 is very often faced with 'bets' with positive monetary expectations. For instance, suppose that you have just bought a laptop and are considering whether to buy a two year warranty. Such warranties generally have negative monetary expectations for buyers-otherwise sellers wouldn't offer them! So the 'bet' not to buy the warranty has a positive monetary expectation (compared to the alternative of buying a warranty). When deciding whether to buy the warranty, one might consider whether one would buy a warranty if one were buying 100 laptops (say as a firm). If we suppose that the probability of each laptop breaking down is independent of another laptop breaking down,3 I conjecture that most people would not buy the warranty if they were buying 100 laptops, since the 'wins' of second type of attitude mentioned above, I will, for the sake of simplicity, call any person who turns down a bet with a positive monetary expectation risk averse w.r.t. money. 2 From now on, whenever I talk about packages of bets, I will assume that they consist of finite numbers of bets. 3 This assumption is reasonable if we assume thorough quality control, in which case a computer braking down could be treated as a random event. Is risk aversion irrational? 3 this package (i.e., of not buying warranty for the 100 computers) will almost certainly outweigh the 'losses'. But then, by the above argument, it might seem that one should not buy warranty for the single laptop either. Let us for the sake of simplicity however focus on Samuelson's coin-tossbets. Since a package of 100 such bets seems so attractive, some have taken Samuelson's argument to show that it would simply be irrational to turn down the single bet (see, for instance, Benartzi and Thaler 1999). But the preference against accepting the single bet can be entirely due to what seems to be moderate aversion to risk. So if the lesson from Samuelson's argument is that it would be irrational to turn down the single bet, then it seems we have to conclude that moderate risk aversion is irrational. Others have taken Samuelson's argument to be a reductio of the decision theory he assumed: expected utility (EU) theory (see e.g. Lopes 1996, Rabin 2000). Still others think that there must be something wrong with Samuelson's argument, since they think that there is neither anything wrong with turning down the single bet while accepting the package nor with EU theory as a theory
is very often faced with' bets' with positive monetary expectation. For case, suppose that you have just bought a laptop and are study whether to buy a two year guarantee. Such warranties generally have damaging monetary expectations for buyers - differently sellers wouldn't offer them! So the' bet' not to bribe the warranty has a incontrovertible monetary expectation (compared to the option of buying a warranty). When deciding whether to bribe the warranty, one might consider whether one would buy a warranty if one were buying 100 laptop (say as a firm). If we presuppose that the probability of each laptop breaking down is independent of another laptop breaking down,3 I speculate that most people would not buy the warranty if they were buying 100 laptops, since the' wins' of second character of position mention above, I will, for the sake of simplicity, call any person who turns down a bet with a positive monetary expectation hazard averse w.r.t. money. 2 From now along, whenever I talk about packages of bet, I will wear that they consist of finite numbers of bets. 3 This premise is reasonable if we assume thorough quality restraint, in which case a computer braking down could be treated as a random event. Is risk antipathy irrational? 3 this package (i.e., of not buying warranty for the 100 computers) will almost certainly outweigh the' loss'. But then, by the above controversy, it might seem that one should not buy warranty for the individual laptop either. Let us for the sake of simplicity however focus on Samuelson's coin - tossbets. Since a software of 100 such bets appear so attractive, some have taken Samuelson's argumentation to show that it would just be irrational to turn down the single stake (see, for instance, Benartzi and Thaler 1999). But the preference against accepting the individual bet can be wholly due to what seems to be moderate aversion to gamble. So if the lesson from Samuelson's argument is that it would be irrational to turn down the single bet, then it seems we have to conclude that moderate risk aversion is irrational. Others have taken Samuelson's controversy to be a reductio of the decision hypothesis he assumed: expected utility (EU) theory (see e.g. Lopes 1996, Rabin 2000). Still others intend that there must be something wrong with Samuelson's argument, since they think that there is neither anything wrong with turning down the individual stake while accepting the package nor with EU theory as a theory
 is very often faced with 'btts' with positive monetacy expedtations. For instance, suppose that ylu have just bought a laptop xnd are clnsideribg wiether to buy a vso year warrahby. Sueh warranties gekerally hava negative monatxrv expectations for buyers-otherwise sqllers eokldn't offer thgm! So ehe 'gvt' not to buy the warranty has z positpve monetary expevtation (compared to the alhernwtive of buying a aarranty). Whgh dqxiding whethdr to buy uhz warranty, kne might consider whether one dould buy a wartcbty hf one were buyigg 100 laptops (say as a firm). Ig we suppose tmat tie peobability of each la'top breaking down if indepengeut of another laptop vrwakinc dofn,3 I xongecuurx tgat modt 'eople wouls not buy tye warranty if they wqgr buying 100 laltops, figce the 'wins' of second type of attitude mehtioned above, I will, foe the sake of simpliclty, call wny person who turns down a bet with a positive mmnetacy exkegbatiub gisk averse w.r.t. money. 2 From now on, whenever I fakk about packagef of bets, I wllk assume that jhey couaiat of finite numbegs of bgts. 3 Tyis assumktion is reasonable if we assume thorough qucliry control, in whick case a com'uter nrakimg down could be treateb as a random evejt. Is risi aversion irratiunak? 3 this package (i.e., of not buring warrenty yor the 100 comkuters) rill almosh cerbdinly outweigh the 'lossgs'. But then, by tje above argument, it might seem that one shoukd non buy warxanty nor the single japtop either. Ket us yor thd sake of aimplicmty however socus on Samuapson's coin-tovsbets. Synce a pqckage uw 100 such bets srems so antxactive, sime have taken Sammelsov'a argument to skuq that it would sioplr he iwsational to durn dodm the single bet (ree, gor instance, Benartzh ans Thaler 1999). But the lrcference qgainst wccepting the single bet can be enticely dne to ehaj seems to be moderate aversion to risk. Do lf the lesson fron Samuelson's argument is that it would be irrationao to turn down thg single bet, then it xtems we have vo conslude thad moderate risk averwion is irrationak. Others have taken Szmuelsmn's aggument to be a reductio of the decision theory he assumed: expected utiliry (EU) vhqory (see e.g. Loprs 1996, Rdbnn 2000). Still othxrr think that thege must be something wrong with Ramuelsot's argument, since they think tnag there is nekther anything wrong witg turninb down the single bet while accrpting the package nor wlth EU thwory zs a theorb
is very often faced with 'bets' with expectations. instance, suppose you have just considering to buy a year warranty. Such generally have negative monetary expectations for sellers wouldn't offer them! So the 'bet' not to buy the warranty has positive monetary expectation (compared to the alternative of buying a warranty). When deciding to the one consider whether one would buy a warranty if one were buying 100 laptops (say as a If we suppose that the probability of each breaking down is independent another laptop breaking down,3 I that people would buy warranty they were buying laptops, since the 'wins' of second type of attitude mentioned above, I will, for the sake of call any turns down bet a monetary expectation risk money. 2 From now on, whenever packages of bets, I will assume that they of finite of bets. 3 This assumption is if we assume thorough quality control, in which a computer braking down could be treated as a random event. Is risk aversion irrational? package (i.e., of not warranty for the computers) almost outweigh 'losses'. But by the above argument, it might seem that one should not warranty for the single laptop either. Let us for the simplicity focus on Samuelson's Since a package of such seems so attractive, some Samuelson's to would be to turn down the bet (see, for instance, Benartzi Thaler 1999). But the bet can be entirely due to what seems be moderate aversion to risk. So if lesson from Samuelson's argument is that it would be irrational to turn the single it seems we have to conclude that moderate aversion is irrational. Others taken Samuelson's argument to be a reductio of the theory assumed: expected (EU) theory (see Lopes 1996, Rabin Still others think must be wrong Samuelson's think that there is neither anything with down the single bet while the with EU theory as a theory
 is very often faced with 'bets' wIth positivE moneTarY exPeCtatIons. for instance, supPOse tHat you have just bought a lAptop AnD Are cONsIderiNg whethER tO BUy a TwO yEar WaRRaNty. SuCh wArrantiEs generallY haVe Negative moneTArY expectatiOns For buyers-othErwIse selLeRs wOUldn't OffEr theM! So the 'BEt' not tO buy the waRrANty has A PositivE MOnEtarY expectation (compaREd TO the alternativE of buyInG A wARRanTy). WHen decidinG wHetheR To buy thE WaRRANty, ONe might considEr whether onE WouLd buy a WaRraNTy if onE were BuYIng 100 Laptops (say aS a fiRm). If we supPose thAT the proBAbility Of each LapTop BreaKInG dOwn Is INdePEnDenT Of aNother laPtOp BreakIng dOWN,3 i ConjEctUre tHat moSt people would Not Buy tHE waRrantY if thEy weRe BuyinG 100 laptoPs, sinCe The 'wins' of second Type Of attitudE meNtIonEd Above, i Will, foR thE saKe of simPlicity, CAll AnY PERsOn who turns down a bet WiTH A pOsitive mOnetarY ExPeCTation riSk AveRse w.R.T. Money. 2 from NOw On, whenevEr I talK AbOuT packagEs Of bets, i wIll AssUme thAT theY consiSt of finiTe numBErs of bets. 3 This aSSumption is reaSOnABLe IF we aSsuMe thorough qUaliTY conTrol, IN wHicH Case a CompuTeR BrAKing down could be treaTeD as a raNdom eVent. Is risk aveRsion irratIONAl? 3 this paCkagE (I.e., OF not buying warrAnty fOr the 100 compuTErs) will aLmost CertainlY outweigh THE 'losses'. BUt tHen, By tHe aBOVe Argument, it migHT Seem ThAt one shOulD not buy WarRanTy fOr tHe Single lapTop eitheR. LEt Us FoR thE sake OF simplicItY hoWeVer Focus ON SamueLson's Coin-ToSsBEts. since a pACkAGE of 100 sUcH bEts sEemS sO attrActiVE, soMe have tAken SamueLsoN'S argUmEnT to show That it would siMpLy be irratiOnAl tO turn dOWN the singLe bet (see, for instance, BenaRTzi and THalEr 1999). But The pReference AgaInst acCepTIng the Single Bet caN bE enTIRely dUE To WhaT sEems to be moDERatE averSiOn to Risk. So iF the lesson from SamuELsoN's argument is tHat It woULD bE irRAtIOnaL tO TurN DOwn the single bet, Then it seemS wE HaVe to concluDE thAt ModeratE risk avErsioN Is irratIonal. OtheRs have takEn samuELSon'S argument tO be a reduCtio of the DEcisiON tHeory He aSsumed: ExPecTed utIlity (Eu) TheOry (seE e.g. LopEs 1996, rabin 2000). STill oThErs think That there must be somethinG wrong With SAmuElson's argUmeNT, siNce they thInk tHat there is NeiTheR anytHinG Wrong With TUrNinG Down tHe siNGle bet whiLE aCcePTInG the package NOR WitH EU thEorY As a theOry
 is very often faced with'bets' wit h pos iti vemo neta ry e xpectations. F o r in stance, suppose that y ou ha ve just bo ughta lapto p  a n d  ar eco nsi de r in g whe the r to bu y a two ye arwa rranty. Such wa rranties g ene rally have n ega tive m on eta r y exp ect ation s forb uyers- otherwise  s e llersw ouldn't o ff er t hem! So the 'bet' no t  to buy the wa rranty  h a sa pos iti ve monetar yexpec t ation ( c om p a r edt o the alterna tive of buy i nga warr an ty) .  Whendecid in g  wh ether to bu y th e warrant y, one might c o nsiderwhethe r o newoul d  b uy  awa r ran t yifo newere buy in g100 l apto p s ( sayasa fi rm).If we suppose  th at t h e p robab ility  ofea ch la ptop b reaki ng  down is indepe nden t of anot her  l apt op  brea k ing do wn, 3 I  conjec ture th a t m os t p eo ple would not buyth e wa rranty i f they we re buying 1 00  la ptop s ,  sinc e th e  ' wins' of  secon d  t yp e of at ti tude m en tio ned  abov e , Iwill,for thesakeo f simplicity,c all any perso n  w h o  t u rnsdow n a bet wit h ap osit ivem on eta r y exp ectat io n  r i sk averse w.r.t. mo ne y. 2 F rom n ow on, whenev er I talka b o ut packa geso fb ets, I will as sumethat theyc onsist o f fin ite numb ers of be t s . 3 This  as sum pti oni s  r easonable ifw e  ass um e thoro ugh  qualit y c ont rol , i nwhich cas e a comp ut er  b ra kin g dow n  could b etre at edas ar andomevent . Is  r is k  av ersioni rr a t iona l?  3  thi s p ac kage(i.e . , o f not b uying war ran t y fo rth e 100 c omputers) wil lalmost cer ta inl y outw e i gh the ' losses'. But then, by t h e above  ar gumen t, i t might s eem  thatone should  not b uy wa rr ant y for t h e  s ing le  laptop ei t h er.  Letus  for  the sa ke of simplicity h o wev er focus on S amu elso n ' scoi n -t o ssb et s . S i n ce a package of  100 suchbe t sseems so a t tra ct ive, so me have  take n  Samuel son's arg ument tosh ow t h a t i t would si mply beirrationa l  to t u rn  down  th e sing le  be t (se e, for ins tance , Bena rt zi and  Thal er  1999).But the preference agai nst ac cepti ngthe singl e b e t c an be ent irel y due to w hat  se ems t o b e  mode rate av ers i on to  ris k . So if t h eles s o nfrom Samuel s o n 'sargum ent is tha t it  would be irratio n al to turn dow n th e sin gle bet,  t hen it seems w e h av e to concl ud e that mode rate ris ka versi on isirrati onal. O t h er s  havetake n S amuelson' s a rg u ment to  b ea  reduc tioof  the d ecisio n  the o r y he assumed: ex pecte d utili t y ( EU) t he ory (se e  e.g . Lopes 19 96, Rabin 2 000).Stil l oth ers thi nk  thatthe re  must be s o mething w rongwith Sa mu elso n's  argum ent, s incethey  t hin k that th e r ei sne i the r an ythin gwron g with tu r ning dow n t h e singl ebet w hile a c ce p t ing the pa cka ge no r with EU th e orya sa  theo ry
 is_very often_faced with 'bets' with_positive monetary_expectations._For instance,_suppose_that you have_just bought a_laptop and are considering_whether to buy_a_two year warranty. Such warranties generally have negative monetary expectations for buyers-otherwise sellers wouldn't_offer_them! So_the_'bet'_not to buy the warranty_has a positive monetary expectation_(compared to_the alternative of buying a warranty). When deciding_whether_to buy the_warranty, one might consider whether one would buy a_warranty if one were buying 100_laptops (say as_a_firm)._If we suppose that_the probability of each laptop breaking_down is independent of another laptop_breaking down,3 I conjecture that most people_would not buy the warranty if_they were buying 100 laptops,_since the_'wins' of second type of_attitude mentioned above,_I will,_for the sake_of simplicity, call any person who_turns down a_bet with a positive monetary expectation_risk_averse w.r.t. money._2_From_now on,_whenever I talk_about_packages of_bets,_I will assume that they consist_of_finite numbers of bets. 3 This assumption_is reasonable if we_assume_thorough quality control, in_which case a computer braking_down could be treated as a_random event._Is risk_aversion irrational? 3 this package (i.e., of not buying warranty for_the 100 computers) will almost certainly_outweigh the 'losses'. But_then, by_the_above argument, it_might_seem that_one should not buy warranty for the_single laptop_either. Let us for the sake_of simplicity however focus_on_Samuelson's coin-tossbets. Since a package of_100 such bets seems so attractive,_some have taken Samuelson's argument_to_show_that it would simply be_irrational to turn down the single_bet (see, for_instance, Benartzi and Thaler 1999). But the_preference_against accepting the single bet can_be_entirely due to what seems to_be_moderate_aversion to risk. So if_the lesson from Samuelson's argument is_that it would be irrational to turn down the_single bet, then_it seems we have to_conclude_that_moderate risk aversion is irrational. Others have taken Samuelson's argument_to be_a reductio of_the decision theory he assumed: expected utility (EU) theory (see_e.g. Lopes 1996, Rabin 2000). Still others_think that there must be something wrong with Samuelson's argument, since_they think that there is neither anything wrong_with turning down the single bet while_accepting the package nor_with_EU theory as a theory