? 13 Bradley and Stefánsson 2017), then EWD is not rationally required. Hence, since the strongest case for Samuelson's claim that one cannot rationally accept a package of bets of a particular kind while turning down a single bet of that kind essentially depends on EWD, the claim should be rejected by anyone who thinks that risk aversion is rationally permissible. More generally, Samuelson's argument does not show risk aversion to be irrational. 5 Concluding remarks The axiomatic argument presented above shows that if both Transitivity and Event-Wise Dominance are requirements of rationality, then one cannot rationally turn down a single coin-toss-bet for all levels of wealth while accepting some package of such bets. So, if one is to vindicate a preference like that of Samuelson's colleague-and, it would seem, if one wants to allow for moderate risk aversion-one has to give up either Transitivity or Event-Wise Dominance. However, those who think that risk aversion can be rational-and, in particular, those who think that the orthodox treatment of risk attitudes in decision theory and economics is flawed-should be skeptical of EWD anyway, for reasons I have discussed. In fact, theories that have been developed as alternatives to expected utility theory, in particular to allow for a wider range of risk attitudes than those for which EU theory can account, typically allow for violations of EWD (see e.g. Kahneman and Tversky 1979, Buchak 2013, Bradley and Stefánsson 2017). And these theories are indeed consistent with preference patterns like those reported by Samuelson's colleague. However, since these theories allow for violations of EWD-and, in particular, since they allow agents to evaluate bets differently depending on whether they are embedded in a larger bet or not-applications of them can have different implications depending on how a decision-problem is framed. In particular, as Thoma (ta.) stresses, theories that allow for violations of EWD may recommend the rejection of a bet when it is formulated as a one-off decision, while recommending the acceptance of the same bet when it is formulated as part of, say, the bundle of bets that the decision-maker in question will be faced with for the rest of her life. In contrast, theories that include EWD will deliver the same verdict irrespective of which of these two ways of viewing a bet is adopted, and can thus be safely combined with a
? 13 Bradley and Stefánsson 2017), then EWD is not rationally required. Hence, since the strongest case for Samuelson's title that one cannot rationally bear a package of bets of a particular kind while change state down a single bet of that kind basically depends on EWD, the claim should be rejected by anyone who think that risk aversion is rationally permissible. More broadly, Samuelson's argument does not show hazard aversion to be irrational. 5 Concluding remarks The axiomatic argument presented above shows that if both Transitivity and Event - Wise Dominance are requirements of rationality, then one cannot rationally turn down a individual coin - toss - bet for all levels of wealth while accept some package of such bets. So, if one is to vindicate a predilection like that of Samuelson's colleague - and, it would seem, if one want to allow for moderate risk aversion - one give birth to give up either Transitivity or Event - Wise Dominance. However, those who think that risk aversion can be rational - and, in especial, those who think that the orthodox treatment of risk attitudes in decision theory and economics is flawed - should be skeptical of EWD anyway, for reasons I have discourse. In fact, theories that have been developed as option to expect utility program theory, in particular to allow for a wider range of risk attitudes than those for which EU theory can report, typically allow for violations of EWD (see e.g. Kahneman and Tversky 1979, Buchak 2013, Bradley and Stefánsson 2017). And these theories are indeed consistent with preference patterns like those reported by Samuelson's colleague. However, since these theories allow for violations of EWD - and, in especial, since they allow agent to evaluate bets differently depending on whether they are embedded in a larger stake or not - applications of them can have different implications depending on how a decision - problem is framed. In particular, as Thoma (ta .) stress, theories that leave for violations of EWD may commend the rejection of a bet when it is formulated as a one - off decision, while recommending the credence of the same stake when it is formulated as part of, say, the bundle of bet that the decision - manufacturer in question will be faced with for the rest of her life. In contrast, theories that include EWD will deliver the same verdict regardless of which of these two ways of viewing a stake is adopted, and can thus be safely combined with a
? 13 Bgadley and Stefánsson 2017), thtn EWD is not ratninally requided. Hencd, since the strongest case flr Samutjson's claim that ove cannot rationaoly eccept a package of bets of a lwrtieuoar kind while turning dmwn a single bat oy that kind essentially depends on ERD, the vlwim should be tejecued by znyone who thinks that risk aversikn is retionally permixsible. More generally, Samuflsoj's argument does nlt show risj avqesion to be krrational. 5 Concluding remarks The axiomatic argument presznted above syowd that if bovh Tragsitivity and Event-Whse Domonance are reqmiremxnts of rationality, then mne cannot rationajly turn gocn a single coin-toss-bwt for dll neveuw ow wtalvh shile wccxpting some package of such bets. So, if ont if to vindicate a presewence like that of Samuelson's colleague-dnd, it would seem, if one wqnts to allow for modgrate risk aversion-one has to give up either Transitivity os Eveit-Dist Eominxbcf. However, those who think that risk aversion szn bv rational-and, in iarticular, those wno tnynk that the urthodox freatment of risk wttitudgs in eecision uheoru and economics is flawed-shiuld be skepnicao of EWD anyway, fox reasons I kave doscusxed. In fact, theories thct havs been devepoped as zuternatives to ebpebted utility theory, in particujar to aloow yor a wiaer tange os risk attltudes than those for whlch EO theosy can acclunt, typically allow for violatmpns of EWD (sge a.g. Nahneman and Bversky 1979, Buchak 2013, Bradley and Xtefánssjn 2017). Avd these tgeories are indeed consistent whjh preference patternf lije tyose reourted by Samuekson's colleague. Howwver, since these tmeorigs allow for violcuiobs of EWD-and, in paftisupac, sinsa they allow agevts yo evxluate bets aiffrrently depending on whefher they are embecdcd in a lqrger bee or not-applivations of them caj havx diffxrent ompjications depending on how a dscision-prlblcm is framed. Yn pqrticular, as Thoma (ta.) stresses, theories that allow hor violations of EWD mqy recommend the relegtion of a bxt wheg it is fmrmulated as a one-ofd decision, while vecommending the accepfance mf thf same bet when it is formulated as part of, say, the bundle of bets that tye decmsyon-maker in quextion wnll be fased xivh for the rest og her life. In contrast, theories that inwlbde EWD will deliver the same vdrdict irrespgctive of which of these tso ways pf viewing a bet is adopted, and can thus be safely comblned with a
? 13 Bradley and Stefánsson 2017), then not required. Hence, the strongest case cannot accept a package bets of a kind while turning down a single of that kind essentially depends on EWD, the claim should be rejected by who thinks that risk aversion is rationally permissible. More generally, Samuelson's argument does show aversion be 5 Concluding remarks The axiomatic argument presented above shows that if both Transitivity and Event-Wise Dominance requirements of rationality, then one cannot rationally turn a single coin-toss-bet for levels of wealth while accepting package such bets. if is vindicate a preference that of Samuelson's colleague-and, it would seem, if one wants to allow for moderate risk aversion-one has give up or Event-Wise However, who that risk aversion rational-and, in particular, those who think treatment of risk attitudes in decision theory and is flawed-should skeptical of EWD anyway, for reasons have discussed. In fact, theories that have been as alternatives to expected utility theory, in particular to allow for a wider range of than those for which theory can account, allow violations EWD e.g. Kahneman Tversky 1979, Buchak 2013, Bradley and Stefánsson 2017). And these theories indeed consistent with preference patterns like those reported by Samuelson's since theories allow for of EWD-and, in particular, they agents to evaluate bets on they a bet not-applications of them can different implications depending on how decision-problem is framed. In theories that allow for violations of EWD may the rejection of a bet when it formulated as a one-off decision, while recommending the acceptance of the same when it as part of, say, the bundle of bets the decision-maker in question be faced with for the rest of her life. contrast, that include will deliver the verdict irrespective of of these two viewing a is and safely combined with a
? 13 Bradley and Stefánsson 2017), then EwD is not ratIonalLy rEquIrEd. HeNce, sInce the strongeST casE for Samuelson's claim thaT one cAnNOt raTIoNally Accept a PAcKAGe oF bEtS of A pARtIculaR kiNd while Turning dowN a sInGle bet of that KInD essentialLy dEpends on EWD, tHe cLaim shOuLd bE RejecTed By anyOne who THinks tHat risk avErSIon is rATionallY PErMissIble. More generally, sAmUElson's argument Does noT sHOw RISk aVerSion to be irRaTionaL. 5 concludINg REMArkS the axiomatic aRgument presENteD above ShOws THat if bOth TrAnSItiVity and EvenT-WisE DominancE are reQUiremenTS of ratiOnalitY, thEn oNe caNNoT rAtiOnALly TUrN doWN a sIngle coiN-tOsS-bet fOr alL LEVEls oF weAlth While Accepting some PacKage OF suCh betS. So, if One iS tO vindIcate a PrefeReNce like that of SaMuelSon's colleAguE-aNd, iT wOuld sEEm, if onE waNts To allow For modeRAte RiSK AVeRsion-one has to give uP eITHeR TransitIvity oR evEnT-wise DomiNaNce. howeVER, thosE who THiNk that riSk averSIoN cAn be ratIoNal-and, In ParTicUlar, tHOse wHo thinK that the OrthoDOx treatment of rISk attitudes in DEcISIoN TheoRy aNd economics Is flAWed-sHoulD Be SkePTical Of EWD AnYWaY, For reasons I have discUsSed. In fAct, thEories that havE been develOPED as alterNatiVEs TO expected utiliTy theOry, in partiCUlar to alLow foR a wider rAnge of risK ATtitudes ThaN thOse For WHIcH EU theory can aCCOunt, TyPically AllOw for viOlaTioNs oF EWd (sEe e.g. KahneMan and TvErSkY 1979, BUcHak 2013, bradlEY and StefÁnSsoN 2017). ANd tHese tHEories Are inDeed CoNsISteNt with pREfEREnce PaTtErns LikE tHose rEporTEd bY SamuelSon's colleAguE. howeVeR, sInce theSe theories allOw For violatiOnS of eWD-and, IN ParticulAr, since they allow agents tO EvaluatE beTs difFereNtly depenDinG on wheTheR They arE embedDed in A lArgER Bet or NOT-aPplIcAtions of thEM Can Have dIfFereNt impliCations depending on HOw a Decision-problEm iS fraMED. IN paRTiCUlaR, aS thoMA (Ta.) stresses, theorIes that allOw FOr Violations OF EWd mAy recomMend the RejecTIon of a bEt when it iS formulatEd As a oNE-Off Decision, whIle recomMending thE AccepTAnCe of tHe sAme bet WhEn iT is foRmulatED as Part oF, say, thE bUndle oF bets ThAt the decIsion-maker in question wilL be facEd witH foR the rest oF heR LifE. In contraSt, thEories that IncLudE EWD wIll DEliveR the SAmE veRDict iRresPEctive of wHIcH of THEsE two ways of vIEWIng A bet iS adOPted, anD can Thus be safely combiNEd with a
? 13 Bradley and Stefánsso n 2017), t hen E WDisno t ra tion ally required. Henc e, since the strongest  case  f o r Sa m ue lson' s claim th a t  on eca nno tr at ional lyaccepta packageofbe ts of a part i cu lar kind w hil e turning do wna sing le  be t  of t hat  kind  essen t iallydepends o nE WD, th e  claims h ou ld b e rejected by any o ne who thinks tha t risk  a v er s i onisrationally  p ermis s ible. M o re g e ner a lly, Samuelso n's argumen t  do es not  s how risk a versi on tobe irration al.5 Conclud ing re m arks Th e  axioma tic ar gum ent  pre s en te d a bo v e s h ow s t h atif bothTr an sitiv itya n d Even t-W iseDomin ance are requ ire ment s  of  rati onali ty,th en on e cann ot ra ti onally turn dow n asingle co in- to ss- be t for all le vel s o f wealt h while acc ep t i n gsome package of su ch b et s. So, i f onei sto vindicat ea p refe r e nce l iket ha t of Sam uelson ' sco lleague -a nd, it  w oul d s eem,i f on e want s to all ow fo r  moderate risk aversion-oneh as t og iveupeither Tran siti v ityor E v en t-W i se Do minan ce .  H o wever, those who th in k that  risk  aversion can  be ration a l - and, inpart i cu l ar, those whothink  that theo rthodoxtreat ment ofrisk atti t u des in d eci sio n t heo r y  a nd economicsi s  fla we d-shoul d b e skept ica l o f E WDan yway, for  reasons  I  h av edis cusse d . In fac t,  th eo rie s tha t  havebeendeve lo pe d  as  altern a ti v e s to  e xp ecte d u ti litytheo r y,in part icular to  al l ow f or  a  widerrange of risk  a ttitudes t ha n t hose f o r  which E U theory can account, t y pically  al low f or v iolations  of  EWD ( see e.g. K ahnema n and  T ver s k y 197 9 ,  B uch ak  2013, Bra d l eyand S te fáns son 201 7). And these theo r ies  are indeed c ons iste n t  w ith pr e fer en c e p a t terns like thos e reported  b y  S amuelson's col le ague. H owever,  sinc e  thesetheoriesallow for  v iola t i ons  of EWD-an d, in pa rticular, since th ey al low  agent stoevalu ate be t s d iffer entlyde pendin g onwh ether th ey are embedded in a la rger b et or  no t-applica tio n s o f them ca n ha ve differe ntimp licat ion s  depe ndin g  o n h o w a d ecis i on-proble m  i s f r a me d. In parti c u l ar,  as T hom a  (ta.)  str esses, theories t h at allow for v iola t i ons  of EWDma y recommend th e r ej e c tion ofabet when it  is form ul a ted a s a on e-offdecisio n ,  w h ile re comm end ing the a cce pt a nce ofth es ame be t wh en  it is  formu l ated a s part of, say,the b u n dle o f  be ts th at  the de c isio n-maker in  question w ill be  fac ed wi th forth e rest  of  h er life. I n  contrast , the ories t ha t in clu de EWD  wil l deliv er t he  sa me verdic t ir r es pe c tiv e of  whic hof t hese twow ays of v iew i ng a be tisa d opted, an d can thus b e s afely c ombined wi t h a
? 13_Bradley and_Stefánsson 2017), then EWD_is not_rationally_required. Hence,_since_the strongest case_for Samuelson's claim_that one cannot rationally_accept a package_of_bets of a particular kind while turning down a single bet of that kind_essentially_depends on_EWD,_the_claim should be rejected by_anyone who thinks that risk_aversion is_rationally permissible. More generally, Samuelson's argument does not_show_risk aversion to_be irrational. 5 Concluding remarks The axiomatic argument presented_above shows that if both Transitivity_and Event-Wise Dominance_are_requirements_of rationality, then one_cannot rationally turn down a single_coin-toss-bet for all levels of wealth_while accepting some package of such bets._So, if one is to vindicate_a preference like that of_Samuelson's colleague-and,_it would seem, if one_wants to allow_for moderate_risk aversion-one has_to give up either Transitivity or_Event-Wise Dominance. However,_those who think that risk aversion_can_be rational-and, in_particular,_those_who think_that the orthodox_treatment_of risk_attitudes_in decision theory and economics is_flawed-should_be skeptical of EWD anyway, for reasons_I have discussed. In_fact,_theories that have been_developed as alternatives to expected_utility theory, in particular to allow_for a_wider range_of risk attitudes than those for which EU theory can account,_typically allow for violations of EWD_(see e.g. Kahneman and_Tversky 1979,_Buchak_2013, Bradley and_Stefánsson_2017). And_these theories are indeed consistent with preference_patterns like_those reported by Samuelson's colleague. However,_since these theories allow_for_violations of EWD-and, in particular, since_they allow agents to evaluate bets_differently depending on whether they_are_embedded_in a larger bet or_not-applications of them can have different_implications depending on_how a decision-problem is framed. In particular,_as_Thoma (ta.) stresses, theories that allow_for_violations of EWD may recommend the_rejection_of_a bet when it is_formulated as a one-off decision, while_recommending the acceptance of the same bet when it_is formulated as_part of, say, the bundle_of_bets_that the decision-maker in question will be faced with for_the rest_of her life._In contrast, theories that include EWD will deliver the same_verdict irrespective of which of these two_ways of viewing a bet is adopted, and can thus be_safely combined with a