 Bradley 2018). Although some (e.g. Hansson 1988) would argue that the behaviour should only be called 'risk averse' when it is caused by the 2 H. Orri Stefánsson offered a package of such bets on multiple coin tosses (a bet on each toss)? If the number of bets in the package is great enough, then since each bet has a positive monetary expectation (and since probabilistic independence holds between the coin tosses), the package might seem to be worth the risk, even though a single bet from the package would not. For instance, a package consisting of 100 bets of this kind has an expectation of $5,000 and comes with only a 1/2,300 chance (about 0.04%) of leading to a loss of money. Daniel Kahneman is in no doubt about what one should do if offered such a package of bets: "the offer of a hundred [bets] is so attractive that no sane person would reject it" (2012: 337). Paul Samuelson (1963) famously claimed that the above reasoning is a fallacy. He called it 'The fallacy of large numbers', since he thought that it consisted in a misapplication of the law of large numbers. The law entails that a package consisting of an infinite number of bets of the above kind is guaranteed to result in a payoff equal to its expectation, and that the probability that the payoff equals the expectation approaches certainty as the number of bets approaches infinity. But as Samuelson rightly pointed out, the 100 bet package has a (tiny) chance of resulting in a huge loss, which it would be unreasonable to completely ignore. Moreover, Samuelson proved that if an expected utility maximiser turns down a single bet of a particular kind, and would moreover do so for all wealth levels, then she will not accept a package consisting of multiple (but finite2) independent bets of that kind. Therefore, if expected utility theory is the correct theory of practical rationality, it follows that one cannot rationally turn down the single bet for all levels of wealth while accepting the package. It is worth emphasising that although one might never be offered a cointoss-bet like the one under discussion, the above conclusion-if sound-has far-reaching practical implications. A 'bet', as I am using the term, can be any prospect that has some chance of the 'bettor' getting a good result and some chance of her getting a bad result. Thus understood, one
Bradley 2018). Although some (e.g. Hansson 1988) would argue that the behaviour should only be called' hazard averse' when it is cause by the 2 H. Orri Stefánsson offered a package of such stake on multiple coin pass (a bet on each toss)? If the issue of bet in the package is bang-up enough, then since each bet has a positivist monetary expectation (and since probabilistic independence holds between the coin tosses), the software might seem to be worth the risk, even though a single bet from the package would not. For instance, a software consisting of 100 bets of this kind has an arithmetic mean of $ 5,000 and comes with only a 1/2,300 opportunity (about 0.04 %) of lead to a loss of money. Daniel Kahneman is in no doubt about what one should do if offered such a package of bets: " the offer of a hundred [ stake ] is so attractive that no sane person would reject it " (2012: 337). Paul Samuelson (1963) famously claimed that the above reasoning is a fallacy. He called it' The fallacy of large numbers', since he thought that it consisted in a misapplication of the law of large numbers. The law entails that a package dwell of an infinite number of bet of the above kind is undertake to result in a payoff equal to its anticipation, and that the probability that the payoff equals the expectation approaches certainty as the numeral of bets approaches infinity. But as Samuelson rightly pointed out, the 100 bet package accept a (tiny) chance of resulting in a huge loss, which it would be excessive to completely neglect. furthermore, Samuelson raise that if an expected utility maximiser turns down a individual bet of a particular kind, and would moreover cause so for all wealth levels, then she will not accept a package consist of multiple (but finite2) independent bet of that kind. Therefore, if expected utility program theory is the correct theory of practical rationality, it watch that one cannot rationally turn down the individual bet for all levels of wealth while accept the package. It is worth emphasising that although one might never be offered a cointoss - bet like the one under discussion, the above conclusion - if sound - has far - reaching practical implications. A' bet', as I am use the term, can be any prospect that have some chance of the' bettor' getting a good result and some chance of her getting a regretful result. Thus understood, one
 Brwdley 2018). Although some (e.g. Mansson 1988) would atgye thav the bshaviour should only be called 'risk everwe' whtu it is caused by thd 2 H. Orri Stefánssin ohfered a package of such bets kk mulci'le coin tosses (a bet on aach toss)? If tve nbmber of bets in the package is greae enougn, hhen since eacr beu hws a iowitive monetary expectation (ahd sinct probabilistic incependence holds between tje clin tosses), the pacnage might weem ro be worth ghe risk, enzn though a single bet from the package wojld npt. For insjcbce, d package cinsisning of 100 bets of this kind hss an expectatlon oh $5,000 abd comes with only a 1/2,300 chance (about 0.04%) of jeading tm c loss of money. Danieo Jahnekan hs iv no dohbv agout wjat one shouls do if offwred such a package os bets: "the offsr of w rundred [bets] is so attractive that no sdne person would reject it" (2012: 337). Paul Samuelson (1963) falously clwimed that the above reasoning is a fallacy. He canled mt 'Tht nwuoafy of large numbers', since he thought that it sknxixted in a misaiplication of the kaa ps large numbets. The law entails that a pafkage cjnsisring of ag inginite number of bets of thw above kind us guaranteed to rzsult in a pcyoff gqual yo its expectation, and chat tge probabillty that ffe payoff equals thv ex[ectation approaches certaynty as tie nukber of betx apprjaches inflnity. But as Samuelson rlghtli poinded out, thf 100 bet package has a (tiny) chancx of resultinb hn d huge ljss, wmich it would bq unreasonable to com'letelh ignore. Mkreover, Samuelson [roved that ix an expected utility maxumiswr turnr down a single bet of a particulae kind, and would mpreuber do so for aol qealth levels, tnen shq aikl tot accept a pacyagd consksting of mmltkple (but finite2) independant gets of that kind. Yhcrefore, id expectqd utility throry is the correcu theocy of 'ractival rationality, it follows that ohe cannot rabionally turn dowk thg single bec for all levels of wealth while acceptiig the package. It is woeth emphasising thaj akthough one mighe never ba offered a cointoss-vet like the one mnder discussion, the agove cmncludion-if sound-has far-reaching practical implications. A 'bet', as I am using thw term, can be any lroslect nhac hcs some chaicx of the 'bettor' gvtting a good result and some chence of hes yetting a bad result. Thus undrrrtood, one
Bradley 2018). Although some (e.g. Hansson 1988) that behaviour should be called 'risk by 2 H. Orri offered a package such bets on multiple coin tosses bet on each toss)? If the number of bets in the package is enough, then since each bet has a positive monetary expectation (and since probabilistic holds the tosses), package might seem to be worth the risk, even though a single bet from the package not. For instance, a package consisting of 100 of this kind has expectation of $5,000 and comes only 1/2,300 chance 0.04%) leading a loss of Daniel Kahneman is in no doubt about what one should do if offered such a package of "the offer hundred [bets] so that sane person would (2012: 337). Paul Samuelson (1963) famously above reasoning is a fallacy. He called it fallacy of numbers', since he thought that it in a misapplication of the law of large The law entails that a package consisting of an infinite number of bets of the is guaranteed to result a payoff equal its and the that the equals the expectation approaches certainty as the number of bets approaches But as Samuelson rightly pointed out, the 100 bet package (tiny) of resulting in huge loss, which it be to completely ignore. Moreover, that an turns a bet of a particular and would moreover do so all wealth levels, then package consisting of multiple (but finite2) independent bets that kind. Therefore, if expected utility theory the correct theory of practical rationality, it follows that one cannot rationally down the for all levels of wealth while accepting the It is worth emphasising although one might never be offered a cointoss-bet like one discussion, the conclusion-if sound-has far-reaching implications. A 'bet', I am using can be prospect has the 'bettor' getting a good result some of her getting a bad Thus
 Bradley 2018). Although some (e.g. HansSon 1988) would arGue thAt tHe bEhAvioUr shOuld only be callED 'risK averse' when it is caused bY the 2 H. orRI SteFÁnSson oFfered a PAcKAGe oF sUcH beTs ON mUltipLe cOin tossEs (a bet on eaCh tOsS)? If the number OF bEts in the paCkaGe is great enoUgh, Then siNcE eaCH bet hAs a PositIve monETary exPectation (AnD Since pRObabiliSTIc IndePendence holds betwEEn THe coin tosses), thE packaGe MIgHT SeeM to Be worth the RiSk, eveN Though a SInGLE Bet FRom the package Would not. For INstAnce, a pAcKagE ConsisTing oF 100 bETs oF this kind haS an eXpectatioN of $5,000 and COmes witH Only a 1/2,300 chAnce (abOut 0.04%) Of lEadiNG tO a LosS oF MonEY. DAniEL KaHneman is In No Doubt AbouT WHAT one ShoUld dO if ofFered such a pacKagE of bETs: "tHe offEr of a HundReD [bets] Is so atTractIvE that no sane persOn woUld reject It" (2012: 337). PAuL SaMuElson (1963) FAmouslY clAimEd that tHe above REasOnING Is A fallacy. He called it 'thE FAlLacy of laRge numBErS', sINce he thoUgHt tHat iT COnsisTed iN A mIsapplicAtion oF ThE lAw of larGe NumberS. THe lAw eNtailS That A packaGe consisTing oF An infinite numbER of bets of the aBOvE KInD Is guAraNteed to resuLt in A PayoFf eqUAl To iTS expeCtatiOn, ANd THat the probability thAt The payOff eqUals the expectAtion approACHEs certaiNty aS ThE Number of bets apProacHes infinitY. but as SamUelsoN rightly Pointed ouT, THe 100 bet pacKagE haS a (tIny) CHAnCe of resulting IN A hugE lOss, whicH it Would be UnrEasOnaBle To CompletelY ignore. MOrEoVeR, SAmuElson PRoved thaT iF an ExPecTed utILity maXimisEr tuRnS dOWn a Single bET oF A PartIcUlAr kiNd, aNd Would MoreOVer Do so for All wealth LevELs, thEn ShE will noT accept a packaGe Consisting Of MulTiple (bUT Finite2) inDependent bets of that kind. tHereforE, if ExpecTed uTility theOry Is the cOrrECt theoRy of prActicAl RatIONalitY, IT fOllOwS that one caNNOt rAtionAlLy tuRn down tHe single bet for all lEVelS of wealth whilE acCeptING tHe pACkAGe. IT iS WorTH Emphasising that Although onE mIGhT never be ofFEreD a CointosS-bet likE the oNE under dIscussion, The above cOnClusION-if Sound-has faR-reachinG practicaL ImpliCAtIons. A 'Bet', As I am uSiNg tHe terM, can be ANy pRospeCt that HaS some cHance Of The 'bettoR' getting a good result and sOme chaNce of Her Getting a bAd rESulT. Thus undeRstoOd, one
 Bradley 2018). Although s ome (e.g.Hanss on198 8)  wou ld a rgue that theb ehav iour should only be ca lled'r i sk a v er se' w hen iti sc a use dby  th e2  H . Orr i S tefánss on offered  apa ckage of suc h  b ets on mul tip le coin toss es(a bet  o n e a ch to ss) ? Ifthe nu m ber of  bets inth e  packa g e is gr e a tenou gh, then since ea c hb et has a posit ive mo ne t ar y exp ect ation (and  s incep robabil i st i c ind e pendence hold s between t h e c oin to ss es) ,  the p ackag em igh t seem to b e wo rth the r isk, e v en thou g h a sin gle be t f rom  the pa ck age  w o uld no t.F orinstance ,apacka ge c o n s i stin g o f 10 0 bet s of this kin d h as a n  ex pecta tionof $ 5, 000 a nd com es wi th  only a 1/2,300  cha nce (abou t 0 .0 4%)  o f lea d ing to  alos s of mo ney. Da n iel  K a h n em an is in no doubtab o u twhat one  shoul d  d oi f offere dsuc h ap a ckage  ofb et s: "theoffero fahundred  [ bets]is  so  at tract i ve t hat no  sane pe rsonw ould reject it "  (2012: 337). Pa u l  S a muel son  (1963) fam ousl y  cla imed th att he ab ove r ea s on i ng is a fallacy. He  c alledit 'T he fallacy of  large num b e r s', sinc e he th o ught that it c onsis ted in a m i sapplica tionof the l aw of lar g e  numbers . T helaw  en t a il s that a pack a g e co ns istingofan infi nit e n umb erof  bets ofthe abov eki nd  i s g uaran t eed to r es ult  i n a  payo f f equa l toitsex pe c tat ion, an d  t h a t th epr obab ili ty  that  the pay off equ als the e xpe c tati on  a pproach es certaintyas  the numbe rofbets a p p roachesinfinity. But as Samuel s on righ tly  poin tedout, the100  bet p ack a ge has  a (ti ny) c ha nce o f res u l ti ngin  a huge lo s s , w hichit  wou ld be u nreasonable to com p let ely ignore. M ore over , Sa mue l so n  pr ov e d t h a t if an expecte d utilityma x im iser turns dow na singl e bet o f a p a rticula r kind, a nd wouldmo reov e r  do  so for al l wealth  levels,t hen s h ewillnot  accep ta p ackag e cons i sti ng of  multi pl e (but  fini te 2) indep endent bets of that kin d. The refor e,if expect edu til ity theor y is  the corre ctthe ory o f p r actic al r a ti ona l ity,it f o llows tha t  o nec a nn ot rational l y tur n dow n t h e sing le b et for all levels of wealth whil e ac c e pti ngt he p ac kage. It is wo rth  e m p hasising  t hat althoug h one mi gh t  neve r be o ffered  a coin t o ss - bet li ke t heone under  di sc u ssion,th ea bove c oncl us ion-if  sound - hasf a r-reaching pract icali m plica t ion s. A'b et', as I am  using the  term, canbe any  pro spect  that h as  somecha nc e of the ' b ettor' ge tting  a good  r esul t a nd som e ch a n ce of  her  g ett ing a bad r es u lt .T hus  und ersto od , on e
 Bradley_2018). Although_some (e.g. Hansson 1988)_would argue_that_the behaviour_should_only be called_'risk averse' when_it is caused by_the 2 H._Orri_Stefánsson offered a package of such bets on multiple coin tosses (a bet on_each_toss)? If_the_number_of bets in the package_is great enough, then since_each bet_has a positive monetary expectation (and since probabilistic_independence_holds between the_coin tosses), the package might seem to be worth_the risk, even though a single_bet from the_package_would_not. For instance, a_package consisting of 100 bets of_this kind has an expectation of_$5,000 and comes with only a 1/2,300_chance (about 0.04%) of leading to_a loss of money. Daniel_Kahneman is_in no doubt about what_one should do_if offered_such a package_of bets: "the offer of a_hundred [bets] is_so attractive that no sane person_would_reject it" (2012:_337)._Paul_Samuelson (1963)_famously claimed that_the_above reasoning_is_a fallacy. He called it 'The_fallacy_of large numbers', since he thought that_it consisted in a_misapplication_of the law of_large numbers. The law entails_that a package consisting of an_infinite number_of bets_of the above kind is guaranteed to result in a payoff_equal to its expectation, and that_the probability that the_payoff equals_the_expectation approaches certainty_as_the number_of bets approaches infinity. But as Samuelson_rightly pointed_out, the 100 bet package has_a (tiny) chance of_resulting_in a huge loss, which it_would be unreasonable to completely ignore._Moreover, Samuelson proved that if_an_expected_utility maximiser turns down a_single bet of a particular kind,_and would moreover_do so for all wealth levels, then_she_will not accept a package consisting_of_multiple (but finite2) independent bets of_that_kind._Therefore, if expected utility theory_is the correct theory of practical_rationality, it follows that one cannot rationally turn down_the single bet_for all levels of wealth_while_accepting_the package. It is worth emphasising that although one might_never be_offered a cointoss-bet_like the one under discussion, the above conclusion-if sound-has far-reaching_practical implications. A 'bet', as I am_using the term, can be any prospect that has some chance_of the 'bettor' getting a good result and_some chance of her getting a bad_result. Thus understood, one