Contrite Strategies and The Need For Standards

Link post

Epistemic Sta­tus: Confident

There’s a re­ally in­ter­est­ing pa­per from 1996 called The Logic of Con­tri­tion, which I’ll sum­ma­rize here. In it, the au­thors iden­tify a strat­egy called “Con­trite Tit For Tat”, which does bet­ter than ei­ther Pavlov or Gen­er­ous Tit For Tat in Iter­ated Pri­soner’s Dilemma.

In Con­trite Tit For Tat, the player doesn’t only look at what he and the other player played on the last term, but also an­other vari­able, the stand­ing of the play­ers, which can be good or bad.

If Bob defected on Alice last round but Alice was in good stand­ing, then Bob’s stand­ing switches to bad, and Alice defects against Bob.

If Bob defected on Alice last round but Alice was in bad stand­ing, then Bob’s stand­ing stays good, and Alice co­op­er­ates with Bob.

If Bob co­op­er­ated with Alice last round, Bob keeps his good stand­ing, and Alice co­op­er­ates.

This al­lows two Con­trite Tit For Tat play­ers to re­cover quickly from ac­ci­den­tal defec­tions with­out defect­ing against each other for­ever;

D/​C → C/​D → C/​C

But, un­like Pavlov, it con­sis­tently re­sists the “always defect” strategy

D/​C → D/​D → D/​D → D/​D …

Like TFT (Tit For Tat) and un­like Pavlov and gTFT (Gen­er­ous Tit For Tat), cTFT (Con­trite Tit For Tat) can in­vade a pop­u­la­tion of all Defec­tors.

A re­lated con­trite strat­egy is Re­morse. Re­morse co­op­er­ates only if it is in bad stand­ing, or if both play­ers co­op­er­ated in the pre­vi­ous round. In other words, Re­morse is more ag­gres­sive; un­like cTFT, it can at­tack co­op­er­a­tors.

Against the strat­egy “always co­op­er­ate”, cTFT always co­op­er­ates but Re­morse al­ter­nates co­op­er­at­ing and defect­ing:

C/​C → C/​D → C/​C → C/​D …

And Re­morse defends effec­tively against defec­tors:

D/​C → D/​D → D/​D → D/​D…

But if one Re­morse ac­ci­den­tally defects against an­other, re­cov­ery is more difficult:

C/​D → D/​C → D/​D → C/​D → …

If the Pri­soner’s Dilemma is re­peated a large but finite num­ber of times, cTFT is an evolu­tion­ar­ily sta­ble state in the sense that you can’t do bet­ter for your­self when play­ing against a cTFT player through do­ing any­thing that de­vi­ates from what cTFT would recom­mend. This im­plies that no other strat­egy can suc­cess­fully in­vade a pop­u­la­tion of all cTFT’s.

REMORSE can some­times be in­vaded by strate­gies bet­ter at co­op­er­at­ing with them­selves, while Pavlov can some­times be in­vaded by Defec­tors, de­pend­ing on the pay­off ma­trix; but for all Pri­soner’s Dilemma pay­off ma­tri­ces, cTFT re­sists in­va­sion.

Defec­tor and a similar strat­egy called Grim Trig­ger (if a player ever defects on you, keep defect­ing for­ever) are evolu­tion­ar­ily sta­ble, but not good out­comes — they re­sult in much lower scores for ev­ery­one in the pop­u­la­tion than TFT or its var­i­ants. By con­trast, a whole pop­u­la­tion that adopts cTFT, gTFT, Pavlov, or Re­morse on av­er­age gets the pay­off from co­op­er­at­ing each round.

The bot­tom line is, adding “con­tri­tion” to TFT makes it quite a bit bet­ter, and al­lows it to keep pace with Pavlov in ex­ploit­ing TFT’s, while do­ing bet­ter than Pavlov at ex­ploit­ing Defec­tors.

This is no longer true if we add noise in the per­cep­tion of good or bad stand­ing; con­trite strate­gies, like TFT, can get stuck defect­ing against each other if they er­ro­neously per­ceive bad stand­ing.

The moral of the story is that there’s a game-the­o­retic ad­van­tage to not only hav­ing re­ciproc­ity (TFT) but stan­dards (cTFT), and in fact re­ciproc­ity alone is not enough to out­perform strate­gies like Pavlov which don’t map well to hu­man moral max­ims.

What do I mean by stan­dards?

There’s a differ­ence be­tween say­ing “Be­hav­ior X is bet­ter than be­hav­ior Y” and say­ing “Be­hav­ior Y is un­ac­cept­able.”

The con­cept of “un­ac­cept­able” be­hav­ior func­tions like the con­cept of “stand­ing” in the game the­ory pa­per. If I do some­thing “un­ac­cept­able” and you re­spond in some nega­tive way (you get mad or pun­ish me or w/​e), I’m not sup­posed to re­tal­i­ate against your nega­tive re­sponse, I’m sup­posed to ac­cept it.

Pure re­ciproc­ity re­sults in blood feuds — “if you kill one of my fam­ily I’ll kill one of yours” is perfectly sound Tit For Tat rea­son­ing, but it means that we can’t stop kil­ling once we’ve started.

Ar­bi­trary for­give­ness fixes that prob­lem and al­lows par­ties to rec­on­cile even if they’ve been fight­ing, but still leaves you vuln­er­a­ble to an at­tacker who just won’t quit.

Con­trite strate­gies are like hav­ing a court sys­tem. (Though not an en­force­ment sys­tem! They are still “an­ar­chist” in that sense — all cTFT bots are equal.) The “stand­ing” is an as­sess­ment at­tached to each per­son of whether they are in the wrong and thereby re­stricted in their per­mis­sion to re­tal­i­ate.

In gen­eral, for ac­tions not cov­ered by the le­gal sys­tem and even for some that are, we don’t have widely shared stan­dards of ac­cept­able vs. un­ac­cept­able be­hav­ior. We’re aware (and es­pe­cially so given the in­ter­net) that these stan­dards differ from sub­cul­ture to sub­cul­ture and con­text to con­text, and we’re of­ten aware that they’re ar­bi­trary, and so we have enor­mous difficulty get­ting widely shared clar­ity on claims like “he was de­cep­tive and that’s not OK”. Be­cause…was he de­cep­tive in a way that counts as fraud? Was it just “puffery” of the kind that’s nor­mal in PR? Was it a white lie to spare some­one’s feel­ings? Was it “just vent­ing” and thus not ex­pected to be as nu­anced or fact-checked as more for­mal speech? What level or stan­dard of hon­esty could he rea­son­ably have been ex­pected to be liv­ing up to?

We can’t say “that’s not OK” with­out some kind of un­der­stand­ing that he had failed to live up to a shared ex­pec­ta­tion. And where is that bar? It’s go­ing to de­pend who you ask and what lo­cal con­text they’re liv­ing in. And not only that, but the fact that no­body is keep­ing track of where even the sep­a­rate, lo­cal stan­dards are, even­tu­ally stan­dards will have to be dropped to the low­est com­mon de­nom­i­na­tor if not made ex­plicit.

MBTI isn’t sci­ence but it’s illus­tra­tive de­scrip­tively, and it seems to me that the differ­ence be­tween “Per­ceivers” and “Judgers”, which is ba­si­cally the differ­ence be­tween the kinds of peo­ple who get called “judg­men­tal” in or­di­nary English and the peo­ple who don’t, is that “Judgers” have a clear idea of where the line is be­tween “ac­cept­able” and “un­ac­cept­able” be­hav­ior, while Per­ceivers don’t. I’m a Per­ceiver, and I’ve of­ten had this ex­pe­rience where some­one is say­ing “that’s just Not OK” and I’m like “whoa, where are you get­ting that? I can cer­tainly see that it’s sub­op­ti­mal, this other thing would be bet­ter, but why are you draw­ing the line for ac­cept­abil­ity here in­stead of some­where else?”

The les­son of cTFT is that hav­ing a line in the first place, hav­ing a stan­dard that you can ei­ther be in line with or in vi­o­la­tion of, has sur­vival value.

No reviews.