

Buy­ing a po­ten­tial fe­male a drink at the bar is a perfect ex­am­ple of an ex­pired method. The Buy You a Drink rou­tine the­o­ret­i­cally makes sense (shows eco­nomic sta­tus), as it abides by the LOAs. The prob­lem is that this method is too widely used and ex­poses the PA or AFC as pre­dictable, un­o­rigi­nal, un­ro­man­tic, and bad in­ten­tioned. This failure should em­pha­sis the im­por­tance of us­ing per­son­al­ized and origi­nal meth­ods.

• @Mike Plotz:

I guess you missed the whole point of Eliezer’s post. What you said is ex­actly wrong for the rea­sons stated!

Btw, rou­tines are still the best strat­egy even if you want to have mean­ingful re­la­tion­ships. The rou­tines are there to cover the first 10-20 min­utes of a cold ap­proach(where you and the woman are strangers to each oth­ers). After that you should have mu­tual at­trac­tion in most cases(that’s where the ran­dom­ness comes in and the im­por­tance of hav­ing a sys­tem­atic win­ning strat­egy, see the post). Then it’s the time where you drop the rou­tines and can start hav­ing deeper con­ver­sa­tions. It’s called the com­fort phase.

Btw, you shouldn’t use rou­tines in warm ap­proach(where the woman knows you be­cause she is in your so­cial cir­cle or in­tro­duced through friends). That’s a differ­ent game.

The thing with cold ap­proach is that you only have a limited timeframe(min­utes) to cre­ate a pos­i­tive im­pres­sion. Think of meet­ing a woman in a night­club or walk­ing in the mall. You want to op­ti­mize this ini­tial in­ter­ac­tion to guaran­tee a chance to see her again. From 100 women you ap­proach how many will find you at­trac­tive based on the per­son­al­ity you man­age to con­vey in those few first min­utes? A good pickup artist can have a suc­cess rate of 10% or higher. That’s the art.

• I’m as­sum­ing the cards were not taken from a countable pile? Can some­one con­firm this?

• Peter de Blanc, I don’t have an ex­am­ple, just a vague mem­ory of read­ing about min­i­max-op­ti­mal de­ci­sion rules in J. O. Berger’s Statis­ti­cal De­ci­sion The­ory and Bayesian Anal­y­sis. (That same text notes that min­i­max rules are Bayes rules un­der the as­sump­tion that your op­po­nent is out to get you.)

• Chicken is a game where it is best to be ran­dom. You are ran­dom be­cause you don’t want to be pre­dictable and thus ex­ploitable.

• If you’re pre­dictably com­mit­ted to win­ning the game of chicken, then you have es­sen­tially already won, at least against a ra­tio­nal op­po­nent. Though you’d have to won­der how you wound up with a ra­tio­nal op­po­nent if the game is chicken.

• “For ex­am­ple, sub­jects who were paid a nickel for each cor­rect pre­dic­tion over a thou­sand tri­als… pre­dicted [the more com­mon event] 76% of the time.”

How it could be? Psy­chic power?

• Eliezer: how does this square with Robin’s re­cent What Belief Con­for­mity?

He quoted:

“physi­cists and math­e­mat­i­ci­ans perform best in terms of “ra­tio­nal­ity” (i.e. perfor­mance ac­cord­ing to the­ory) and psy­chol­o­gists worst. How­ever, since “ra­tio­nal” be­hav­ior is only prof­itable when other sub­jects also be­have ra­tio­nally … the rank­ing in terms of prof­its is just the op­po­site: psy­chol­o­gists are best and physi­cists are worst.”

• Cyan:

I think you might be con­flat­ing ig­no­rance by one­self of one’s own fu­ture ac­tions with ig­no­rance by an op­po­nent of one’s fu­ture ac­tions, but I’d like to see your ex­am­ple be­fore I judge you.

• Mike Plotz: I got the point of Eliezer’s post, and I don’t see why I’m wrong. Could you tell me more speci­fi­cally than “for the rea­sons stated” why I’m wrong? And while you’re at it, ex­plain to me your op­ti­mal strat­egy in An­neC’s vari­a­tion of the game (you’re shot if you get one wrong), as­sum­ing you can’t effec­tively cheat.

In some games, your kind of strat­egy might work, but in this one it doesn’t. From the prob­lem state­ment, we are to as­sume the cards are re­placed and reshuffled be­tween each tri­als so that ev­ery trial has a 70% chance of be­ing blue or red.

In ev­ery sin­gle case, it is more likely that the next card is blue. Even in the game where you are shot if you get one wrong, you should still pick blue ev­ery time. The rea­son is that of all the pos­si­ble com­bi­na­tions of cards cho­sen for the whole game, the com­bi­na­tion that con­sists of all blue cards is the most likely one. It is more likely than any par­tic­u­lar com­bi­na­tion that in­cludes a red card. Be­cause at ev­ery step, a blue card is more likely than a red one. Just be­cause you pick a red card, doesn’t give you credit for any­where a red card might pop up. You have to pick it in the right spot if you want to live. And your chances of do­ing that in any par­tic­u­lar spot are less than the chances of pick­ing the blue card cor­rectly.

There are games where you adopt a strat­egy with greater var­i­ance in or­der to max­i­mize the pos­si­bil­ity of an un­likely win, rather than go for the high­est ex­pected value (within the game), be­cause the best ex­pected out­come is a loss. Clas­sic ex­am­ple would be the hail mary pass in foot­ball. Ex­pected out­come is worse (in yards) than just run­ning a nor­mal play, or teams would do it all the time. But if there are only 5 sec­onds on the clock and you need a touch­down, the nor­mal play might win 1 in 1000 games, while the hail mary wins 1 in 50. But there is no differ­ence in var­i­ance in choos­ing red or blue in the game de­scribed here, so that kind of strat­egy doesn’t ap­ply.

• In sum­mary.

This ar­ti­cle seems to re-af­firm: You de­velop a the­ory and test it by mak­ing fur­ther ob­ser­va­tions and fol­low­ing sci­en­tific method. (which you should all have mem­o­rised)

How­ever one crit­i­cism i have is of the statis­tics gained at the be­gin­ning. Surly the challenge is to de­velop an op­ti­mum the­ory to pre­dict the right card most of­ten. Surly this ob­jec­tive is the same no mat­ter who is be­ing tested, or how many peo­ple are be­ing tested. The ques­tion would then be­come; what the­ory did you use to get your high score? And most an­swers would be; card count­ing.