Decision Making - The University of Edinburgh · 2018-03-20 · Argument thus far in DMR has been...

DecisionMakingin Robots and Autonomous Agents

BehaviouralIssues:

Heuris6cs&Biases,etc.

SubramanianRamamoorthySchoolofInforma6cs

16March,2018

TheRa'onalAnimalTheGreeks(Aristotle)thoughtthathumansarera'onalanimals.

–  Manyancientphilosophersagreed–  Clearly,evenAristotlewasawarethatpeople’s

judgments,decisions&behaviorarenotalwaysra'onal.–  Amoreplausiblerevisedclaim:allnormalhumanshave

thecompetencetobera'onal.ArgumentthusfarinDMRhasbeeninthisspirit:

–  “correct”principlesofreasoning&decisionmakingareinourminds,evenifwedon’talwaysusethem

–  “Excep'ons”werethingslikeBernoulli’sobserva'onthatwebecomeprogressivelymoreindifferenttolargergains

16/03/2018 2

16/03/2018 3

Heuris'csandBiases

•  TverskyandKahnemandrama'callyextendedBernoulli’saccount,andprovidedextensivepsychologicalevidencefortheirmodel.

•  Whattheyshowedisthathumansdepartinmul'plewaysfromaclassicalpictureofra'onalbehavior.

•  ManyhaveinterpretedtheKahneman&TverskyprogramasshowingthatAristotlewaswrong.–  mostpeopledonothavethecorrectprinciplesforreasoning&decisionmaking

–  wegetbywithmuchsimplerprincipleswhichonlysome/mesgettherightanswer

Amos Tversky1937 - 1996

Daniel Kahneman

AnIntui'onfromGigerenzer

Which US city has more inhabitants, San Diego or San Antonio?•  62%ofAmericansgotthiscorrect•  100%ofGermansgotthiscorrect

TheRecogni'onHeuris'c:Ifoneoftwoobjectsisrecognizedandtheotherisnot,theninferthattherecognizedobjecthasthehighervalue.

EcologicalRa'onality:Heuris'cworkswhenignoranceissystema'c(non–random),i.e.,whenlackofrecogni'oncorrelateswiththecriterion.

16/03/2018 4Goldstein & Gigerenzer, 2002, Psychological Review

ExperimentalStudiesofHumanReasoning

•  TheConjunc'onFallacy•  BaseRateNeglect•  Overconfidence•  Framing

16/03/2018 5

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. Please rank the following statements by their probability, using 1 for the most probable and 8 for the least probable.

(a) Linda is a teacher in elementary school. (b) Linda works in a bookstore and takes Yoga classes. (c) Linda is active in the feminist movement. (d) Linda is a psychiatric social worker. (e) Linda is a member of the League of Women Voters. (f) Linda is a bank teller. (g) Linda is an insurance sales person. (h) Linda is a bank teller & is active in the feminist movement.

Naïve subjects: (h) > (f) 89%

Sophisticated subjects: 85% 16/03/2018 6

Johnis19,wearsglasses,isalieleshyunlessyoutalktohimaboutStarTrekorLordoftheRings,andstaysuplatemostnightsplayingvideogames.Whichismorelikely?1.  JohnisaCSmajorwholovescontemporarysculpture

andgolf,or2.  Johnlovescontemporarysculptureandgolf?

Onproblemslikethis,peopletendtopick(1)above(2),incontradic'ontoprobabilitytheory.

16/03/2018 7

ExperimentalStudiesofHumanReasoning

•  TheConjunc'onFallacy•  BaseRateNeglect•  Overconfidence•  Framing

16/03/2018 8

A panel of psychologists have interviewed and administered personality tests to 30 engineers and 70 lawyers [70 engineers and 30 lawyers], all successful in their respective fields. On the basis of this information, thumbnail descriptions of the 30 engineers and 70 lawyers [70 engineers and 30 lawyers], have been written. You will find on your forms five descriptions, chosen at random from the 100 available descriptions. For each description, please indicate your probability that the person described is an engineer, on a scale from 0 to 100.

16/03/2018 9

Jack is a 45-year-old man. He is married and has four children. He is generally conservative, careful and ambitious. He shows no interest in political and social issues and spends most of his free time on his many hobbies which include home carpentry, sailing, and mathematical puzzles.

Dick is a 30-year-old man. He is married with no children. A man of high ability and high motivation, he promises to be quite successful in his field. He is well liked by his colleagues.

16/03/2018 10

BaseRateandRepresenta'veness

Withnopersonalitysketch,simplyaskedfortheprobabilitythatanunknownindividualwasanengineer–  subjectscorrectlygavetheresponses0.7and0.3

Whenpresentedwithatotallyuninforma'vedescrip'on

–  thesubjectsgavetheprobabilitytobe0.5

Kahneman&Tverskyconcludedthatwhennospecificevidenceisgiven,priorprobabili'esareusedproperly;whenworthlessevidenceisgiven,priorprobabili'esareignored.

16/03/2018 11

If a test to detect a disease whose prevalence is 1/1000 has a false positive rate of 5%, what is the chance that a person found to have a positive result actually has the disease, assuming that you know nothing about the person’s symptoms or signs?

____%

Harvard Medical School: “2%” = 18%; “95%” = 45%

16/03/2018 12

16/03/2018 13

Whyisthecorrectanswer2%?

•  Thinkofapopula'onof10,000people.•  Wewouldexpectjust10peopleinthispopula'ontohavethe

disease(1/1000x10,000=10)•  Ifyoutesteverybodyinthepopula'onthenfalseposi'verate

meansthat,inaddi'ontothe10peoplewhodohavethedisease,another500(5%)willbewronglydiagnosedashavingit.

•  Inotherwordsonlyabout2%ofthepeoplediagnosedposi've(10/510)actuallyhavethedisease.

•  Whenpeoplegiveahighanswerlike95%theyareignoringtheverylowprobability(i.e.rarity)ofhavingthedisease.Incomparison,probabilityofafalseposi'vetestisrela'velyhigh.

ExperimentalStudiesofHumanReasoning

•  TheConjunc'onFallacy•  BaseRateNeglect•  Overconfidence•  Framing

16/03/2018 14

In each of the following pairs, which city has more inhabitants?

§  (a) Las Vegas (b) Miami How confident are you that your answer is correct? 50% 60% 70% 80% 90% 100%

§  (a) Sydney (b) Melbourne How confident are you that your answer is correct? 50% 60% 70% 80% 90% 100%

§  (a) Hyderabad (b) Islamabad How confident are you that your answer is correct? 50% 60% 70% 80% 90% 100%

16/03/2018 15

Overconfidenceeffect

•  Person'ssubjec'veconfidenceinhisorherjudgementsisreliablygreaterthantheobjec'veaccuracyofthosejudgements–  especiallywhenconfidenceishigh

•  Manifestedindifferentways:–  overes/ma/onofone'sactualperformance–  overplacementofone'sperformancerela'vetoothers–  overprecisioninexpressingunwarrantedcertaintyintheaccuracyofone'sbeliefs.

16/03/2018 16

ExperimentalStudiesofHumanReasoning

•  TheConjunc'onFallacy•  BaseRateNeglect•  Overconfidence•  Framing

16/03/2018 17

Imagine the U.S. is preparing for the outbreak of anunusual Asian disease which is expected to kill 600people. Two alterna've programs to combat thedisease have been proposed. Assume that the exactscien'fices'matesoftheconsequencesoftheprogramareasfollows:

16/03/2018 18

–  IfprogramAisadopted,200peoplewillbesaved.

–  IfprogramBisadopted,thereisa1/3probabilitythat600peoplewillbesavedanda2/3probabilitythatnopeoplewillbesaved.

16/03/2018 19

–  IfprogramAisadopted,200peoplewillbesaved.

–  IfprogramBisadopted,thereisa1/3probabilitythat600peoplewillbesavedanda2/3probabilitythatnopeoplewillbesaved.

16/03/2018 20

–  IfprogramCisadopted,400peoplewilldie.

–  IfprogramDisadopted,thereisa1/3probabilitythatnobodywilldieanda2/3probabilitythat600peoplewilldie.

16/03/2018 21

–  IfprogramCisadopted,400peoplewilldie.

–  IfprogramDisadopted,thereisa1/3probabilitythatnobodywilldieanda2/3probabilitythat600peoplewilldie.

16/03/2018 22

–  IfprogramAisadopted,200peoplewillbesaved.

–  IfprogramBisadopted,thereisa1/3probabilitythat600peoplewillbesavedanda2/3probabilitythatnopeoplewillbesaved.

–  IfprogramCisadopted,400peoplewilldie.

–  IfprogramDisadopted,thereisa1/3probabilitythatnobodywilldieanda2/3probabilitythat600peoplewilldie.

16/03/2018 23

ProgramAversusB

•  TverskyandKahneman(1981)foundthatthemajoritychoice(72%)forananalogueofproblem1usingananonymous“Asiandisease”(notSARS)wasanswerA.

•  Theprospectofsaving200liveswithcertaintywasmorepromisingthantheprobabilityofaone-in-threechanceofsaving600lives.

16/03/2018 24

AandBhavetheSameU'lity

•  Thestandardwayofcalcula'ngexpectedu'lity:•  ΣiP(oi)xU(oi)•  whereeachoiisapossibleoutcome,P(oi)isits

probabilityandU(oi)isitsu'lityorvalue.

•  Onthisbasis,op'onB(ariskyprospect)wouldbeofequalexpectedvaluetothefirstprospectA.

•  Sointhiscasesubjectsarenotsimplyusingexpectedu'lity:theyareriskaverse.

16/03/2018 25

ProgramCversusD

•  Themajorityofrespondentsinthesecondproblem(78%)chosetheriskierop'on.

•  Thecertaindeathof400peopleisapparentlylessacceptablethanthetwo-in-threechancethat600peoplewilldie.

•  Onceagain,thereisnodifferencebetweentheop'ons(CandD)instandardexpectedu'lity.

•  Wesayinthiscasethatpeopleareriskseeking.

16/03/2018 26

Framing

•  TverskyandKahneman’sinten'onwasthatProblem1andProblem2areunderlyinglyiden'cal,butpresentedindifferentways.

•  Totheextentthattheyareright,wesaythattheyaredifferentframingsofthesameproblem:thedifferentresponsesforthetwoproblemsarewhatwecallframingeffects.

•  Yetanotherwayinwhichpeople’sdecisionsdifferfromwhatwouldbepredictedonthestandardviewofexpectedu'lity.

16/03/2018 27

16/03/2018 28

ProspectTheory:S-curveofValue

Actual gain

Perceivedgain

Actual loss

PerceivedLoss

•  Small gain good,•  Big gain not much

better,•  Small loss terrible,•  Big loss not much

worse.

Thus we are generally:•  Loss averse,•  Risk averse for gains,

but•  Risk seeking for losses.

Reference point

16/03/2018 29

Es'ma'onofRisk

Estimates of Probabilities of Death From Various Causes:

Cause Stanford graduate estimates Statistical estimatesHeart Disease 0.22 0.34Cancer 0.18 0.23Other Natural Causes 0.33 0.35All Natural Causes 0.73 0.92

Accident 0.32 0.05Homicide 0.10 0.01Other Unnatural 0.11 0.02All Unnatural 0.53 0.08

(BasedonastudybyAmosTversky,ThayerWatkin’sreport)

BigandSmallProbabili'es

•  Smallprobabilityeventsareoverrated.

•  Moregenerally,behaviordepartsfromclassicalra'onalitysubstan'allyasregardsverysmallandverylargeprobabili'es.

•  Evenwhentoldthefrequencyofevents,subjectstendtoviewthedifferencebetween0and0.001(orthatbetween0.999and1)asmoresignificantthanthatbetween.5and.5001.

16/03/2018 30

The“BleakImplica'ons”Hypothesis

•  These results have“bleak implica'ons” for the ra'onalityofordinarypeople(Nisbeeetal.)

•  “Itappearsthatpeoplelackthecorrectprogramsformanyimportant judgmental tasks…. We have not had theopportunity to evolve an intellect capable of dealingconceptually with uncertainty.” (Slovic, Fischhoff andLichtenstein,1976)

16/03/2018 31

The“BleakImplica'ons”Hypothesis

“I am par'cularly fond of [the Linda] example, because Iknow that the [conjunc'on] is least probable, yet a lielehomunculus ismy head con'nues to jump up and down,shou'ngatme–“butshecan’t justbeabankteller;readthe descrip'on.” … Why do we consistently make thissimple logical error? Tversky and Kahneman argue,correctlyIthink,thatourmindsarenotbuilt(forwhateverreason) towork by the rules of probability.” (Stephen J.Gould,1992,p.469)

16/03/2018 32

ChallengefromEvolu'onaryPsychology

•  The“frequen'st”hypothesis–  Usefulinforma'onaboutprobabili'eswasavailableto

ourancestorsintheformoffrequencies•  e.g.,3ofthelast12huntsnearriversweresuccessful

–  Informa'onabouttheprobabili'esofsingleeventswasnotavailable

–  Soperhapsweevolvedamentalcapacitythatisgoodatdealingwithprobabilis'cinforma'on,butonlywhenthatinforma'onispresentedinafrequencyformat.

16/03/2018 33

MakingtheConjunc'onFallacy“Disappear”…

16/03/2018 34

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. Please rank the following statements by their probability, using 1 for the most probable and 8 for the least probable.

(a) Linda is a teacher in elementary school. (b) Linda works in a bookstore and takes Yoga classes. (c) Linda is active in the feminist movement. (d) Linda is a psychiatric social worker. (e) Linda is a member of the League of Women Voters. (f) Linda is a bank teller. (g) Linda is an insurance sales person. (h) Linda is a bank teller and is active in the feminist movement.

16/03/2018 35

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

There are 100 people who fit the description above. How many of them are:

…

(f) bank tellers?

(h) bank tellers and active in the feminist movement?

...

(h) > (f) = 13%

16/03/2018 36

Level-kReasoning

Thecen'pedegame:

•  Intheonlyequilibriuminvolvingra'onalplayers,player1choosesdowninthefirst'memove

•  Whatexactlydorealpeopledo?–  Humansubjectsdon’tchoosethedownop'onrightaway–  Howdoweunderstandtheirbehaviour?

16/03/2018 37

HideandSeekGames

•  Youropponenthashiddenaprizeinoneoffourboxesarrangedinarow.

•  Theboxesaremarkedasshownbelow:A,B,A,A•  Yourgoalis,ofcourse,tofindtheprize.•  Hisgoalisthatyouwillnotfindit.•  Youareallowedtoopenonlyonebox.•  Whichboxareyougoingtoopen?

16/03/2018 38

FolkWisdom

•  “…inLakeWobegon,thecorrectanswerisusually‘c’.” –GarrisonKeillor(1997)onmul'ple-choicetests

•  CommentonpoisoningofUkrainian’spresiden'alcandidate:“Anygovernmentwan'ngtokillanopponent…wouldnottryitatamee'ngwithgovernmentofficials.” –ViktorYushchenko(2004)

16/03/2018 39

UniqueEquilibriumofHideandSeekGame

•  Ifbothplayersrandomizeuniformly:

Expectedpayoffs:Hider3/4,Seeker1/4

16/03/2018 40

BehaviouralExperimentinHideandSeek

•  CentralA(or3)ismostprevalentforbothHidersandSeekers•  CentralAisevenmoreprevalentforSeekers

–  Asaresult,Seekersdobeeerthaninequilibrium•  Shouldn’tHidersrealizethatSeekerswillbejustastemptedto

lookthere?•  “Thefindingthatbothchoosersandguessersselectedtheleast

salientalterna'vesuggestslieleornostrategicthinking.”

16/03/2018 41

p-BeautyContestGames(Keynes,1936)

“…professionalinvestmentmaybelikenedtothosenewspapercompe''onsinwhichthecompe'torshavetopickoutthesixprevestfacesfromahundredphotographs,

theprizebeingawardedtothecompe'torwhosechoicemostnearlycorrespondstotheaveragepreferencesofthecompe'torsasawhole….

Itisnotacaseofchoosingthose[faces]that,tothebestofone’sjudgment,arereallytheprevest,noreventhosethataverageopiniongenuinelythinkstheprevest.

16/03/2018 42

p-BeautyContestGames

•  Wehavereachedthethirddegreewherewedevoteourintelligencesto…an'cipa'ngwhataverageopinionexpectstheaverageopiniontobe.

•  Andtherearesome,Ibelieve,whoprac'cethefourth,fiHhandhigherdegrees.”

–Keynes,GeneralTheory,1936,pp.155-56

16/03/2018 43

Level-kReasoning

Onecouldplayatvaryinglevelsofdepthofreasoning:•  Level-0:Randomplay•  Level-1:BRtoRandomplay•  Level-2:BRtoLevel-1•  Nash:PlayNashEquilibrium(level-∞?)•  Worldly:BRtodistribu'onofLevel-0,Level-1andNashtypes

StahlandWilson(GEB1995)

16/03/2018 44

Level-kforHideandSeek

•  Level-k:EachroleisfilledbyLktypes:L0,L1,L2,L3,orL4(probabili'estobees'mated…) –Note:InHideandSeekthetypescycleaxerL4…

•  HightypesanchorbeliefsinanaïveL0typeandadjustswith

iteratedbestresponses: –L1bestrespondstoL0(withuniformerrors) –L2bestrespondstoL1(withuniformerrors) –LkbestrespondstoLk-1(withuniformerrors)

16/03/2018 45

Level-kforHideandSeek

•  L0HidersandSeekersaresymmetric–Favorsalientloca'onsequally1.Favor“B”:choosewithprobabilityq>1/42.Favor“endA”:choosewithprob.p/2>1/4 –Choiceprobabili'es:(p/2,q,1-p-q,p/2)

•  Note:Specifica'onofAnchoringTypeL0isthekeytomodel’sexplanatorypower –Can’tuseuniformL0(coincidewithequilibrium)…

16/03/2018 46

ModernPerspec've:DiversityinModesofThinking

•  Automa'cSystem(Type1)–  Fast,unconscious–  Parallel,associa've–  Lowenergy–  “Doer”

•  Reflec'veSystem(Type2)–  Slow,conscious–  Serial–  Expensive–  “Planner”

16/03/2018 47

TrainingtoGoBetweenModesExample:BoardMemoryinChess

heps://www.youtube.com/watch?v=rWuJqCw|jc

16/03/2018 48

U'lisingTypeIThinking

•  frombehavioralscience•  arguesthatposi've

reinforcementandindirectsugges'onstotrytoachievenon-forcedcompliancecaninfluencemo'ves,incen'vesanddecisionmaking

•  atleastaseffec'vely–ifnotmoreeffec'vely-thandirectinstruc'on,legisla'on,orenforcement

16/03/2018 49

Applica'onExample:PersuasiveTechnology(Beeminder)

16/03/2018 50

Applica'onExample:ChangingDrivingBehaviour-LoeeryIncen've

•  Enterpeopleinaloeeryiftheycometocampusoff-peak•  Observethatthissmallprobabilityofearningsactuallycauses

non-essen'altravellerstoaltertheirbehaviour

16/03/2018 51

Summary

•  Muchofthecourseprogressedundertheassump'onofafairlystrictformofra'onality–  Nobodyactuallybelievesthatthisiswhatpeoplealwaysdo–  Instead,animplicitclaimisthatpeoplehavethecapacityforthiskind

ofreasoning

•  Inthislecture,welookedathowpeoplesystema'callydeviatefromsuchano'onofra'onality

•  Thishasmajorimplica'onsforcomputa'onalagents–  Intheend,youwantthemtoworkwithrealpeople–  Modelling“realpeople”ischallenging,butul'matelytheraisond’etre

16/03/2018 52

Acknowledgements

ManyoftheseslidesareadaptedfromJurafskyetal.’sSymbolicSystemscourseatStanford

16/03/2018 53