 which might make her willing to incur the slightly higher risk of ending up with nothing by going for the bet with the considerably higher expectation.15 otherwise we would have g ≺ f. But then f ′(E) g′(E), which by EWD entails f ′ g′. Assuming f ′ g′ would have allowed us to derive f g in a similar manner. Hence, EWD and completeness of the conditional preference relation entail the STP. 14 Critics of expected utility theory are faced with well-known dynamic arguments in favour of the theory theory, that can in fact be formulated as arguments in favour of EventWise Dominance. For a detailed discussion of ways in which those who are critical of expected utility theory can respond to these arguments, see McClennen (1990). 15 Another related way in which a person might be risk averse, is if she, in addition to caring about the expected values of prospects, also cares about the dispersion in the monetary values of the possible outcomes (McClennen 1990). Again, such a person might prefer B to A conditional on E (since the former has minimal dispersion but the latter has quite a lot), 12 H. Orri Stefánsson A more general worry about EWD, that can be illustrated by again considering the bets in Table 2, concerns the demand that if there is any partition of the state space into events such that B is weakly preferred to A conditional on every event, then B should be preferred to A. Notice that there is a refinement of the {E,¬E} partition according to which the dominance relation no longer holds: further partition E according to whether ticket 1 is drawn (event F ) or not (¬F ). Then it is no longer the case that B event-wise dominates A, since the latter is preferred conditional on event E∧¬F. Recall that the same point holds for the axiomatic version of Samuelson's argument: the smaller package does not event-wise dominate the larger one once the partition is fine enough to determine the outcome of the extra bet that differentiates the large package from the smaller one. So, one might reasonably wonder why the {E,¬E} partition should be decisive when it comes to determining the rational preference between A and B, rather than, say, the maximally fine partition. Similarly, in the case of Samuelson's colleague's preferences, one might wonder why the partition according to how the coin lands on the first i tosses should be
which might make her willing to incur the slightly eminent hazard of ending up with nothing by going for the stake with the considerably high expectation.15 otherwise we would hold g ≺ f. But then f ′(E) g′(E), which by EWD entails f ′ g′. Assuming f ′ g′ would have allow us to derive f g in a exchangeable manner. Hence, EWD and completeness of the conditional preference relation back entail the STP. 14 Critics of expected utility theory are face with well - known dynamic arguments in party favor of the theory theory, that can in fact be formulated as arguments in favor of EventWise Dominance. For a detailed discussion of ways in which those who are critical of expected utility theory can respond to these arguments, witness McClennen (1990). 15 Another related way in which a person might be risk averse, is if she, in addition to caring about the expected value of prognosis, also cares about the dispersion in the monetary values of the possible outcomes (McClennen 1990). Again, such a person might choose B to A conditional on E (since the erstwhile has minimal dispersion but the latter has quite a fortune), 12 H. Orri Stefánsson A more general worry about EWD, that can be illustrated by again regard the bets in Table 2, concerns the demand that if there is any division of the state space into events such that B is weakly preferred to A conditional on every event, then B should be preferred to A. Notice that there is a refinement of the { E,¬E } partition according to which the dominance relation back no longer holds: further division east according to whether ticket 1 is drawn (event F) or not (¬F). Then it is no longer the shell that B event - wise dominates A, since the latter is prefer conditional on event E∧¬F. Recall that the same point hold for the axiomatic version of Samuelson's argumentation: the smaller package does not consequence - wise dominate the larger one once the partition is all right enough to determine the outcome of the excess bet that differentiates the large package from the smaller one. indeed, one might reasonably wonder why the { E,¬E } partition should be decisive when it comes to determining the rational preference between A and B, rather than, say, the maximally fine division. Similarly, in the case of Samuelson's colleague's preferences, one might wonder why the division according to how the coin lands on the first i convulse should be
 whlch might make her willikg to incur the slightlb highed risk ow ending up with nothing by joint for the bet with the conskderably jigher ezpecuation.15 otherwise xs would have f ≺ f. Yuv then f ′(E) g′(E), wmich by EWD entails f ′ g′. Dsruling f ′ g′ would have allowed us to qerive g h in a similar manmqr. Hsnce, EWD and completeness of the cknditioial preference telation entail the STP. 14 Cgitifs of expected utipity theory are daced with wdll-known djuamic argumgnts in favour of the theory theury, tkat can in daxt hg formulated as agguments in favour of EventWose Dominance. Nor a derailed discussion of xays in which those rho are csicical of expected utioiry thgory wan fwspund tp fhese wrgnments, see JcClennen (1990). 15 Another related wau yb which a peraon midhe be risk averse, is if she, in addition uo cading about the expected values of prospects, wlso caref about the dispersion in the monetary values of dhe pkrsiyoe ougxoles (McClennen 1990). Again, such a person might prefqd N no A conditional jn E (since yhf gjrmer has minkmal dnapsrsion but the lather has quitw a lot), 12 R. Orti Stefánsson A more general worry about WWD, that can be ilpustrated bv agaim conxidering the bets in Tayle 2, ckncerns the demand tgxt if there is avy iarthtion of the state space igto eventw sueh that C is weaklr preferref to A conditional on evfry erent, dhen B shokld be preferred to A. Notice thev there is a tefhnekent of che {E,¬E} partition acsording to whieh the djminavce relatikn no lmnger holds: further parthjion E accordmng to whqthee tixket 1 ir drawn (event F ) or not (¬Y ). Thwn it is no longer thg dase that B eveuu-wiwe dominates A, xinze ehv letter hs preferred conaitkpnal un evenu E∧¬N. Rdcalk that the same poind homds for the axiomayig version of Samuqlson's argumemt: the smaller pacnage voes nut evrnt-rise dominate the larger one ohce the pwrtltion is fine enomgh jo determinz the outcome of the extra bet that diffxrentiates the large paxkage from the smalktr one. So, one mighe reasonatly wonder why the {E,¬W} partition shoulc be decisive when it comes to dftermining the rational preference between A and B, rather than, say, the mazimallb sine partitjon. Ximildrjv, in thq cadx of Samuelson's cplleague's preferences, one might wonder fhv the partition according to nod the coin lavds on the first i tossea should be
which might make her willing to incur higher of ending with nothing by the higher expectation.15 otherwise would have g f. But then f ′(E) g′(E), by EWD entails f ′ g′. Assuming f ′ g′ would have allowed to derive f g in a similar manner. Hence, EWD and completeness of conditional relation the 14 Critics of expected utility theory are faced with well-known dynamic arguments in favour of the theory, that can in fact be formulated as in favour of EventWise For a detailed discussion of in those who critical expected theory can respond these arguments, see McClennen (1990). 15 Another related way in which a person might be risk averse, if she, to caring the values prospects, also cares dispersion in the monetary values of (McClennen 1990). Again, such a person might prefer to A on E (since the former has dispersion but the latter has quite a lot), H. Orri Stefánsson A more general worry about EWD, that can be illustrated by again bets in Table 2, the demand that there any of state space events such that B is weakly preferred to A conditional on event, then B should be preferred to A. Notice that a of the {E,¬E} according to which the relation longer holds: further partition to ticket (event ) not (¬F ). Then is no longer the case B event-wise dominates A, conditional on event E∧¬F. Recall that the same holds for the axiomatic version of Samuelson's the smaller package does not event-wise dominate the larger one once the is fine determine the outcome of the extra bet that the large package from smaller one. So, one might reasonably wonder why the partition be decisive it comes to the rational preference A and B, say, the fine Similarly, of Samuelson's colleague's preferences, one might why partition according to how the lands first i tosses should be
 which might make her willing tO incur the sLightLy hIghEr Risk Of enDing up with nothINg by Going for the bet with the cOnsidErABly hIGhEr expEctatioN.15 OtHERwiSe We WouLd HAvE g ≺ f. BuT thEn f ′(E) g′(E), wHich by EWD eNtaIlS f ′ g′. Assuming f ′ G′ WoUld have allOweD us to derive f G in A similAr ManNEr. HenCe, EwD and CompleTEness oF the condiTiONal preFErence rELAtIon eNtail the STP. 14 CriticS Of EXpected utility Theory ArE FaCED wiTh wEll-known dyNaMic arGUments iN FaVOUR of THe theory theorY, that can in fACt bE formuLaTed AS argumEnts iN fAVouR of EventWisE DomInance. For A detaiLEd discuSSion of wAys in wHicH thOse wHO aRe CriTiCAl oF ExPecTEd uTility thEoRy Can reSponD TO THese ArgUmenTs, see mcClennen (1990). 15 AnotHer RelaTEd wAy in wHich a PersOn Might Be risk AversE, iS if she, in additioN to cAring abouT thE eXpeCtEd valUEs of prOspEctS, also caRes abouT The DiSPERsIon in the monetary vaLuES Of The possiBle outCOmEs (mCClennen 1990). agAin, Such A PErson MighT PrEfer B to A ConditIOnAl On E (sincE tHe formEr Has MinImal dISperSion buT the lattEr has QUite a lot), 12 H. Orri STEfánsson A more GEnERAl WOrry AboUt EWD, that caN be iLLustRateD By AgaIN consIderiNg THe BEts in Table 2, concerns tHe Demand That iF there is any paRtition of tHE STate spacE intO EvENts such that B is WeaklY preferred TO A conditIonal On every eVent, then B SHOuld be prEfeRreD to a. NoTICe That there is a rEFInemEnT of the {E,¬e} paRtition AccOrdIng To wHiCh the domiNance relAtIoN nO lOngEr holDS: further PaRtiTiOn E AccorDIng to wHetheR ticKeT 1 iS DraWn (event f ) Or NOT (¬F ). ThEn It Is no LonGeR the cAse tHAt B Event-wiSe dominatEs A, SInce ThE lAtter is Preferred condItIonal on eveNt e∧¬F. REcall tHAT the same Point holds for the axiomatIC versioN of samueLson'S argument: The SmalleR paCKage doEs not eVent-wIsE doMINate tHE LaRgeR oNe once the pARTitIon is FiNe enOugh to dEtermine the outcome OF thE extra bet that DifFereNTIaTes THe LArgE pACkaGE From the smaller oNe. So, one migHt REaSonably wonDEr wHy The {E,¬E} paRtition ShoulD Be decisIve when it Comes to deTeRminING thE rational pReferencE between A ANd B, raTHeR than, Say, The maxImAllY fine PartitIOn. SImilaRly, in tHe Case of samueLsOn's colleAgue's preferences, one mighT wondeR why tHe pArtition aCcoRDinG to how the Coin Lands on the FirSt i TosseS shOUld be
 which might make her will ing to inc ur th e s lig ht ly h ighe r risk of endi n g up  with nothing by going  forth e  bet wi th th e consi d er a b lyhi gh erex p ec tatio n.1 5 other wise we wo uld  h ave g ≺ f. B u tthen f ′(E ) g ′(E), whichbyEWD en ta ils f ′ g ′.Assum ing f′  g′ wo uld haveal l owed u s  to der i v ef gin a similar mann e r. Hence, EWD and  compl et e ne s s  of  th e conditio na l pre f erencer el a t i one ntail the STP . 14 Critic s  of  expec te d u t ilitytheor ya refaced withwell -known dy namica rgument s  in fav our of  th e t heor y  t he ory ,t hat ca n i n  fa ct be fo rm ul atedas a r g u m ents  in  fav our o f EventWise D omi nanc e . F or adetai leddi scuss ion of  ways  i n which those w ho a re critic alof  ex pe ctedu tility  th eor y can r espondt o t he s e ar guments, see McCle nn e n  ( 1990). 1 5 Anot h er  r e lated wa yinwhic h a per sonm ig ht be ri sk ave r se ,is if s he , in a dd iti onto ca r ingaboutthe expe ctedv alues of prosp e cts, also car e sa b ou t  the  di spersion in  the mone tary va lue s  of t he po ss i bl e  outcomes (McClenne n1990).  Agai n, such a per son mightp r e fer B to  A c o nd i tional on E (s incethe former has mini mal d ispersio n but the l atter ha s q uit e a  lo t ) ,12 H. Orri St e f ánss on  A more  ge neral w orr y a bou t E WD , that ca n be ill us tr at ed  by  agai n  conside ri ngth e b ets i n  Table  2, c once rn st hedemandt ha t if t he re  isany  p artit iono f t he stat e space i nto even ts  s uch tha t B is weakly  p referred t oA c onditi o n al on ev ery event, then B shoul d  be pre fer red t o A.  Notice t hat  there  is a refi nement  of t he  {E , ¬ E} pa r t it ion  a ccording t o whi ch th edomi nance r elation no longerh old s: further pa rti tion E  a cco r di n g t ow het h e r ticket 1 is d rawn (even tF  )  or not (¬ F  ).  T hen itis no l onger the cas e that Bevent-wis edomi n a tes  A, sincethe latt er is pre f erred co nditi ona l on e ve ntE∧¬F.  Recal l  th at th e same  p oint h oldsfo r the ax iomatic version of Samu elson' s arg ume nt: the s mal l erpackage d oesnot event- wis e d omina tet he la rger on e o n ce th e pa r tition is fi nee n ou gh to deter m i n e t he ou tco m e of t he e xtra bet that dif f erentiates the  lar g e  pa cka g e fr om  the smaller o ne.  S o ,  one mig ht  reasonably  wonderwh y  the{E,¬E}  parti tion sh o u ld be dec isiv e w hen it co mes  t o  determ in in g  the r atio na l pref erence betw e e n A and B, rathe r tha n ,  say, the  maxi ma lly fin e  par tition. Si milarly, in  the c aseof Sa muelson 's  colle agu e' s preferen c es, one m ightwonderwh y th e p artiti on a c c ordin g to  h owthe coinl a nd s  o nt hefirs t i t os sesshould be 
 which_might make_her willing to incur_the slightly_higher_risk of_ending_up with nothing_by going for_the bet with the_considerably higher expectation.15_otherwise_we would have g ≺ f. But then f ′(E) g′(E), which by EWD_entails_f ′_g′._Assuming_f ′ g′ would have_allowed us to derive f_g in_a similar manner. Hence, EWD and completeness of_the_conditional preference relation_entail the STP. 14 Critics of expected utility theory_are faced with well-known dynamic arguments_in favour of_the_theory_theory, that can in_fact be formulated as arguments in_favour of EventWise Dominance. For a_detailed discussion of ways in which those_who are critical of expected utility_theory can respond to these_arguments, see_McClennen (1990). 15 Another related_way in which_a person_might be risk_averse, is if she, in addition_to caring about_the expected values of prospects, also_cares_about the dispersion_in_the_monetary values_of the possible_outcomes_(McClennen 1990)._Again,_such a person might prefer B_to_A conditional on E (since the former_has minimal dispersion but_the_latter has quite a_lot), 12 H. Orri Stefánsson_A more general worry about EWD,_that can_be illustrated_by again considering the bets in Table 2, concerns the demand_that if there is any partition_of the state space_into events_such_that B is_weakly_preferred to_A conditional on every event, then B_should be_preferred to A. Notice that there_is a refinement of_the_{E,¬E} partition according to which the_dominance relation no longer holds: further_partition E according to whether_ticket_1_is drawn (event F )_or not (¬F ). Then it_is no longer_the case that B event-wise dominates A,_since_the latter is preferred conditional on_event_E∧¬F. Recall that the same point_holds_for_the axiomatic version of Samuelson's_argument: the smaller package does not_event-wise dominate the larger one once the partition is_fine enough to_determine the outcome of the_extra_bet_that differentiates the large package from the smaller one. So,_one might_reasonably wonder why_the {E,¬E} partition should be decisive when it comes to_determining the rational preference between A and_B, rather than, say, the maximally fine partition. Similarly, in the_case of Samuelson's colleague's preferences, one might wonder_why the partition according to how the_coin lands on the_first_i tosses should be