 [bet]" (Samuelson, 1963: 51). To examine this pair of preferences, Samuelson assumed that his colleague would still turn down an offer of the single bet if his wealth increased or decreased by the maximum amount that he could gain ($20,000) or lose ($10,000) from the package of 100 bets7 (an innocent assumption, he thought, given what distinguished MIT scholars typically earn).8 On the basis of this assumption, Samuelson proved that if his colleague were an expected utility maximiser, as utility is typically defined,9 then he would not accept the package consisting of 100 bets, since he did not accept the single bet. The logic behind Samuelson's argument is very simple (1963: 53): If you will not accept one toss, you cannot accept two-since the latter could be thought of as consisting of the (unwise) decision to accept one plus the open decision to accept a second. Even if you were stuck with the first outcome, you would cut your further (utility) losses and refuse the terminal throw. By extending the reasoning from 2 to 3 = 2 + 1,..., and from n-1 to n, we rule out any sequence [i.e., any package of bets] at all. In other words, the conclusion is that since SC preferred his status quo to accepting the single coin-toss-bet, and assuming that he would continue to do so for all wealth levels, he should prefer his status quo to any package of such bets. Samuelson's (informal) illustration of his argument is rather unfortunate, since it makes it seem as if the argument depends on the assumption that his colleague would turn down the first coin-toss-bet in a sequence of such bets. But foreseeing the sequence, the colleague might accept the first bet. As Lara Buchak (2013: 219) puts it: By assuming that an agent will reject [the first bet], the argument ignores the fact that just as the act of taking a bet cannot be fully described, in the framework of decision theory, without knowing an agent's current holdings-which bets an agent accepted in the past- the act of taking a bet also cannot be fully described without knowing what choices an agent will be offered in the future. 7 Strictly speaking, the argument only requires the assumption that SC would turn down the single bet for any level of wealth in the range that the first 99 bets could result in. Hence, when this assumption is formal
[ bet ] " (Samuelson, 1963: 51). To examine this pair of preferences, Samuelson assume that his colleague would however turn down an offer of the single stake if his wealth increased or decreased by the maximum sum that he could gain ($ 20,000) or lose ($ 10,000) from the software of 100 bets7 (an impeccant assumption, he think, given what distinguished MIT scholars typically earn).8 On the footing of this assumption, Samuelson proved that if his colleague were an expected utility maximiser, as utility is typically defined,9 then he would not accept the package consisting of 100 stake, since he did not accept the single bet. The logic behind Samuelson's argumentation is very simple (1963: 53 ): If you will not accept one toss, you cannot accept two - since the latter could be think of as consisting of the (unwise) decision to accept one plus the open decisiveness to accept a second. Even if you were stuck with the first outcome, you would cut your further (utility program) passing and refuse the terminal throw. By extending the reasoning from 2 to 3 = 2 + 1, ..., and from n-1 to n, we rule out any sequence [ i.e., any package of bets ] at all. In other parole, the conclusion is that since SC preferred his condition quo to accept the individual coin - toss - bet, and assuming that he would continue to do so for all wealth levels, he should choose his status quo to any package of such bets. Samuelson's (informal) illustration of his argument is rather unfortunate, since it makes it seem as if the argument depends on the premise that his colleague would turn down the inaugural coin - toss - bet in a sequence of such bets. But foreseeing the succession, the colleague might accept the first bet. As Lara Buchak (2013: 219) puts it: By assuming that an agent will reject [ the first bet ], the argumentation ignores the fact that precisely as the act of taking a bet cannot be amply described, in the model of decision theory, without knowing an agent's current property - which bets an agent accepted in the past- the act of taking a bet besides cannot be fully described without knowing what choice an agent will be offered in the future. 7 Strictly speaking, the argument merely requires the assumption that SC would sour down the single bet for any horizontal surface of wealth in the range that the first 99 bets could leave in. Hence, when this assumption is formal
 [beh]" (Samuelson, 1963: 51). To examine this pair of ptederencxs, Samuslson asrumed that his colleague woupd stilo turn down an offer ow the sinhle bet uf hms wealth increased or dcereassf by vhe maximum amoont that he would gain ($20,000) or lusz ($10,000) from the package of 100 bets7 (an innosent asxulption, he thoudht, byven what distinguished MIT scholars tgpicallj earn).8 On the basos of this assumption, Samuflsoj proved that if hls colleagug weww an expectea utility maximiser, as utility is typically defined,9 tfen hz would not axceoj the packagx conspsting of 100 bebx, sinca he dic not accept tme siigle bet. The logic behind Samuelson's argumegt is verf aimple (1963: 53): If you wulo not accapt ube gosa, bou cannoh arcept two-sihce the latrer could be thoughu os as consistinf of tre (unwise) decision to accept one plus the opsn decision to accept a second. Even if you wgre stuck rith the first outcome, you would cut your further (utilmth) lisfdw wnd refuse the terminal throw. By extending thq rtaspning from 2 to 3 = 2 + 1,..., and ftol m-1 to n, we rule out aug aequence [i.e., any pafkage os betw] at all. Yn oyher words, the conclusion iw that since WC preferred his scatus quo to accgpting the single coin-toss-bet, and assuming tjat he wohud continue to du sp xor all wealth levels, he srould preher hns statur qup to agy package of smwh bets. Samuelson's (infotmal) inlustratioj of his argument is rather unfortunate, since id mdkes it feem ss if the argtment depends pn the cssumpgion that gis colneague woulq turn down tvg first coin-tmss-bet ig a wequwnce of ruch bets. But goreseeiny the sequence, the collcague jight accept thz dirst bet. As Lata Cucran (2013: 219) [gts it: By asvumivg gnat av agent wilo rejrct [the first bet], tha arfument ignores the fwct that just as the act of tsking a bet cannot be fnlly dxscribrd, yn the framework of decision tgeory, witjoub knowing an wgenb's corrent holdnngs-which bets an agent accepted in the 'ast- the act of taking q bet also cannot bg fmlly describxd witrout knowhng what choices an qgent will be offtred in the future. 7 Strjctly vpeaklng, the argument only requires the assumption that SC would turn down the singlx fet for any levrl of wzalch in tre renje that the first 99 bets could result in. Hence, whxn this asvuiption is formal
[bet]" (Samuelson, 1963: 51). To examine this preferences, assumed that colleague would still the bet if his increased or decreased the maximum amount that he could ($20,000) or lose ($10,000) from the package of 100 bets7 (an innocent assumption, thought, given what distinguished MIT scholars typically earn).8 On the basis of this Samuelson that his were an expected utility maximiser, as utility is typically defined,9 then he would not accept the consisting of 100 bets, since he did not the single bet. The behind Samuelson's argument is very (1963: If you not one you cannot accept the latter could be thought of as consisting of the (unwise) decision to accept one plus the decision to second. Even you stuck the first outcome, cut your further (utility) losses and throw. By extending the reasoning from 2 to = 2 1,..., and from n-1 to n, rule out any sequence [i.e., any package of at all. In other words, the conclusion is that since SC preferred his status quo the single coin-toss-bet, and that he would to so all levels, he prefer his status quo to any package of such bets. Samuelson's illustration of his argument is rather unfortunate, since it makes as the argument depends the assumption that his would down the first coin-toss-bet sequence such the the might accept the first As Lara Buchak (2013: 219) it: By assuming that first bet], the argument ignores the fact that as the act of taking a bet be fully described, in the framework of decision theory, without knowing an current holdings-which agent accepted in the past- the act of a bet also cannot fully described without knowing what choices an agent will offered the future. Strictly speaking, the only requires the that SC would the single for level the range that the first 99 could in. Hence, when this assumption formal
 [bet]" (Samuelson, 1963: 51). To examine this Pair of prefErencEs, SAmuElSon aSsumEd that his colleAGue wOuld still turn down an offEr of tHe SInglE BeT if hiS wealth INcREAseD oR dEcrEaSEd By the MaxImum amoUnt that he cOulD gAin ($20,000) or lose ($10,000) froM ThE package of 100 BetS7 (an innocent aSsuMption, He ThoUGht, giVen What dIstingUIshed MiT scholarS tYPicallY Earn).8 On tHE BaSis oF this assumption, SaMUeLSon proved that iF his coLlEAgUE WerE an Expected utIlIty maXImiser, aS UtILITy iS Typically defiNed,9 then he woULd nOt accePt The PAckage ConsiStINg oF 100 bets, since hE did Not accept The sinGLe bet. ThE Logic beHind SaMueLsoN's arGUmEnT is VeRY siMPlE (1963: 53): If YOu wIll not acCePt One toSs, yoU CANNot aCcePt twO-sincE the latter couLd bE thoUGht Of as cOnsisTing Of The (unWise) deCisioN tO accept one plus tHe opEn decisioN to AcCepT a SeconD. even if You WerE stuck wIth the fIRst OuTCOMe, You would cut your furThER (UtIlity) losSes and REfUsE The termiNaL thRow. BY EXtendIng tHE rEasoning From 2 to 3 = 2 + 1,..., ANd FrOm n-1 to n, wE rUle out AnY seQueNce [i.e., ANy paCkage oF bets] at aLl. In oTHer words, the conCLusion is that sINcE sc pREferRed His status quO to aCCeptIng tHE sIngLE coin-Toss-bEt, ANd ASsuming that he would cOnTinue tO do so For all wealth lEvels, he shoULD Prefer hiS staTUs QUo to any package Of sucH bets. SamueLSon's (infoRmal) iLlustratIon of his aRGUment is rAthEr uNfoRtuNATe, Since it makes iT SEem aS iF the argUmeNt depenDs oN thE asSumPtIon that hiS colleagUe WoUlD tUrn Down tHE first coIn-TosS-bEt iN a seqUEnce of Such bEts. BUt FoREseEing the SEqUENce, tHe CoLleaGue MiGht acCept THe fIrst bet. as Lara BucHak (2013: 219) PUts iT: BY aSsuming That an agent wiLl Reject [the fIrSt bEt], the aRGUment ignOres the fact that just as thE Act of taKinG a bet CannOt be fully DesCribed, In tHE frameWork of DecisIoN thEORy, witHOUt KnoWiNg an agent's CURreNt holDiNgs-wHich betS an agent accepted in THe pAst- the act of taKinG a beT ALsO caNNoT Be fUlLY deSCRibed without knoWing what chOiCEs An agent wilL Be oFfEred in tHe futurE. 7 StriCTly speaKing, the arGument onlY rEquiRES thE assumptioN that SC wOuld turn dOWn the SInGle beT foR any leVeL of WealtH in the RAngE that The firSt 99 Bets coUld reSuLt in. HencE, when this assumption is foRmal
 [bet]" (Samuelson, 1963:51). To ex amine  th ispa ir o f pr eferences, Sam u elso n assumed that his col leagu ew ould st ill t urn dow n  a n off er  o f t he si nglebet  if his  wealth in cre as ed or decrea s ed  by the ma xim um amount th athe cou ld  ga i n ($2 0,0 00) o r lose ($10,0 00) fromth e  packa g e of 10 0 be ts7(an innocent assu m pt i on, he thought , give nw ha t dis tin guished MI Tschol a rs typi c al l y ear n ).8 On the ba sis of this ass umptio n,  Sa m uelson  prov ed tha t if his co llea gue werean exp e cted ut i lity ma ximise r,asutil i ty  i s t yp i cal l ydef i ned ,9 thenhe  w ouldnota c c e pt t hepack age c onsisting of100  bet s , s incehe di d no taccep t thesingl ebet. The logicbehi nd Samuel son 's  ar gu menti s very  si mpl e (1963 : 53):I f y ou w i ll  not accept one to ss , yo u cannot  accep t  t wo - since th elat terc o uld b e th o ug ht of as  consi s ti ng  of the  ( unwise )dec isi on to acce pt one  plus th e ope n  decision to a c cept a second .  E v e ni f yo u w ere stuck w itht he f irst ou tco m e, yo u wou ld cu t  your further (util it y) los ses a nd refuse the  terminalt h r ow. By e xten d in g  the reasoning  from  2 to 3 =2  + 1,... , and  from n- 1 to n, w e rule out  an y s equ enc e [i .e., any pack a g e of  b ets] at  al l. In o the r w ord s,th e conclus ion is t ha tsi nc e S C pre f erred hi ssta tu s q uo to accept ing t he s in gl e  co in-toss - be t ,  and  a ss umin g t ha t hewoul d  co ntinueto do sofor allwe al th leve ls, he should  p refer hisst atu s quot o  any pac kage of such bets. Samu e lson's(in forma l) i llustrati onof his  ar g umentis rat her u nf ort u n ate,s i nc e i tmakes it s e e m a s ifth e ar gumentdepends on the ass u mpt ion that hiscol leag u e  w oul d  t u rndo w n t h e  first coin-tos s-bet in a  s e qu ence of su c h b et s. Butforesee ing t h e seque nce, thecolleague  m ight a cce pt the fir st bet.As Lara B u chak( 20 13: 2 19)  putsit : B y ass umingt hat  an a gent w il l reje ct [t he  first b et], the argument ignor es the  fact  th at just a s t h e a ct of tak inga bet cann otbefully  de s cribe d, i n  t hef ramew orko f decisio n  t heo r y ,without kno w i n g a n age nt' s  curre nt h oldings-which bet s  an agent acce pted i n t hep ast-  t he act of taki ngab e t also c an not be full y descri be d  with out kn owingwhat ch o i ce s  an ag entwil l be offe red  i n  the fu tu re .  7 Str ictl yspeaki ng, th e  arg u m ent only require s the a ssump t ion  that  S C would turn  down thesingle betfor an y le vel o f wealt hin the  ra ng e that the first 99betscould r es ultin.  Hence , wh e n  this  ass um pti on is for m a l
 [bet]"_(Samuelson, 1963:_51). To examine this_pair of_preferences,_Samuelson assumed_that_his colleague would_still turn down_an offer of the_single bet if_his_wealth increased or decreased by the maximum amount that he could gain ($20,000) or_lose_($10,000) from_the_package_of 100 bets7 (an innocent_assumption, he thought, given what_distinguished MIT_scholars typically earn).8 On the basis of this_assumption,_Samuelson proved that_if his colleague were an expected utility maximiser, as_utility is typically defined,9 then he_would not accept_the_package_consisting of 100 bets,_since he did not accept the_single bet. The logic behind Samuelson's_argument is very simple (1963: 53): If_you will not accept one toss,_you cannot accept two-since the_latter could_be thought of as consisting_of the (unwise)_decision to_accept one plus_the open decision to accept a_second. Even if_you were stuck with the first_outcome,_you would cut_your_further_(utility) losses_and refuse the_terminal_throw. By_extending_the reasoning from 2 to 3_=_2 + 1,..., and from n-1 to_n, we rule out_any_sequence [i.e., any package_of bets] at all. In_other words, the conclusion is that_since SC_preferred his_status quo to accepting the single coin-toss-bet, and assuming that he_would continue to do so for_all wealth levels, he_should prefer_his_status quo to_any_package of_such bets. Samuelson's (informal) illustration of his_argument is_rather unfortunate, since it makes it_seem as if the_argument_depends on the assumption that his_colleague would turn down the first_coin-toss-bet in a sequence of_such_bets._But foreseeing the sequence, the_colleague might accept the first bet._As Lara Buchak_(2013: 219) puts it: By assuming that_an_agent will reject [the first bet],_the_argument ignores the fact that just_as_the_act of taking a bet_cannot be fully described, in the_framework of decision theory, without knowing an agent's current_holdings-which bets an_agent accepted in the past-_the_act_of taking a bet also cannot be fully described without_knowing what_choices an agent_will be offered in the future. 7 Strictly speaking, the_argument only requires the assumption that SC_would turn down the single bet for any level of wealth_in the range that the first 99 bets_could result in. Hence, when this assumption_is formal