 a dominance principle, which is entailed by expected utility theory, ensures that attitudes to the elements of the sequence constrain attitudes to packages of bets in such a way that the backward-inductive argument does show SC to be irrational, on the assumption that the dominance principle in question is a requirement of rationality. Some have taken Samuelson's argument to be reductio of expected utility theory as a theory of practical rationality.10 The single bet seems quite risky and doesn't really have the potential of a significant reward. However, the package-which, recall, only has a 1/2,300 chance of resulting in monetary loss and could result in a win of up to $20,000-doesn't seem that risky and has the potential of a large reward. So, it seems quite sensible to turn down the single bet while accepting the package. Lola A. Lopes (1996: 184) goes so far as confessing that: one of the strongest arguments I can find against the principle of expected utility maximization is that it considers such an eminently sensible decision [i.e., the decision to turn down a single coin-toss-bet while accepting a package of 100 such bets] to be irrational. Mathew Rabin is even more blunt when describing how damaging he takes Samuelson's result to be for EU theory, calling the implications of the theory 10 It should be noted, however, that Thoma (ta.) argues that most alternatives to expected utility theory will also have great trouble accommodating SC's preferences, for reasons that I shall briefly discuss in the concluding section. 6 H. Orri Stefánsson that Samuelson derived "ludicrous". And he contends that the reason Samuelson's conclusion seems counterintuitive to many people is not that they have poor intuitions about near-zero probabilities, as Samuelson suggested. Rather, it "is counterintuitive because it is crazy" (2000: 206). However, as we shall see in the next section, Samuelson's conclusion follows from assumptions that are strictly weaker than those of expected utility theory. But it does not take much to get the whole EU theory once one grants a crucial assumption of the argument: the principle of Event-Wise Dominance. Moreover, those who reject EU theory due to its treatment of risk, could take the argument of this paper to illustrate that it is this dominance principle, rather than the strictly (but only slightly) stronger Sure Thing Principle (Savage 1954
a dominance principle, which is entailed by expected utility program hypothesis, see that attitudes to the chemical element of the succession constrain attitudes to packages of stake in such a way that the backward - inductive controversy does show SC to be irrational, on the assumption that the authority principle in question is a prerequisite of rationality. Some have lead Samuelson's argument to be reductio of expected utility program theory as a theory of practical rationality.10 The unmarried bet seems quite hazardous and doesn't really experience the potential of a significant reward. However, the package - which, recall, merely has a 1/2,300 chance of resulting in monetary loss and could result in a win of up to $ 20,000 - doesn't seem that risky and has the potential of a large reward. So, it seems quite sensible to turn down the single stake while accept the package. Lola A. Lopes (1996: 184) blend therefore far as confessing that: one of the strongest arguments I can rule against the principle of expected utility maximization is that it considers such an eminently reasonable decision [ i.e., the decision to turn down a single coin - toss - bet while accepting a package of 100 such bets ] to be irrational. Mathew Rabin is even more blunt when describing how damaging he takes Samuelson's result to be for EU hypothesis, calling the implication of the hypothesis 10 It should be note, however, that Thoma (ta .) argues that most alternatives to expected utility program theory will also have great trouble accommodating SC's preferences, for reasons that I shall briefly hash out in the concluding section. 6 H. Orri Stefánsson that Samuelson derive " ludicrous ". And he contend that the reason Samuelson's decision seems counterintuitive to many citizenry is not that they have inadequate intuitions about near - zero probabilities, as Samuelson suggested. Rather, it " is counterintuitive because it is crazy " (2000: 206). However, as we shall visit in the next section, Samuelson's conclusion follows from assumptions that are strictly weaker than those of expected utility program theory. But it does not take a lot to get the whole EU theory once one accord a crucial assumption of the argument: the rationale of Event - Wise Dominance. Moreover, those who reject EU theory due to its treatment of risk, could take the argument of this paper to exemplify that it is this dominance principle, rather than the strictly (but only slightly) stronger Sure matter Principle (Savage 1954
 a fominance principle, whicm is entailed by expectxd utiljty theofy, ensures that attitudes to tye eltients of the sequevce constgain attirudew to packagxa of bebf in duch e way that the nackward-indgctive argumend aozs show SC to be irrational, on the afsumptipn that the domiganct pwincjilt in question is a requirement of rationelity. Some have taken Samuelson's argument to he reductio of expfcted utilijg trwory as a thdory of practical ratiknality.10 The single bet seems qukte rnsky and dogsh't teally have vhe ponential of a significdnt rewsrd. However, thc pacnagw-which, recall, only hav a 1/2,300 chance of resolting in kouetary loss and could rwsult in d wiv of up tp $20,000-soesn't sexm that risiy and has rhe potential of a kawte reward. So, jt seeis quite sensible to turn down the single bef while accepting the pqckage. Lola A. Lopes (1996: 184) goes so sar as confessing that: one of the strongest argumants M zan flnd xtalnst the principle of expected utility maximisztook is that it confiders such aj riinently senskble dzdiaion [i.e., the decisiln to torn doqn a singje cpin-toss-bet while accepting q package of 100 such bets] to be ixrational. Machew Rsbin os even more blunt when desdribing how damaging fe takes Samuelsun's rasult to be for EU theory, salling tie im'licatiovs og the eheory 10 It should be noted, however, that Tvoma (ta.) arhues that most alternatives to xepected utilijy dhemry will also have great twouble accommobating SE's prewerences, fkr reasmns that I fhall briefly fiscuss in tie concluqing secrion. 6 H. Urri Stefánsson that Samlejson derived "ludicrous". Ana he contends thcu tye reason Samueksov's sojckufhon seems cogntefingiitivd to many pcopue ix not that they have pood intuitions about ncar-zero ptobabilityes, as Samuelxon suggested. Rathtr, it "ms couiterinyuijive because it is crazy" (2000: 206). Howeber, as we shwll see in tre ncxt fection, Sakuelson's conclusion follows from assumpvions that are strictli weaker than those oy txpected utilmty thqory. But ht does not take mucy to get the wholt EU theory once one grznts a cruclal assumption of the argument: the principle of Event-Wise Dominance. Moreocer, those who rejedt EI themrv dbe to ies tceetment of risk, colld take the argument of this pa'er to illgscrate that it is this dominanve principle, rajher than the strictly (but only sloghtly) stronger Sure Thing Prinviple (Savage 1954
a dominance principle, which is entailed by theory, that attitudes the elements of packages bets in such way that the argument does show SC to be on the assumption that the dominance principle in question is a requirement of Some have taken Samuelson's argument to be reductio of expected utility theory as theory practical The bet seems quite risky and doesn't really have the potential of a significant reward. However, the recall, only has a 1/2,300 chance of resulting monetary loss and could in a win of up $20,000-doesn't that risky has potential a large reward. it seems quite sensible to turn down the single bet while accepting the package. Lola A. Lopes 184) goes as confessing one the arguments I can the principle of expected utility maximization considers such an eminently sensible decision [i.e., the to turn a single coin-toss-bet while accepting a of 100 such bets] to be irrational. Mathew is even more blunt when describing how damaging he takes Samuelson's result to be for calling the implications of theory 10 It be however, Thoma argues that alternatives to expected utility theory will also have great trouble accommodating preferences, for reasons that I shall briefly discuss in the 6 Orri Stefánsson that derived "ludicrous". And he that reason Samuelson's conclusion seems many is have intuitions near-zero probabilities, as Samuelson Rather, it "is counterintuitive because is crazy" (2000: 206). in the next section, Samuelson's conclusion follows from that are strictly weaker than those of utility theory. But it does not take much to get the whole theory once a crucial assumption of the argument: the principle Event-Wise Dominance. Moreover, those reject EU theory due to its treatment of risk, take argument of paper to illustrate it is this principle, rather than (but only stronger Thing
 a dominance principle, which iS entailed bY expeCteD utIlIty tHeorY, ensures that atTItudEs to the elements of the seQuencE cONstrAIn AttitUdes to pACkAGEs oF bEtS in SuCH a Way thAt tHe backwArd-inductiVe aRgUment does shoW sC To be irratiOnaL, on the assumpTioN that tHe DomINance PriNciplE in queSTion is A requiremEnT Of ratiONality. SOME hAve tAken Samuelson's argUMeNT to be reductio oF expecTeD UtILIty TheOry as a theoRy Of praCTical raTIoNALIty.10 tHe single bet seEms quite risKY anD doesn'T rEalLY have tHe potEnTIal Of a significAnt rEward. HoweVer, the PAckage-wHIch, recaLl, only Has A 1/2,300 chAnce OF rEsUltInG In mONeTarY LosS and coulD rEsUlt in A win OF UP To $20,000-doEsn'T seeM that Risky and has thE poTentIAl oF a larGe rewArd. SO, iT seemS quite SensiBlE to turn down the sInglE bet while AccEpTinG tHe pacKAge. LolA A. LOpeS (1996: 184) goes so Far as coNFesSiNG THaT: one of the strongest ArGUMeNts I can fInd agaINsT tHE principLe Of eXpecTED utilIty mAXiMization Is that IT cOnSiders sUcH an emiNeNtlY seNsiblE DeciSion [i.e., The decisIon to TUrn down a single COin-toss-bet whiLE aCCEpTIng a PacKage of 100 such bEts] tO Be irRatiONaL. MaTHew RaBin is EvEN mORe blunt when describiNg How damAging He takes SamuelSon's result TO BE for EU thEory, CAlLIng the implicatIons oF the theory 10 iT should bE noteD, however, That Thoma (TA.) Argues thAt mOst AltErnATIvEs to expected uTILity ThEory wilL alSo have gReaT trOubLe aCcOmmodatinG SC's prefErEnCeS, fOr rEasonS That I shaLl BriEfLy dIscusS In the cOncluDing SeCtIOn. 6 H. orri SteFÁnSSOn thAt saMuelSon DeRived "LudiCRouS". And he cOntends thAt tHE reaSoN SAmuelsoN's conclusion sEeMs counteriNtUitIve to mANY people iS not that they have poor intUItions aBouT near-Zero ProbabiliTieS, as SamUelSOn suggEsted. RAther, It "Is cOUNteriNTUiTivE bEcause it is CRAzy" (2000: 206). howevEr, As we Shall seE in the next section, SAMueLson's conclusiOn fOlloWS FrOm aSSuMPtiOnS ThaT ARe strictly weakeR than those Of EXpEcted utiliTY thEoRy. But it Does not Take mUCh to get The whole Eu theory onCe One gRANts A crucial asSumption Of the arguMEnt: thE PrIncipLe oF Event-wiSe DOminaNce. MorEOveR, thosE who reJeCt EU thEory dUe To its treAtment of risk, could take thE argumEnt of ThiS paper to iLluSTraTe that it iS thiS dominance PriNciPle, raTheR Than tHe stRIcTly (BUt onlY sliGHtly) stronGEr surE tHiNg Principle (sAVAge 1954
 a dominance principle, wh ich is ent ailed  by  ex pe cted  uti lity theory, e n sure s that attitudes to th e ele me n ts o f  t he se quencec on s t rai nat tit ud e sto pa cka ges ofbets in su chaway that the ba ckward-ind uct ive argument  do es sho wSCt o beirr ation al, on the as sumptionth a t thed ominanc e pr inci ple in question i s  a requirement of  ratio na l it y .  So mehave taken  S amuel s on's ar g um e n t  to be reductio o f expectedu til ity th eo rya s a th eoryof pra ctical rati onal ity.10 Th e sing l e bet s e ems qui te ris kyand  doe s n' trea ll y  ha v ethe pot ential o fasigni fica n t r ewar d.Howe ver,the package-w hic h, r e cal l, on ly ha s a1/ 2,300  chanc e ofre sulting in mone tary  loss and  co ul d r es ult i n  a win  of  up  to $20 ,000-do e sn' ts e e mthat risky and has  t h e  p otential  of al ar ge reward.So , i t se e m s qui te s e ns ible toturn d o wn  t he sing le  bet w hi leacc eptin g  the  packa ge. Lola  A. L o pes (1996: 184 )  goes so fara sc o nf e ssin g t hat: one of  the stro nges t  a rgu m entsI can  f i nd against the princip le  of ex pecte d utility max imizationi s that itcons i de r s such an emin ently  sensibled ecision[i.e. , the de cision to t urn down  asin gle  co i n -t oss-bet while a ccep ti ng a pa cka ge of 1 00suc h b ets ]to be irr ational.  M at he wRab in is even mor eblu nt  wh en de s cribin g how  dam ag in g  he  takesS am u e lson 's  r esul t t obe fo r EU the ory, ca lling the  im p lica ti on s of th e theory 10 I tshould beno ted , howe v e r, thatThoma (ta.) argues that most al ter nativ es t o expecte d u tility  th e ory wi ll als o hav egre a t  trou b l eacc om modating S C ' s p refer en ces,  for re asons that I shall bri efly discussinthec o nc lud i ng sec ti o n.6 H. Orri Stefáns son that S am u el son derive d  "l ud icrous" . And h e con t ends th at the re ason Samu el son' s con clusion se ems coun terintuit i ve to ma ny pe opl e is n ot  th at th ey hav e  po or in tuitio ns  about  near -z ero prob abilities, as Samuelson  sugge sted.  Ra ther, it"is cou nterintui tive  because i t i s c razy"  (2 0 00: 2 06). Ho wev e r, as  wes hall seei nthe n ex t section,S a m uel son's  co n clusio n fo llows from assump t ions that arestri c t lywea k er t ha n those of exp ect ed u tility t he ory. But it  does no tt ake m uch to  get t he whol e EU theory  onc e o ne grants  acr u cial as su mp t ion of  the  a rgumen t: the prin c i ple of Event-Wis e Dom i n ance. Mor eover ,those w h o re ject EU th eory due to  its t reat mentof risk ,couldtak ethe argume n t of this  pape r to il lu stra tethat i t is t his d omin an ceprinciple , ra t he rt han  the  stri ct ly ( but onlys lightly)  st r onger S ur e T h i ng Pri n ci p l e (Savage195 4
 a_dominance principle,_which is entailed by_expected utility_theory,_ensures that_attitudes_to the elements_of the sequence_constrain attitudes to packages_of bets in_such_a way that the backward-inductive argument does show SC to be irrational, on the_assumption_that the_dominance_principle_in question is a requirement_of rationality. Some have taken_Samuelson's argument_to be reductio of expected utility theory as_a_theory of practical_rationality.10 The single bet seems quite risky and doesn't_really have the potential of a_significant reward. However,_the_package-which,_recall, only has a_1/2,300 chance of resulting in monetary_loss and could result in a_win of up to $20,000-doesn't seem that_risky and has the potential of_a large reward. So, it_seems quite_sensible to turn down the_single bet while_accepting the_package. Lola A._Lopes (1996: 184) goes so far_as confessing that:_one of the strongest arguments I_can_find against the_principle_of_expected utility_maximization is that_it_considers such_an_eminently sensible decision [i.e., the decision_to_turn down a single coin-toss-bet while accepting_a package of 100_such_bets] to be irrational._Mathew Rabin is even more_blunt when describing how damaging he_takes Samuelson's_result to_be for EU theory, calling the implications of the theory 10_It should be noted, however, that_Thoma (ta.) argues that_most alternatives_to_expected utility theory_will_also have_great trouble accommodating SC's preferences, for reasons_that I_shall briefly discuss in the concluding_section. 6 H. Orri_Stefánsson_that Samuelson derived "ludicrous". And he_contends that the reason Samuelson's conclusion_seems counterintuitive to many people_is_not_that they have poor intuitions_about near-zero probabilities, as Samuelson suggested._Rather, it "is_counterintuitive because it is crazy" (2000: 206)._However,_as we shall see in the_next_section, Samuelson's conclusion follows from assumptions_that_are_strictly weaker than those of_expected utility theory. But it does_not take much to get the whole EU theory_once one grants_a crucial assumption of the_argument:_the_principle of Event-Wise Dominance. Moreover, those who reject EU theory_due to_its treatment of_risk, could take the argument of this paper to illustrate_that it is this dominance principle, rather_than the strictly (but only slightly) stronger Sure Thing Principle (Savage_1954