 of practical rationality (e.g. Aloysius 2007). The aim of this paper is to examine more carefully than has previously been done the argument that one cannot rationally turn down the single bet while accepting the package-or, as I shall call it, the argument for "Samuelson's claim"4-and the more general claim that moderate risk aversion is irrational. After formulating an axiomatic argument that I take to be the strongest case for Samuelson's claim, I show that the argument essentially depends on the principle of Event-Wise Dominance, which those who think that risk aversion can be rational have a good reason to reject. Hence, I conclude, the argument is question begging if intended as a general argument against the possibility of rational risk aversion.5 2 Samuelson's argument The starting point of Samuelson's discussion was the observation that one of his colleagues at MIT-a "distinguished scholar", he says-did in fact turn down Samuelson's offer of a 'coin-toss-bet'6 like the one discussed above, while at the same time confessing his willingness to accept a package consisting of 100 such bets. Samuelson's colleague, whom I will henceforth refer to as SC, justified his attitude by saying that although the single bet was not enough to make it "reasonably sure that the law of averages will turn out in my favor", 4 As a referee correctly points out, it is not clear whether Samuelson (1963) was concerned with showing that turning down the single bet while accepting the package would be irrational. Rather, he seems to have been more concerned with showing that such behaviour would be inconsistent with expected utility maximisation. Nevertheless, for the sake of simplicity, and since Samuelson did endorse expected utility theory in much of his writings, I will occasionally refer to the claim in question as "Samuelson's claim". 5 It should be noted that this is not how Samuelson himself interpreted his result. 6 In what follows, a 'coin-toss-bet' is a bet that pays bettors $200 if their chosen side of a coin comes up on a particular toss but has them paying $100 otherwise. 4 H. Orri Stefánsson the law of large numbers would make a package consisting of 100 such bets very attractive. "I am, so to speak, virtually sure to come out ahead in such a sequence, and that is why I accept the sequence while rejecting the single
of practical rationality (e.g. Aloysius 2007). The aim of this paper is to test more cautiously than has previously been done the argument that one cannot rationally change by reversal down the unmarried bet while accepting the software - or, as I shall call it, the argument for " Samuelson's claim"4 - and the more general title that moderate risk aversion is irrational. After formulate an axiomatic argument that I take to be the potent case for Samuelson's claim, I show that the argument essentially depends on the rationale of Event - Wise Dominance, which those who think that risk aversion can be intellectual have a good reason to reject. Hence, I reason, the argument is motion begging if intended as a general controversy against the possibility of rational risk aversion.5 2 Samuelson's argument The starting point of Samuelson's discussion was the observation that one of his colleagues at MIT - a " distinguished scholar ", he says - did in fact turn down Samuelson's offer of a' coin - toss - bet'6 like the one discussed above, while at the same time confessing his willingness to bear a package consisting of 100 such bet. Samuelson's colleague, whom I will henceforth denote to as SC, justified his attitude by saying that although the individual bet was not enough to make it " reasonably indisputable that the law of averages will turn out in my favor ", 4 As a reviewer correctly points out, it is not clear whether Samuelson (1963) was concerned with showing that turning down the single bet while accept the software would be irrational. Rather, he seems to have been more concerned with showing that such behaviour would be inconsistent with expected utility maximization. Nevertheless, for the sake of chasteness, and since Samuelson did endorse expected utility program theory in much of his writings, I will occasionally refer to the claim in question as " Samuelson's title ". 5 It should be noted that this is not how Samuelson himself interpret his result. 6 In what watch, a' coin - toss - stake' is a bet that pays bettors $ 200 if their choose english of a coin comes up on a particular toss but has them paying $ 100 otherwise. 4 H. Orri Stefánsson the law of large numbers would make a software consisting of 100 such bets very attractive. " I am, thus to speak, virtually sure to come out ahead in such a sequence, and that is why I accept the sequence while disapprove the single
 of practical rationality (e.n. Aloysius 2007). The cum of vhis paler is tu examine more carefully thai haw preciously been done the xrgument nhat one xannir rationally turn down tgc sinylx bet while accgpting the pdckage-or, as I vhxlp call it, the argument for "Samuelsog's claik"4-ajd the more gegerak clajm that moderate risk aversion is jrratioial. After formukating an axiomatic argumejt tjat I take to be tje strongesj cafw for Samuelron's claim, I show that the argument essentially depenas on the princupoe lx Event-Wise Domigance, which bnose wvo thinl that risk avcrsioi cab be rational have a jood reason to rejecj. Hence, I wouclude, the argument iw wuesthon teggkbg kf jnvensed as a jeneral arghment againwt the possibility pf gstional risk aversyog.5 2 Samuelson's argument The starting poitt kf Samuelson's discussiob was the observation that one of his colleagues at MIT-a "distinguished scholar", ve sabs-aid ik fazr hurn down Samuelson's offer of a 'coin-toss-bet'6 lyie tme one discussed above, whilr wt jhe same time zonfessinf his willingness ho accekt a pqckage cogsisying of 100 such bets. Samuelsob's colleague, qhom I will henceflrth refer co as XC, juxtified his attitude by sayjng that alhhough ths single bet was vot etough to make it "reasonablr sure thet thz law of avetages wyll turn okt in my favor", 4 As a reffree eorrewtly pointd out, it is not clear whether Sekuelson (1963) was cmncvrned witk showlng that turnind down the sinyle bet chile xccepting nhe packaje would be yrrational. Radjer, he seems to have beeb moee concdfned with showong that such behavuour would be incoksistgnf with expected utulity maximisatoon. Nedegthxless, xor the sake of rimokicith, and since Ramurlson did endorse ex[ectsd utility theory on much of his wrieings, I will pccasionally refer to tie clamm in aueftion as "Samuelson's claim". 5 It ahould be nobed that this is kot row Samuelxon himself interpreted his result. 6 In xhat follows, a 'coin-toss-vet' is a bet that pcyx bettors $200 mf theyr chosen side of a coin comew up on a particukar toss but has them payinc $100 otjerwise. 4 H. Orri Stefánsson the law of large numbers would make a package cinsistmnd of 100 such gets very actrcctive. "Y am, ro to speak, virtlally sure to come out ahead in ruch a saqbence, and that is why I accepy ghe sequence dhile rejecting the singme
of practical rationality (e.g. Aloysius 2007). The this is to more carefully than argument one cannot rationally down the single while accepting the package-or, as I call it, the argument for "Samuelson's claim"4-and the more general claim that moderate aversion is irrational. After formulating an axiomatic argument that I take to be strongest for claim, show that the argument essentially depends on the principle of Event-Wise Dominance, which those who think risk aversion can be rational have a good to reject. Hence, I the argument is question begging intended a general against possibility rational risk aversion.5 Samuelson's argument The starting point of Samuelson's discussion was the observation that one of his colleagues at "distinguished scholar", in fact down offer a 'coin-toss-bet'6 like discussed above, while at the same willingness to accept a package consisting of 100 bets. Samuelson's whom I will henceforth refer to SC, justified his attitude by saying that although single bet was not enough to make it "reasonably sure that the law of averages out in my favor", As a referee points it not whether Samuelson was concerned with showing that turning down the single bet while the package would be irrational. Rather, he seems to have concerned showing that such would be inconsistent with utility Nevertheless, for the sake and Samuelson utility in of his writings, I occasionally refer to the claim question as "Samuelson's claim". that this is not how Samuelson himself interpreted result. 6 In what follows, a 'coin-toss-bet' a bet that pays bettors $200 if their chosen side of a comes up particular toss but has them paying $100 otherwise. H. Orri Stefánsson the of large numbers would make a package consisting of such very attractive. am, so to virtually sure to out ahead in sequence, and is I while rejecting the single
 of practical rationality (e.g. ALoysius 2007). The Aim of ThiS paPeR is tO exaMine more carefuLLy thAn has previously been donE the aRgUMent THaT one cAnnot raTIoNALly TuRn DowN tHE sIngle Bet While acCepting the PacKaGe-or, as I shall CAlL it, the arguMenT for "SamuelsoN's cLaim"4-anD tHe mORe genEraL claiM that mODerate Risk aversIoN Is irraTIonal. AfTER fOrmuLating an axiomatic ARgUMent that I take tO be the StROnGESt cAse For SamuelsOn'S claiM, i show thAT tHE ARguMEnt essentiallY depends on tHE prInciplE oF EvENt-Wise dominAnCE, whIch those who ThinK that risk AversiON can be rATional hAve a goOd rEasOn to REjEcT. HeNcE, i coNClUde, THe aRgument iS qUeStion BeggING IF intEndEd as A geneRal argument agAinSt thE PosSibilIty of RatiOnAl risK aversIon.5 2 SaMuElson's argument THe stArting poiNt oF SAmuElSon's dIScussiOn wAs tHe obserVation tHAt oNe OF HIs Colleagues at MIT-a "diStINGuIshed schOlar", he SAyS-dID in fact tUrN doWn SaMUElson'S offER oF a 'coin-toSs-bet'6 lIKe ThE one disCuSsed abOvE, whIle At the SAme tIme conFessing hIs wilLIngness to accepT A package consiSTiNG Of 100 SUch bEts. samuelson's cOlleAGue, wHom I WIlL heNCeforTh refEr TO aS sC, justified his attitUdE by sayIng thAt although the Single bet wAS NOt enough To maKE iT "Reasonably sure That tHe law of aveRAges will Turn oUt in my faVor", 4 As a refEREe correcTly PoiNts Out, IT Is Not clear whethER samuElSon (1963) was cOncErned wiTh sHowIng ThaT tUrning dowN the singLe BeT wHiLe aCceptINg the pacKaGe wOuLd bE irraTIonal. RAther, He seEmS tO HavE been moRE cONCernEd WiTh shOwiNg That sUch bEHavIour wouLd be inconSisTEnt wItH eXpected Utility maximiSaTion. NevertHeLesS, for thE SAke of simPlicity, and since SamuelsoN Did endoRse ExpecTed uTility theOry In much Of hIS writiNgs, I wiLl occAsIonALLy refER To The ClAim in questION as "samueLsOn's cLaim". 5 It sHould be noted that thIS is Not how SamuelsOn hImseLF InTerPReTEd hIs REsuLT. 6 in what follows, a 'cOin-toss-bet' Is A BeT that pays bETtoRs $200 If their Chosen sIde of A Coin comEs up on a paRticular tOsS but HAS thEm paying $100 otHerwise. 4 H. orri StefáNSson tHE lAw of lArgE numbeRs WouLd makE a packAGe cOnsisTing of 100 SuCh bets Very aTtRactive. "I Am, so to speak, virtually surE to comE out aHeaD in such a sEquENce, And that is Why I Accept the sEquEncE whilE reJEctinG the SInGle
 of practical rationality(e.g. Aloy sius200 7).  T he a im o f this paper i s  toexamine more carefully  than  h a s pr e vi ously  been d o ne t hear gu men tt ha t one  ca nnot ra tionally t urn  d own the sing l ebet whileacc epting the p ack age-or ,asI  shal l c all i t, the argume nt for "S am u elson' s  claim" 4 - an d th e more general cl a im that moderaterisk a ve r si o n  is  ir rational.Af ter f o rmulati n ga n axi o matic argumen t that I ta k e t o be t he  st r ongest  case  f o r S amuelson'sclai m, I show  thatt he argu m ent ess ential lydep ends on  t hepr i nci p le  of Eve nt-WiseDo mi nance , wh i c h thos e w ho t hinkthat risk ave rsi on c a n b e rat ional  hav ea goo d reas on to  r eject. Hence, I  con clude, th e a rg ume nt  is q u estion  be ggi ng if i ntended asag e n er al argument agains tt h epossibil ity of ra ti o nal risk  a ver sion . 5  2 Sa muel s on 's argum ent Th e  s ta rting p oi nt ofSa mue lso n's d i scus sion w as the o bserv a tion that oneo f his colleag u es a tM IT-a  "d istinguishe d sc h olar ", h e  s ays - did i n fac tt ur n  down Samuelson's o ff er ofa 'co in-toss-bet'6  like theo n e  discuss ed a b ov e , while at the  same  time conf e ssing hi s wil lingness  to accep t a packag e c ons ist ing o f100 such bets . Samu el son's c oll eague,who m I  wi llhe nceforthrefer to  a sSC ,jus tifie d  his att it ude  b y s aying that a lthou gh t he  s i ngl e bet w a sn o t en ou gh  tomak eit "r easo n abl y surethat thelaw of a ve ra ges wil l turn out in  m y favor",4Asa refe r e e correc tly points out, it is n o t clear  wh ether  Sam uelson (1 963 ) wascon c ernedwith s howin gtha t turni n g  d own  t he singleb e t w hileac cept ing the  package would bei rra tional. Rathe r,he s e e ms  to ha v e b ee n  mo r e  concerned with  showing t ha t  s uch behavi o urwo uld beinconsi stent with ex pected ut ility max im isat i o n.Neverthele ss, forthe sakeo f sim p li city,  an d sinc eSam uelso n dide ndo rse e xpecte dutilit y the or y in muc h of his writings, I wi ll occ asion all y refer t o t h e c laim in q uest ion as "Sa mue lso n's c lai m ". 5It s h ou ldb e not ed t h at this i s  n oth o wSamuelson h i m s elf  inte rpr e ted hi s re sult. 6 In what f o llows, a 'coin -tos s - bet ' i s  a b et  that pays bet tor s$ 2 00 if th ei r chosen si de of aco i n com es upon a p articul a r  t o ss but  has  th em paying  $1 00 otherwi se .4  H. Or ri S te fánsso n thel aw o f large numbers wo uld m a k e a p a cka ge co ns istingo f 10 0 such bet s very attr active . "I  am,so to s pe ak, vi rtu al ly sure to come outahead  in suc ha se que nce, a nd t h a t iswhyIacc ept the s e q ue n ce  w h ile  rej ectin gthesingle
 of_practical rationality_(e.g. Aloysius 2007). The_aim of_this_paper is_to_examine more carefully_than has previously_been done the argument_that one cannot_rationally_turn down the single bet while accepting the package-or, as I shall call it,_the_argument for_"Samuelson's_claim"4-and_the more general claim that_moderate risk aversion is irrational._After formulating_an axiomatic argument that I take to be_the_strongest case for_Samuelson's claim, I show that the argument essentially depends_on the principle of Event-Wise Dominance,_which those who_think_that_risk aversion can be_rational have a good reason to_reject. Hence, I conclude, the argument_is question begging if intended as a_general argument against the possibility of_rational risk aversion.5 2 Samuelson's_argument The_starting point of Samuelson's discussion_was the observation_that one_of his colleagues_at MIT-a "distinguished scholar", he says-did_in fact turn_down Samuelson's offer of a 'coin-toss-bet'6_like_the one discussed_above,_while_at the_same time confessing_his_willingness to_accept_a package consisting of 100 such_bets._Samuelson's colleague, whom I will henceforth refer_to as SC, justified_his_attitude by saying that_although the single bet was_not enough to make it "reasonably_sure that_the law_of averages will turn out in my favor", 4 As a_referee correctly points out, it is_not clear whether Samuelson_(1963) was_concerned_with showing that_turning_down the_single bet while accepting the package would_be irrational._Rather, he seems to have been_more concerned with showing_that_such behaviour would be inconsistent with_expected utility maximisation. Nevertheless, for the_sake of simplicity, and since_Samuelson_did_endorse expected utility theory in_much of his writings, I will_occasionally refer to_the claim in question as "Samuelson's claim"._5_It should be noted that this_is_not how Samuelson himself interpreted his_result._6_In what follows, a 'coin-toss-bet'_is a bet that pays bettors_$200 if their chosen side of a coin comes_up on a_particular toss but has them_paying_$100_otherwise. 4 H. Orri Stefánsson the law of large numbers_would make_a package consisting_of 100 such bets very attractive. "I am, so to_speak, virtually sure to come out ahead_in such a sequence, and that is why I accept the_sequence while rejecting the single