 are assuming that the agent is certain that she will act on her preferences at each point in time. Hence, from (1) it follows that Assumption 1 also holds when Bi = B99. So, we have: {B98} {B99} (2) By iterating this reasoning: {B97} {B98}... {B0} {B1} To connect this sequence of pair-wise comparisons, we only need to assume that the preference is transitive. I will not provide any argument for this assumption, which is sometimes justified on the grounds that a person who violates it is vulnerable to being'money pumped'. Is risk aversion irrational? 9 Assumption 3 (Transitivity) For any alternatives A, B, and C: If A B and B C then A C Transitivity entails, in the presence of Assumptions 1 and 2, that the agent prefers no bet to the package consisting of 100 bets (and, indeed, to any package): Conclusion: If a person satisfies Assumptions 1 to 3, then she will turn down a package consisting of up to and including 100 coin-toss-bets, since {B0} {Bn} whenever 1 ≥ n ≤ 100. So if Transitivity and Dominance are requirements of rationality, and given that Assumption 1 is, as a matter of fact, true of Samuelson's colleague, it would seem that Samuelson's colleague is indeed irrational. 4 Event-Wise and State-Wise Dominance I will, for the sake of the argument, grant that Transitivity is a requirement of rationality. But what about Dominance? As previously mentioned, Tversky and Bar-Hillel provide a similar axiomatisation of Samuelson's argument to the one provided above. Moreover, they suggest that the axiomatic formulation shows that the argument depends only on assumptions that, first, are weaker than those of expected utility theory, and, second, seem "unobjectionable on normative grounds" (Tversky and Bar-Hillel 1983: 716). In response to Tversky and Bar-Hillel's first claim, it should be pointed out that while it is, strictly speaking, true that the argument depends on assumptions that are strictly weaker than those of EU theory, it nevertheless contains an assumption, Dominance, that I think is not-and certainly should not be-accepted by those who reject EU theory due to its treatment of risk aversion.11
are assuming that the agent is certain that she will act on her preference at each item in time. Hence, from (1) it follows that Assumption 1 besides holds when Bi = B99. So, we have: { B98 } { B99 } (2) By repeat this reasoning: { B97 } { B98 }... { B0 } { B1 } To connect this sequence of couple - fresh comparisons, we entirely need to assume that the predilection is transitive. I will not provide any argument for this assumption, which is sometimes justified on the grounds that a person who violates it is vulnerable to being'money pumped'. Is hazard aversion irrational? 9 Assumption 3 (Transitivity) For any alternatives A, B, and speed of light: If A B and B C then A C Transitivity entail, in the presence of premise 1 and 2, that the agent prefers no bet to the package consisting of 100 stake (and, indeed, to any package ): Conclusion: If a person satisfies Assumptions 1 to 3, then she will turn down a package consisting of up to and including 100 coin - toss - bets, since { B0 } { Bn } whenever 1 ≥ n ≤ 100. So if Transitivity and Dominance are requirements of rationality, and given that Assumption 1 is, as a matter of fact, true of Samuelson's colleague, it would seem that Samuelson's colleague is indeed irrational. 4 Event - Wise and State - Wise Dominance I will, for the sake of the argument, allow that Transitivity is a requirement of rationality. But what about Dominance? As previously mentioned, Tversky and Bar - Hillel leave a similar axiomatisation of Samuelson's argument to the one provided above. Moreover, they indicate that the axiomatic formulation shows that the argument depends merely on assumptions that, first, are weaker than those of expected utility theory, and, second, appear " unobjectionable on normative grounds " (Tversky and Bar - Hillel 1983: 716). In response to Tversky and Bar - Hillel's inaugural claim, it should be sharpen out that while it is, strictly speaking, true that the argument depends on assumption that are strictly weaker than those of EU theory, it however contains an presumption, Dominance, that I think is not - and certainly should not be - accept by those who reject EU theory due to its treatment of risk aversion.11
 arf assuming that the agenu is certain that she winl act on her oreferences at each point in tume. Htuce, from (1) it follows that Asslmption 1 qlso yolds when Bi = B99. So, we hzye: {B98} {Y99} (2) By iterating jhis reasonitg: {B97} {B98}... {B0} {B1} To wovnzct this sequence of pair-wise comparysons, wr lnly need to afsumt trat fhe preference is transitive. I wilm not pgovide any argumemt for this assumption, whifh id sometimes justifled on the trouges that a pefson who vpmlates it js vulnerable to being'money pumoed'. Ix risk avetsjoj irrational? 9 Asslmption 3 (Transitivity) For anu alternatives A, U, ane C: If A B and B C thxn A C Transitivity gntails, in tke presence of Assumpriins 1 dnd 2, thag thd afeit lreferd nk bet to tge package xonsisting of 100 bets (age, indeed, to ahy pachade): Conclusion: If a person satisfies Asslmptjons 1 to 3, then she will turn down a package fonsistind of up to and including 100 coin-toss-bets, since {B0} {Bn} whenxvdr 1 ≥ k ≤ 100. Ri lf Transitivity and Dominance are requirementf og gationality, and glven that Assumptipn 1 of, as a matter of faef, frue of Samuelson's colleadue, ir would stem tnat Samuelson's colleague is indeed irranionql. 4 Event-Wise and Dtate-Wise Duminsnce O will, for the sake of che arfument, granh that Trzvsitivity is a rdqupremant of rationality. But whae about Dimincnce? As orevoously mentioned, Tversky and Bar-Hillel pgovidg a sikilar axiolatisation of Samuelson's argumeiv to the one kroeidvd above. Ioreoyer, they suggese that the axipmatic yormulxtion showa that vhe argument depends only ln assumptiois that, fyrst, are weaker ghan those of rxpected ltnlity theiry, and, second, seek "uvkbjectionable ou bormative grouncs" (Gvewsny agg Bar-Hillel 1983: 716). In rerlonse to Tversky xnd Nar-Hillel's first clahm, if should be pointec jut that while ie is, strictly speaking, true thau the ergumeit deprndf on assumptions that are stridtly weakfr bhan those of EU bheoty, it nevercheless contains an assumption, Dominance, that I think is nit-and certainly shoold not be-acce'ted br those wvo reject EU theory eue to its treatmtnt of risk aversion.11
are assuming that the agent is certain will on her at each point it that Assumption 1 holds when Bi B99. So, we have: {B98} {B99} By iterating this reasoning: {B97} {B98}... {B0} {B1} To connect this sequence of comparisons, we only need to assume that the preference is transitive. I will provide argument this which is sometimes justified on the grounds that a person who violates it is vulnerable to pumped'. Is risk aversion irrational? 9 Assumption 3 For any alternatives A, and C: If A B B then A Transitivity in presence of Assumptions and 2, that the agent prefers no bet to the package consisting of 100 bets (and, indeed, any package): a person Assumptions to then she will a package consisting of up to coin-toss-bets, since {B0} {Bn} whenever 1 ≥ n 100. So Transitivity and Dominance are requirements of and given that Assumption 1 is, as a of fact, true of Samuelson's colleague, it would seem that Samuelson's colleague is indeed irrational. and State-Wise Dominance I for the sake the grant Transitivity a requirement rationality. But what about Dominance? As previously mentioned, Tversky and Bar-Hillel a similar axiomatisation of Samuelson's argument to the one provided they that the axiomatic shows that the argument only assumptions that, first, are those expected second, "unobjectionable normative grounds" (Tversky and 1983: 716). In response to and Bar-Hillel's first claim, that while it is, strictly speaking, true that argument depends on assumptions that are strictly than those of EU theory, it nevertheless contains an assumption, Dominance, that think is should not be-accepted by those who reject EU due to its treatment risk aversion.11
 are assuming that the agent is Certain thaT she wIll Act On Her pRefeRences at each poINt in Time. Hence, from (1) it follows That ASsUMptiON 1 aLso hoLds when bI = B99. sO, We hAvE: {B98} {b99} (2) By ItERaTing tHis ReasoniNg: {B97} {B98}... {B0} {B1} To coNneCt This sequence OF pAir-wise comParIsons, we only nEed To assuMe ThaT The prEfeRence Is tranSItive. I Will not prOvIDe any aRGument fOR ThIs asSumption, which is soMEtIMes justified on The groUnDS tHAT a pErsOn who violaTeS it is VUlnerabLE tO BEIng'MOney pumped'. Is rIsk aversion IRraTional? 9 asSumPTion 3 (TrAnsitIvITy) FOr any alternAtivEs A, B, and C: IF A B and b c then A C tRansitiVity enTaiLs, iN the PReSeNce Of aSsuMPtIonS 1 And 2, That the aGeNt PrefeRs no BET TO the PacKage ConsiSting of 100 bets (anD, inDeed, TO anY packAge): CoNcluSiOn: If a Person SatisFiEs Assumptions 1 to 3, Then She will tuRn dOwN a pAcKage cONsistiNg oF up To and inCluding 100 COin-ToSS-BEtS, since {B0} {Bn} whenever 1 ≥ n ≤ 100. so IF trAnsitiviTy and DOMiNaNCe are reqUiRemEnts OF RatioNaliTY, aNd given tHat AssUMpTiOn 1 is, as a MaTter of FaCt, tRue Of SamUElsoN's collEague, it wOuld sEEm that SamuelsoN'S colleague is iNDeED IrRAtioNal. 4 event-Wise anD StaTE-WisE DomINaNce i Will, fOr the SaKE oF The argument, grant thaT TRansitIvity Is a requiremenT of rationaLITY. But what AbouT doMInance? As previoUsly mEntioned, TvERsky and BAr-HilLel proviDe a similaR AXiomatisAtiOn oF SaMueLSOn'S argument to thE ONe prOvIded aboVe. MOreover, TheY suGgeSt tHaT the axiomAtic formUlAtIoN sHowS that THe argumeNt DepEnDs oNly on ASsumptIons tHat, fIrSt, ARe wEaker thAN tHOSe of ExPeCted UtiLiTy theOry, aND, seCond, seeM "unobjectIonABle oN nOrMative gRounds" (Tversky AnD Bar-Hillel 1983: 716). in ResPonse tO tVersky anD Bar-Hillel's first claim, it SHould be PoiNted oUt thAt while it Is, sTrictlY spEAking, tRue thaT the aRgUmeNT DepenDS On AssUmPtions that ARE stRictlY wEakeR than thOse of EU theory, it nevERthEless contains An aSsumPTIoN, DoMInANce, ThAT I tHINk is not-and certaInly should NoT Be-Accepted by THosE wHo rejecT EU theoRy due TO its treAtment of rIsk aversiOn.11
 are assuming that the age nt is cert ain t hat  sh ewill  act  on her prefer e nces  at each point in time . Hen ce ,  fro m  ( 1) it  follow s  t h a t A ss um pti on 1alsohol ds when  Bi = B99.  So ,we have: {B9 8 }{B99} (2)Byiterating th isreason in g:{ B97}{B9 8}...  {B0}{ B1} To  connectth i s sequ e nce ofp a ir -wis e comparisons, we on l y need to assu me tha tt he p ref ere nce is tra ns itive .  I will no t p rov i de any argume nt for this ass umptio n,  wh i ch issomet im e s j ustified on  the  groundsthat a personw ho viol ates i t i s v ulne r ab le  to  b e ing ' mo ney pum ped'. Is  r is k ave rsio n i r rati ona l? 9  Assu mption 3 (Tra nsi tivi t y)For a ny al tern at ivesA, B,and C :If A B and B Cthen  A C Tran sit iv ity  e ntail s , in t hepre sence o f Assum p tio ns 1 an d 2, that the agen tp r ef ers no b et tot he  p a ckage co ns ist ingo f  100bets (a nd, inde ed, to an ypackage ):  Concl us ion : I f a p e rson  satis fies Ass umpti o ns 1 to 3, the n  she will tur n  d o w na  pac kag e consistin g of up t o an d  i ncl u ding100 c oi n -t o ss-bets, since {B0}  { Bn} wh eneve r 1 ≥ n ≤ 100 . So if Tr a n s itivityandD om i nance are requ ireme nts of rat i onality,  andgiven th at Assump t i on 1 is,  as  amat ter o ffact, true of S amue ls on's co lle ague, i t w oul d s eem  t hat Samue lson's c ol le ag ue  is  inde e d irrati on al.  4  Ev ent-W i se and  Stat e-Wi se  D o min ance Iw il l ,  for  t he  sak e o fthe a rgum e nt,  grantthat Tran sit i vity  i sa requi rement of rat io nality. Bu twha t abou t Dominanc e? As previously mentio n ed, Tve rsk y and  Bar -Hillel p rov ide asim i lar ax iomati satio nofS a muels o n 's  ar gu ment to th e one  prov id ed a bove. M oreover, they sugg e stthat the axio mat ic f o r mu lat i on sho ws tha t the argument de pends only  o n  a ssumptions tha t,  first,  are we akert han tho se of exp ected uti li ty t h e ory , and, sec ond, see m "unobje c tiona b le  on n orm ativegr oun ds" ( Tversk y  an d Bar -Hille l1983:716).  I n respon se to Tversky and Bar-H illel' s fir stclaim, it  sh o uld  be point ed o ut that wh ile  it  is,str i ctlyspea k in g,t rue t hatt he argume n tdep e n ds  on assumpt i o n s t hat a res trictl y we aker than those o f  EU theory, it  nev e r the les s  con ta ins an assumpt ion ,D o minance,  t hat I think  is not- an d  cert ainlyshould  not be - a cc e pted b y th ose  who reje ctEU theorydu et o itstrea tm ent of  riska vers i o n.11
 are_assuming that_the agent is certain_that she_will_act on_her_preferences at each_point in time._Hence, from (1) it_follows that Assumption_1_also holds when Bi = B99. So, we have: {B98} {B99} (2) By iterating_this_reasoning: {B97}_{B98}..._{B0}_{B1} To connect this sequence_of pair-wise comparisons, we only_need to_assume that the preference is transitive. I will_not_provide any argument_for this assumption, which is sometimes justified on the_grounds that a person who violates_it is vulnerable_to_being'money_pumped'. Is risk aversion_irrational? 9 Assumption 3 (Transitivity) For_any alternatives A, B, and C:_If A B and B C then_A C Transitivity entails, in the_presence of Assumptions 1 and_2, that_the agent prefers no bet_to the package_consisting of_100 bets (and,_indeed, to any package): Conclusion: If_a person satisfies_Assumptions 1 to 3, then she_will_turn down a_package_consisting_of up_to and including_100_coin-toss-bets, since_{B0}_{Bn} whenever 1 ≥ n ≤_100._So if Transitivity and Dominance are requirements_of rationality, and given_that_Assumption 1 is, as_a matter of fact, true_of Samuelson's colleague, it would seem_that Samuelson's_colleague is_indeed irrational. 4 Event-Wise and State-Wise Dominance I will, for the_sake of the argument, grant that_Transitivity is a requirement_of rationality._But_what about Dominance?_As_previously mentioned,_Tversky and Bar-Hillel provide a similar axiomatisation_of Samuelson's_argument to the one provided above._Moreover, they suggest that_the_axiomatic formulation shows that the argument_depends only on assumptions that, first,_are weaker than those of_expected_utility_theory, and, second, seem "unobjectionable_on normative grounds" (Tversky and Bar-Hillel_1983: 716). In_response to Tversky and Bar-Hillel's first claim,_it_should be pointed out that while_it_is, strictly speaking, true that the_argument_depends_on assumptions that are strictly_weaker than those of EU theory,_it nevertheless contains an assumption, Dominance, that I think_is not-and certainly_should not be-accepted by those_who_reject_EU theory due to its treatment of risk aversion.11