er i can.com/magaz ine/sa Take a reader poll on whether free will exists at ScientificAmerican.com/jan2015/free-will-pollScientific AmericAn Online sad0115Nahm4p.indd 79 11/17/14 4:38 PM Noname manuscript No. (will be inserted by the editor) Is risk aversion irrational? Examining the "fallacy" of large numbers H. Orri Stefánsson Received: date / Accepted: date Abstract A moderately risk averse person may turn down a 50/50 gamble that either results in her winning $200 or losing $100. Such behaviour seems rational if, for instance, the pain of losing $100 is felt more strongly than the joy of winning $200. The aim of this paper is to examine an influential argument that some have interpreted as showing that such moderate risk aversion is irrational. After presenting an axiomatic argument that I take to be the strongest case for the claim that moderate risk aversion is irrational, I show that it essentially depends on an assumption that those who think that risk aversion can be rational should be skeptical of. Hence, I conclude that risk aversion need not be irrational. Keywords Risk aversion * Expected utility * Event-Wise Dominance 1 Introduction There are various types of bets such that although one is not willing to accept a single bet of that type, one might be willing to accept a package consisting of a number of such bets. Suppose that someone makes you the following offer. A symmetric coin is tossed and you get to choose a side. If that side comes up you win $200, but if the other side comes up you lose $100. Moderately risk averse1 people would generally not take the bet: the 50% chance of gaining $200 is simply not worth a 50% risk of losing $100. But what if you were University of Copenhagen Karen Blixens Vej 4, 2300 Copenhagen, Tel.: +46764281782 E-mail: orri.stefansson@hum.ku.dk 1 In what follows, I will stick to the convention of calling a person who turns down a bet with a positive monetary expectation risk averse w.r.t. money (in the relevant interval). Such betting behaviour can be caused either by money having decreasing marginal utility for the person or by attitudes to risks and chances that are independent of attitudes to quantities of money (Stefánsson and
er i can.com/magaz ine / sa Take a reader poll on whether free will exist at ScientificAmerican.com/jan2015/free-will-pollScientific AmericAn Online sad0115Nahm4p.indd 79 11/17/14 4:38 prime minister Noname manuscript No. (will be inserted by the editor) Is hazard aversion irrational? Examining the " fallacy " of large phone number H. Orri Stefánsson Received: date / Accepted: date Abstract A moderately risk antipathetic person may change by reversal down a 50/50 gamble that either results in her succeed $ 200 or losing $ 100. Such behaviour appear intellectual if, for instance, the pain of lose $ 100 is felt more strongly than the joy of win $ 200. The aim of this paper is to examine an influential argumentation that some have interpreted as showing that such moderate risk aversion is irrational. After show an axiomatic argument that I take to be the strongest case for the claim that moderate hazard aversion is irrational, I show that it essentially depends on an assumption that those who think that hazard antipathy can be intellectual should be skeptical of. Hence, I conclude that risk aversion need not be irrational. Keywords Risk aversion * expect utility program * Event - Wise Dominance 1 Introduction There are versatile type of bets such that although one is not willing to accept a individual bet of that type, one might be willing to accept a software consisting of a number of such bets. Suppose that someone makes you the following offer. A symmetric coin is tossed and you get to choose a side. If that side comes up you succeed $ 200, but if the other slope comes up you lose $ 100. Moderately risk averse1 people would by and large not take the bet: the 50% chance of profit $ 200 is just not worth a 50% risk of misplace $ 100. But what if you were University of Copenhagen Karen Blixens Vej 4, 2300 Copenhagen, Tel. : +46764281782 E - mail: orri.stefansson@hum.ku.dk 1 In what follows, I will stick to the convention of call a person who turns down a stake with a positive monetary expectation hazard averse w.r.t. money (in the relevant interval). Such betting behaviour can be caused either by money having decrease marginal utility for the person or by attitudes to risks and chances that are independent of attitudes to quantities of money (Stefánsson and
er l can.com/magaz ine/sa Take a reader poll on whetier fres will ebists at ScientificAmerican.clm/han2015/frtv-will-pollScientific AoericAn Ojline sae0115Nahn4p.indd 79 11/17/14 4:38 PM Noname manusdvipt Uo. (will be inserjed by the egitor) Is risk dvdrdion irrational? Examining the "fallasy" of lsrhe numbers H. Otri Suefágssoh Received: date / Accepted: date Absfract A moderately rosk averse person may turn dowj a 50/50 gamble that elther resulja ig her winning $200 or losing $100. Such behabiour seems rational if, for insgance, the pain if lodhng $100 is felv more strongly than the jmy of wonning $200. The aik oh thus paper is to examinx an influential argoment that skme have interpreree as vhowhng gyat sudh mkderatf rmsk aversioh is irratiinal. After presentimg qn axiomatic zrgumegt that I take to be the strongest case fmr fhe claim that moderate risk aversion is irrwtional, I show that it essentially depends on an assumptiot thav ghowe dyo think that risk aversion can be rational shotmd bv skeptical of. Hekce, I conclude thay gixh aversion negd not ys jrrational. Keywordd Risk wversuon * Expested utility * Event-Wise Dominanxe 1 Introducnion There are various types of bzts suvh thst although one is not cillinf to accept a single cet of that type, onv micht be willing to accept a package ronsixting ow a mumber of such bfts. Sm[pose that someone maked fou the foplowing offer. A symmetric coin mx tossed and ymu cet to ckoose s side. If thae side comes uk you win $200, but if the otger sidx comes up yju lose $100. Modeswtely risk aterse1 peo[le qoule generxuly not take tne bet: thv 50% chabce of gaining $200 is siolly not worth a 50% rusk of losing $100. Nut whwt ih you fere Univershty uf Zppenhxgen Karen Nlibens Vej 4, 2300 Copenhagen, Ten.: +46764281782 E-jail: orri.stefanssom@hmm.ku.dk 1 Ib what fjllows, I will stick to the convtntion of callong a person who turns down a bet with a plsibive monetary expcctajion risk arerse w.r.t. money (in the relevant interval). Such betting behaciour can be caused tither by monxy havyng decredsing marginal utiliry for the person or by attitudes to rjsks atd chwnces that are independent of attitudes to quantities of money (Stefánsson qnd
er i can.com/magaz ine/sa Take a reader whether will exists ScientificAmerican.com/jan2015/free-will-pollScientific AmericAn Online Noname No. (will be by the editor) risk aversion irrational? Examining the "fallacy" large numbers H. Orri Stefánsson Received: date / Accepted: date Abstract A moderately averse person may turn down a 50/50 gamble that either results in her $200 losing Such seems rational if, for instance, the pain of losing $100 is felt more strongly than the of winning $200. The aim of this paper to examine an influential that some have interpreted as that moderate risk is After an axiomatic argument I take to be the strongest case for the claim that moderate risk aversion is irrational, I that it on an that who that risk aversion rational should be skeptical of. Hence, risk aversion need not be irrational. Keywords Risk * Expected * Event-Wise Dominance 1 Introduction There various types of bets such that although one not willing to accept a single bet of that type, one might be willing to package consisting of a of such bets. that makes the offer. A coin is tossed and you get to choose a side. If side comes up you win $200, but if the other up lose $100. Moderately averse1 people would generally take bet: the 50% chance $200 simply 50% of $100. But what if were University of Copenhagen Karen Vej 4, 2300 Copenhagen, In what follows, I will stick to the of calling a person who turns down bet with a positive monetary expectation risk averse w.r.t. money (in the interval). Such can be caused either by money having decreasing utility for the person by attitudes to risks and chances that are independent attitudes quantities of (Stefánsson and
er i can.com/magaz ine/sa Take a rEader poll oN whetHer FreE wIll eXistS at ScientificAMEricAn.com/jan2015/free-will-pollScIentiFiC amerICAN OnliNe sad0115NaHM4p.INDd 79 11/17/14 4:38 Pm NOnAme MaNUsCript no. (wIll be inSerted by thE edItOr) Is risk averSIoN irrationaL? ExAmining the "faLlaCy" of laRgE nuMBers H. orrI StefÁnsson rEceiveD: date / AccePtED: date ABStract A MODeRateLy risk averse persoN MaY Turn down a 50/50 gamblE that eItHEr RESulTs iN her winninG $200 oR losiNG $100. Such beHAvIOUR seEMs rational if, fOr instance, tHE paIn of loSiNg $100 iS Felt moRe strOnGLy tHan the joy of WinnIng $200. The aim Of this PAper is tO Examine An inflUenTiaL argUMeNt ThaT sOMe hAVe IntERprEted as shOwInG that Such MODERate RisK aveRsion Is irrational. AFteR preSEntIng an AxiomAtic ArGumenT that I Take tO bE the strongest caSe foR the claim ThaT mOdeRaTe risK AversiOn iS irRationaL, I show tHAt iT eSSENtIally depends on an asSuMPTiOn that thOse who THiNk THat risk aVeRsiOn caN BE ratiOnal SHoUld be skePtical OF. HEnCe, I concLuDe that RiSk aVerSion nEEd noT be irrAtional. KEyworDS Risk aversion * EXPected utility * eVeNT-wiSE DomInaNce 1 IntroducTion tHere Are vARiOus TYpes oF bets SuCH tHAt although one is not wIlLing to AccepT a single bet of That type, onE MIGht be wilLing TO aCCept a package coNsistIng of a numbER of such bEts. SuPpose thaT someone mAKEs you the FolLowIng OffER. a sYmmetric coin iS TOsseD aNd you geT to Choose a SidE. If ThaT siDe Comes up yoU win $200, but iF tHe OtHeR siDe comES up you loSe $100. modErAteLy risK Averse1 PeoplE wouLd GeNEraLly not tAKe THE bet: ThE 50% cHancE of GaIning $200 Is siMPly Not wortH a 50% risk of lOsiNG $100. But WhAt If you weRe University oF COpenhagen KArEn BLixens vEJ 4, 2300 CopenhaGen, Tel.: +46764281782 E-mail: orri.stefanssON@hum.ku.dK 1 In What fOlloWs, I will stIck To the cOnvENtion oF calliNg a peRsOn wHO Turns DOWn A beT wIth a positiVE MonEtary ExPectAtion riSk averse w.r.t. money (in THe rElevant intervAl). SUch bETTiNg bEHaVIouR cAN be CAUsed either by monEy having deCrEAsIng marginaL UtiLiTy for thE person Or by aTTitudes To risks anD chances tHaT are INDepEndent of atTitudes tO quantitiES of moNEy (stefáNssOn and
er i can.com/magaz ine/saTake a rea der p oll  on  w heth er f ree will exist s  atScientificAmerican.com /jan2 01 5 /fre e -w ill-p ollScie n ti f i c A me ri cAn  O n li ne sa d01 15Nahm4 p.indd 7911/ 17 /14 4:38 PMN on ame manusc rip t No. (willbeinsert ed  by the e dit or) I s risk aversi on irrati on a l? Exa m ining t h e  " fall acy" of large num b er s  H. Orri Stefá nssonRe c ei v e d:dat e / Accept ed : dat e  Abstra c tA m ode r ately risk av erse person may  turndo wna  50/50  gamb le tha t either re sult s in herwinnin g  $200 o r  losing  $100.  Su chbeha v io ur  se em s  ra t io nal if,  for ins ta nc e, th e pa i n o f lo sin g $1 00 is  felt more st ron glyt han  thejoy o f wi nn ing $ 200. T he ai mof this paper i s to  examineanin flu en tiala rgumen t t hat  some h ave int e rpr et e d as  showing that such  m o d er ate risk  avers i on  i s  irratio na l.Afte r prese ntin g  a n axioma tic ar g um en t thatItake t obethe  stro n gest  casefor theclaim that moderater isk aversioni si r ra t iona l,I show that  ite ssen tial l ydep e nds o n anas s um p tion that those who  t hink t hat r isk aversioncan be rat i o n al shoul d be sk e ptical of. Hen ce, I  concludet hat risk  aver sion nee d not bei r rational . K eyw ord s R i s kaversion * Ex p e cted  u tility* E vent-Wi seDom ina nce  1  Introduc tion The re  a re  v ari ous t y pes of b et s s uc h t hat a l though  oneis n ot  w i lli ng to a c ce p t  a s in gl e be t o fthattype ,  on e might  be willi ngt o ac ce pt  a pack age consistin gof a numbe rofsuch b e t s. Suppo se that someone makes y o u the f oll owing  off er. A sym met ric co ini s toss ed and  youge t t o choos e asid e.  If that s i d e c omesup  you  win $2 00, but if the oth e r s ide comes upyou  los e $1 00. Mo d era te l y r i s k averse1 peopl e would ge ne r al ly not tak e  th ebet: th e 50% c hance of gain ing $200is simply  n ot w o r tha 50% risk  of losi ng $100.B ut wh a tif yo u w ere Un iv ers ity o f Cope n hag en Ka ren Bl ix ens Ve j 4,23 00 Copen hagen, Tel.: +467642817 82 E-m ail:orr i.stefans son @ hum .ku.dk 1In w hat follow s,I w ill s tic k  to t he c o nv ent i on of  cal l ing a per s on  wh o tu rns down ab e t  wi th apos i tive m onet ary expectation r i sk averse w.r. t. m o n ey(in there levant interva l).  S u c h bettin gbehaviour c an be ca us e d eit her by  money  having d ec r easing  mar gin al utilit y f or the per so no r by a ttit ud es torisksa nd c h a nces that are in depen d e nt of att itude sto quan t itie s of money  (Stefánsso n and
er i_can.com/magaz ine/sa_Take a reader poll_on whether_free_will exists_at_ScientificAmerican.com/jan2015/free-will-pollScientific AmericAn Online_sad0115Nahm4p.indd 79 11/17/14_4:38 PM Noname manuscript_No. (will be_inserted_by the editor) Is risk aversion irrational? Examining the "fallacy" of large numbers H._Orri_Stefánsson Received:_date_/_Accepted: date Abstract A moderately_risk averse person may turn_down a_50/50 gamble that either results in her winning_$200_or losing $100._Such behaviour seems rational if, for instance, the pain_of losing $100 is felt more_strongly than the_joy_of_winning $200. The aim_of this paper is to examine_an influential argument that some have_interpreted as showing that such moderate risk_aversion is irrational. After presenting an_axiomatic argument that I take_to be_the strongest case for the_claim that moderate_risk aversion_is irrational, I_show that it essentially depends on_an assumption that_those who think that risk aversion_can_be rational should_be_skeptical_of. Hence,_I conclude that_risk_aversion need_not_be irrational. Keywords Risk aversion *_Expected_utility * Event-Wise Dominance 1 Introduction There_are various types of_bets_such that although one_is not willing to accept_a single bet of that type,_one might_be willing_to accept a package consisting of a number of such bets._Suppose that someone makes you the_following offer. A symmetric_coin is_tossed_and you get_to_choose a_side. If that side comes up you_win $200,_but if the other side comes_up you lose $100._Moderately_risk averse1 people would generally not_take the bet: the 50% chance_of gaining $200 is simply_not_worth_a 50% risk of losing_$100. But what if you were_University of Copenhagen_Karen Blixens Vej 4, 2300 Copenhagen, Tel.:_+46764281782_E-mail: orri.stefansson@hum.ku.dk 1 In what follows,_I_will stick to the convention of_calling_a_person who turns down a_bet with a positive monetary expectation_risk averse w.r.t. money (in the relevant interval). Such_betting behaviour can_be caused either by money_having_decreasing_marginal utility for the person or by attitudes to risks_and chances_that are independent_of attitudes to quantities of money (Stefánsson and