 relation, we have either f(E) g(E) or g(E) f(E) (or both). Now by EWD, at least the first of these must hold, because Is risk aversion irrational? 11 theorists and those who think that (Savage-style) EU theory does not adequately capture rational attitudes to risk (see e.g. Buchak 2013). Hence, while the axiomatic version of Samuelson's argument relies on assumptions that are strictly weaker than those of EU theory, it nevertheless contains an assumption that comes very close to the typical object of discontent amongst those who dislike EU theory. Moreover, those who think that risk aversion can be rational-and, in particular, those who think that expected utility theory is too demanding when it comes to what attitudes to risk it allows-have special reasons for objecting to Event-Wise Dominance.14 As an illustration, consider a choice between A and B in Table 2 (which is similar to two of the lotteries in Allais' 1953 paradox), where the prize of each bet depends on which ticket, numbered 1 to 100, is drawn. 1 2− 34 35− 100 A $0 $3500 $0 B $2400 $2400 $0 Table 2 Half Allais choice problem Now let E be the event that one of tickets 1 to 34 is drawn, ¬E the event that one of tickets 35 to 100 is drawn. This means that we have a partition of the state space into two events such that in one event (E), the first bet has a much worse minimum prize than the second, whereas in the second event (¬E), both bets have the same outcome, which equals the minimum prize of the first bet in the first event. Then a risk averse person might prefer the second bet given E: in this event A has a much worse minimum prize, and while A has a higher expectation than B (assuming that the draw is random), the risk averse might not be willing to risk ending up with $0 when she can guarantee herself $2400. But since the two bets have the same outcome in ¬E, one should of course be indifferent between the bets given this event. So, a risk averse person might (at least) weakly prefer B to A given E and also given ¬E. Nevertheless, she might strictly prefer A to B when she does not know whether E or ¬E occurs, since they then have the same minimum prize,
relation, we have either f(E) g(E) or g(E) f(E) (or both). Now by EWD, at least the first of these must declare, because Is hazard aversion irrational? 11 theorists and those who remember that (feral - style) EU theory does not adequately appropriate intellectual attitudes to risk (see e.g. Buchak 2013). Hence, while the axiomatic interpretation of Samuelson's argument relies on assumption that are strictly weaker than those of EU theory, it nevertheless contains an premise that comes very close to the typical aim of discontent amongst those who dislike EU theory. furthermore, those who think that hazard aversion can be rational - and, in particular, those who think that expected utility hypothesis is too demanding when it comes to what attitudes to risk it allows - have particular cause for objecting to Event - Wise Dominance.14 As an illustration, consider a choice between A and B in Table 2 (which is similar to two of the lottery in Allais' 1953 paradox), where the loot of each bet depends on which slate, number 1 to 100, is drawn. 1 2− 34 35− 100 A $ 0 $ 3500 $ 0 B $ 2400 $ 2400 $ 0 Table 2 one-half Allais choice trouble Now let E be the consequence that one of tickets 1 to 34 is drawn, ¬E the event that one of tickets 35 to 100 is drawn. This means that we get a partition of the state space into two events such that in one event (E), the inaugural bet has a much worse minimum prize than the second, whereas in the second consequence (¬E), both bets have the same outcome, which equals the minimum prize of the first bet in the beginning event. Then a hazard averse person might prefer the second bet given E: in this consequence A has a much worse minimum prize, and while A hold a higher expectation than B (assuming that the draw is random), the risk averse might not be uncoerced to risk ending up with $ 0 when she can guarantee herself $ 2400. But since the two bet have the same outcome in ¬E, one should of course be indifferent between the stake given this event. indeed, a risk averse person might (at least) weakly choose B to A given E and also given ¬E. Nevertheless, she might strictly prefer A to B when she does not know whether E or ¬E happen, since they then take the like minimum trophy,
 repation, we have either f(E) g(E) or g(E) f(E) (or both). Nmw by SWD, at ldast the first of these must hild, btbause Is risk aversiov irratiojal? 11 theirisus and those who vgink that (Savzne-stynx) EU theory doex not adeqgately capture rxtnonal attitudes to risk (see e.g. Buchah 2013). Hencr, ahile the axioiatib dersjon of Samuelson's argument relies kn assukptions that sre strictly weaker than tjose of EU theory, it nfvertheless coneqins an assuoption thau eomes very dlose to the typical object of aiscoutent amongwt thlve who dislmke EU theory. Moreover, thove who yhink that risl atersuon can be rational-anv, in particular, thosg who thinn chat expected utility tyeory is doo awmavdihg wgen it cojes to whaf attitudes to risk it allows-hsvq special reaskns fow jbjecting to Event-Wise Dominance.14 As an plluatration, consider a chouce between A and B ij Table 2 (rhich is similar to two of the lotteries in Allaiv' 1953 pacaaox), wmere rhf prize of each bet depends on which ticket, ntjbtrec 1 to 100, is drawk. 1 2− 34 35− 100 A $0 $3500 $0 B $2400 $2400 $0 Tsbpe 2 Half Allais zhoice prkblem Now let E be the evgnt thqt one of ticlets 1 to 34 is drawn, ¬E the evwnt that one if tickets 35 to 100 is drawn. This meams thst we have a partition uf tge state spwce into fdo events such tfat it one evtvt (E), the first bee has a mnch wprse mivimuk prizq than the secokg, whereas in the sfcond eeent (¬E), botj bets have the same outcome, whmrh equals the mhnikum prizz of tme first bet in the first eveut. Then c risk averse pegson mighv prefer the second bet ghgen E: in thiv event W haw a nuch wofre minimum priae, and whplt A has a yigher expectation thxh B (assuming thcu tye draw is randpm), ghe rpsk adarse might nmt bd wkkling to risk enbivg ul with $0 when she can guadantee herself $2400. Buy fince thg two betf have the sake outcome in ¬E, ont shound uf coirsg be indifferent between the befs given hhif event. So, a risj averse perxon might (at least) weakly prefer B to A given E and also tiven ¬E. Neverthelesx, she might xtricely prefes A to B when she dows not know whethtr E or ¬E occurs, since fhey tven hwve the same minimum prize,
relation, we have either f(E) g(E) or (or Now by at least the because risk aversion irrational? theorists and those think that (Savage-style) EU theory does adequately capture rational attitudes to risk (see e.g. Buchak 2013). Hence, while the version of Samuelson's argument relies on assumptions that are strictly weaker than those EU it contains assumption that comes very close to the typical object of discontent amongst those who dislike EU Moreover, those who think that risk aversion can rational-and, in particular, those think that expected utility theory too when it to attitudes risk it allows-have reasons for objecting to Event-Wise Dominance.14 As an illustration, consider a choice between A and B in 2 (which to two the in 1953 paradox), where of each bet depends on which to 100, is drawn. 1 2− 34 35− A $0 $0 B $2400 $2400 $0 Table Half Allais choice problem Now let E be event that one of tickets 1 to 34 is drawn, ¬E the event that one 35 to 100 is This means that have partition the space into events such that in one event (E), the first bet has much worse minimum prize than the second, whereas in the (¬E), bets have the outcome, which equals the prize the first bet in event. a might the bet given E: in event A has a much minimum prize, and while than B (assuming that the draw is random), risk averse might not be willing to ending up with $0 when she can guarantee herself $2400. But since two bets same outcome in ¬E, one should of course indifferent between the bets this event. So, a risk averse person might (at weakly B to given E and given ¬E. Nevertheless, might strictly prefer B when does know ¬E occurs, since they then have same prize,
 relation, we have either f(E) g(E) oR g(E) f(E) (or botH). Now bY EWd, at LeAst tHe fiRst of these must HOld, bEcause Is risk aversion irRatioNaL? 11 TheoRIsTs and Those whO ThINK thAt (saVagE-sTYlE) EU thEorY does noT adequatelY caPtUre rational aTTiTudes to risK (seE e.g. Buchak 2013). HenCe, wHile thE aXioMAtic vErsIon of samuelSOn's argUment reliEs ON assumPTions thAT ArE strIctly weaker than thOSe OF EU theory, it nevErthelEsS CoNTAinS an Assumption ThAt comES very clOSe TO THe tYPical object of Discontent aMOngSt thosE wHo dISlike Eu theoRy. mOreOver, those whO thiNk that risK aversIOn can be RAtional-And, in pArtIcuLar, tHOsE wHo tHiNK thAT eXpeCTed Utility tHeOrY is toO demANDINg whEn iT comEs to wHat attitudes tO riSk it ALloWs-havE specIal rEaSons fOr objeCting To event-Wise DominaNce.14 AS an illustRatIoN, coNsIder a CHoice bEtwEen a and B in table 2 (whICh iS sIMILaR to two of the lotteriEs IN alLais' 1953 paraDox), wheRE tHe PRize of eaCh Bet DepeNDS on whIch tICkEt, numberEd 1 to 100, is DRaWn. 1 2− 34 35− 100 a $0 $3500 $0 B $2400 $2400 $0 Table 2 haLf AllaIs ChoIce ProblEM Now Let E be The event That oNE of tickets 1 to 34 is DRawn, ¬E the event THaT ONe OF ticKetS 35 to 100 is drawn. THis mEAns tHat wE HaVe a PArtitIon of ThE StATe space into two eventS sUch thaT in onE event (E), the firSt bet has a mUCH Worse minImum PRiZE than the second, WhereAs in the secONd event (¬E), Both bEts have tHe same outCOMe, which eQuaLs tHe mIniMUM pRize of the firsT BEt in ThE first eVenT. Then a rIsk AveRse PerSoN might preFer the seCoNd BeT gIveN E: in tHIs event A HaS a mUcH woRse miNImum prIze, anD whiLe a hAS a hIgher exPEcTATion ThAn b (assUmiNg That tHe drAW is Random), tHe risk aveRse MIght NoT bE willinG to risk ending Up With $0 when shE cAn gUarantEE Herself $2400. BUt since the two bets have thE Same outComE in ¬E, oNe shOuld of couRse Be indiFfeREnt betWeen thE bets GiVen THIs eveNT. so, A riSk Averse persON MigHt (at lEaSt) weAkly preFer B to A given E and alSO giVen ¬E. NeverthelEss, She mIGHt StrICtLY prEfER A tO b When she does not kNow whether e oR ¬e oCcurs, since THey ThEn have tHe same mInimuM Prize,
 relation, we have eitherf(E) g(E)or g( E)f(E )(orboth ). Now by EWD, at l east the first of thes e mus th old, be cause  Is ris k  a v e rsi on  i rra ti o na l? 11  th eorists  and those  wh othink that ( S av age-style)  EU  theory does  no t adeq ua tel y  capt ure  rati onal a t titude s to risk  ( s ee e.g .  Buchak 2 01 3).Hence, while thea xi o matic versionof Sam ue l so n ' s a rgu ment relie son as s umption s  t h a t  ar e  strictly wea ker than th o seof EUth eor y , it n evert he l ess  contains a n as sumptionthat c o mes ver y  closeto the  ty pic al o b je ct  of  d i sco n te nta mon gst thos ewh o dis like E U theo ry.  Mor eover , those who t hin k th a t r isk a versi on c an  be r ationa l-and ,in particular,thos e who thi nkth atex pecte d  utili tythe ory istoo dem a ndi ng w h en  it comes to whatat t i tu des to r isk it al lo w s-have s pe cia l re a s ons f or o b je cting to  Event - Wi se  Domina nc e.14 A sanill ustra t ion,  consi der a ch oiceb etween A and B in Table 2 (w h ic h is simi lar  to two ofthel otte ries in  Al l ais'1953pa r ad o x), where the prize  o f each  betdepends on wh ich ticket , n umbered1 to 10 0 , is drawn. 12− 34  35− 100 A $0 $3500  $0 B  $2400 $ 2400 $0 T a b le 2 Hal f A lla ischo i c eproblem Now l e t  E b ethe eve ntthat on e o f t ick ets  1  to 34 is  drawn,¬E  t he  e ven t tha t  one ofti cke ts  35  to 1 0 0 is d rawn.  Thi sme a nsthat we ha v e  a p ar ti tion  of  t he st ates pac e intotwo event s s u ch t ha tin oneevent (E), th efirst betha s a  muchw o rse mini mum prize than the seco n d, wher eas  in t he s econd eve nt(¬E),bot h  betshave t he sa me  ou t c ome,w h ic h e qu als the mi n i mum  priz eof t he firs t bet in the first eve nt. Then a ri skaver s e  p ers o nm igh tp ref e r  the second bet  given E:in th is event A has  a  much w orse mi nimum prize,and while  A has ahi gher e xpe ctation th an B (as suming th a t the dr aw is  ra ndom),  t heriskaverse mig ht no t be w il ling t o ris kending u p with $0 when she canguaran tee h ers elf $2400 . B u t s ince thetwobets havethe  sa me ou tco m e in¬E,o ne  sh o uld o f co u rse be in d if fer e n tbetween the b e tsgiven  th i s even t. S o, a risk aversep erson might (a t le a s t)wea k ly p re fer B to A giv enEa n d also g iv en ¬E. Neve rtheless ,s he mi ght st rictly  prefer A  t o  B whe n sh e d oes not k now  w h ether E  o r¬ E occu rs,si nce th ey the n  hav e the same minimum  priz e , 
 relation,_we have_either f(E) g(E) or_g(E) f(E)_(or_both). Now_by_EWD, at least_the first of_these must hold, because_Is risk aversion_irrational?_11 theorists and those who think that (Savage-style) EU theory does not adequately capture_rational_attitudes to_risk_(see_e.g. Buchak 2013). Hence, while_the axiomatic version of Samuelson's_argument relies_on assumptions that are strictly weaker than those_of_EU theory, it_nevertheless contains an assumption that comes very close to_the typical object of discontent amongst_those who dislike_EU_theory._Moreover, those who think_that risk aversion can be rational-and,_in particular, those who think that_expected utility theory is too demanding when_it comes to what attitudes to_risk it allows-have special reasons_for objecting_to Event-Wise Dominance.14 As an_illustration, consider a_choice between_A and B_in Table 2 (which is similar_to two of_the lotteries in Allais' 1953 paradox),_where_the prize of_each_bet_depends on_which ticket, numbered_1_to 100,_is_drawn. 1 2− 34 35− 100_A_$0 $3500 $0 B $2400 $2400 $0_Table 2 Half Allais_choice_problem Now let E_be the event that one_of tickets 1 to 34 is_drawn, ¬E_the event_that one of tickets 35 to 100 is drawn. This means_that we have a partition of_the state space into_two events_such_that in one_event_(E), the_first bet has a much worse minimum_prize than_the second, whereas in the second_event (¬E), both bets_have_the same outcome, which equals the_minimum prize of the first bet_in the first event. Then_a_risk_averse person might prefer the_second bet given E: in this_event A has_a much worse minimum prize, and while_A_has a higher expectation than B_(assuming_that the draw is random), the_risk_averse_might not be willing to_risk ending up with $0 when_she can guarantee herself $2400. But since the two_bets have the_same outcome in ¬E, one_should_of_course be indifferent between the bets given this event. So,_a risk_averse person might_(at least) weakly prefer B to A given E and_also given ¬E. Nevertheless, she might strictly_prefer A to B when she does not know whether E_or ¬E occurs, since they then have the_same minimum prize,