 Following Tversky and Bar-Hillel, I have, so far, not distinguished between State-Wise Dominance and Event-Wise Dominance. As I will explain below, Dominance is an instance of the latter; and, as is well known, one has come a long way towards an expected utility representation once one assumes Event-Wise Dominance. But more importantly, unlike State-Wise Dominance, Event-Wise Dominance is far from being unobjectionable as a requirement of rationality, and will (as I will explain) presumably be rejected by anyone who rejects the (very controversial) Sure Thing Principle. As is conventional, I will use the term'state' for a maximally specific contingency that leaves no uncertainty as to how a prospect will result. An 'event', on the other hand, is a union of states, meaning that an event may 11 Moreover, there are reasons for rejecting Dominance that have nothing to do with risk aversion, as a referee points out; in particular, as Dietrich and List (2005) show, the socalled Two Envelope Paradox calls the principle into question, as a general requirement of rationality. 10 H. Orri Stefánsson not fully determine the result of a risky prospect. State-Wise Dominance can be stated as follows:12 State-Wise Dominance 1 (SWD) For any two bets Bi and Bj, if you weakly prefer Bi to Bj conditional on every possible state of the world, then you should weakly prefer Bi to Bj. If, in addition, there is some state conditional on which you strictly prefer Bi to Bj, then you should strictly prefer Bi to Bj. Event-Wise Dominance, on the other hand, says that: Event-Wise Dominance 1 (EWD) For any two bets Bi and Bj, if there is some partition of the state-space into events such that you weakly prefer Bi to Bj conditional on every event in that partition, then you should weakly prefer Bi to Bj. If, in addition, there is some non-empty event in the partition, conditional on which you strictly prefer Bi to Bj, then you should strictly prefer Bi to Bj. EWD is stronger than SWD. If Bi is weakly preferred to Bj conditional to each event in the maximally fine partition of the state space-i.e., the partition where each 'event' is a state-then the first bet should, according to EWD,
Following Tversky and Bar - Hillel, I have, so far, not distinguished between State - Wise Dominance and Event - Wise Dominance. As I will explain below, Dominance is an case of the latter; and, as is well known, one has hail a long way towards an expected utility theatrical performance once one assumes Event - Wise Dominance. But more importantly, unlike State - Wise Dominance, Event - Wise Dominance is far from being unobjectionable as a requirement of rationality, and will (as I will excuse) presumably be reject by anyone who rejects the (very controversial) certain Thing Principle. As is conventional, I will use the term'state' for a maximally specific eventuality that leaves no uncertainty as to how a prospect will result. An' consequence', on the other hand, is a coupling of states, meaning that an consequence may 11 Moreover, there are reasons for refuse Dominance that have nothing to do with hazard aversion, as a reviewer points out; in particular, as Dietrich and List (2005) show, the socalled Two Envelope Paradox calls the principle into question, as a cosmopolitan requirement of rationality. 10 H. Orri Stefánsson not fully determine the result of a risky prospect. department of state - Wise Dominance can be stated as follows:12 State - Wise Dominance 1 (SWD) For any two bets Bi and Bj, if you weakly prefer Bi to Bj conditional on every possible state of the world, then you should weakly prefer Bi to Bj. If, in addition, there is some state conditional on which you rigorously choose Bi to Bj, then you should strictly prefer Bi to Bj. Event - Wise Dominance, on the other bridge player, says that: Event - Wise Dominance 1 (EWD) For any two bets Bi and Bj, if there is some division of the state - quad into events such that you weakly prefer Bi to Bj conditional on every consequence in that partition, then you should weakly prefer Bi to Bj. If, in addition, there is some non - empty event in the partition, conditional on which you strictly prefer Bi to Bj, then you should strictly prefer Bi to Bj. EWD is stronger than SWD. If Bi is weakly preferred to Bj conditional to each consequence in the maximally fine division of the state space - i.e., the partition where each' event' is a state - then the first stake should, according to EWD,
 Foplowing Tversky and Bar-Hlllel, I have, so yqr, not distihguished between State-Wise Dominance abd Evtut-Wise Dominance. As K will exilain beliw, Dininance is an instance or the oatter; and, as ls well knofn, one has coma x pong way towards an expected utilitr reprexejtation once oge axfumea Event-Wise Dominance. But more impkrtantlj, unlike State-Wisr Dominance, Event-Wise Domijancf is far from beinh unobjectiinabjw as a requifement of gctionality, znd will (as I will explain) presjmablv be rejectgb by dnyone who cejectf the (very controvervial) Sute Thing Princlple. Es iw conventional, I will use the term'state' for a mafijally specific cobtungenwy tvat uwavds ho uhcertalntb as to how a prospect will result. An 'evemt', in the other gand, if w union of states, meaning that an event mag 11 Moreover, there are rwasons for rejecting Fominance that have nothing to do with risk aversion, as a seferxe ponkbs ojr; ln particular, as Dietrich and List (2005) show, the fkcslked Two Enveloie Paradox calls tne ptynciple into duestion, zs a general requigement jf rarionality. 10 H. Prri Stefánsson not fully derermine the gesuot of a risky pros'ect. State-Wire Dpminamce can be stated as foulowa:12 State-Wise Dominancs 1 (SWD) For any twu bvts Ti and Bj, if you weakly prqfer Bi ti Bj conditkonak on edery possihle sbdte of the world, tjen ylu should wewkly prefer Bi to Bj. If, in addivmon, there is xoke vtate couditiokal on which yot strictly preyer Bi tj Bj, ghen you sgould svrictly prefqr Bi to Bj. Eegnt-Wise Dominence, on tre orher hand, sxhs that: Event-Wose Domincuce 1 (EWD) Dor any two bets Bl and Gj, if there is womt partition of tne rtaee-dpece igdo events suwh tfat uou wdakly prefev Bk to Bj conditional on eeery event in that paryibion, then you shotld weakly prrfer Bi to Bj. If, ij addmtion, vhere os fome non-empty event in the parfition, cojdibional on whish yiu strictly 'refer Bi to Bj, then you should strictly prefer Bi to Bj. GWD is stronger than XED. If Bi is weakjy prefersed to Bj conditionao to each event ik the maximally fine pzrtitimn of the state space-i.e., the partition where each 'event' is a state-then the firsr bet should, accorsing to EFD,
Following Tversky and Bar-Hillel, I have, so distinguished State-Wise Dominance Event-Wise Dominance. As is instance of the and, as is known, one has come a long towards an expected utility representation once one assumes Event-Wise Dominance. But more importantly, State-Wise Dominance, Event-Wise Dominance is far from being unobjectionable as a requirement of and (as will presumably be rejected by anyone who rejects the (very controversial) Sure Thing Principle. As is conventional, will use the term'state' for a maximally specific that leaves no uncertainty to how a prospect will An on the hand, a of states, meaning an event may 11 Moreover, there are reasons for rejecting Dominance that have nothing to do with aversion, as points out; particular, Dietrich List (2005) show, Two Envelope Paradox calls the principle a general requirement of rationality. 10 H. Orri not fully the result of a risky prospect. Dominance can be stated as follows:12 State-Wise Dominance (SWD) For any two bets Bi and Bj, if you weakly prefer Bi to Bj every possible state of world, then you weakly Bi Bj. in addition, is some state conditional on which you strictly prefer Bi to then you should strictly prefer Bi to Bj. Event-Wise Dominance, other says that: Event-Wise 1 (EWD) For any bets and Bj, if there partition the such you prefer Bi to Bj on every event in that then you should weakly in addition, there is some non-empty event in partition, conditional on which you strictly prefer to Bj, then you should strictly prefer Bi to Bj. EWD is than SWD. is weakly preferred to Bj conditional to each in the maximally fine of the state space-i.e., the partition where each 'event' a the first should, according to
 Following Tversky and Bar-HilLel, I have, so Far, noT diStiNgUishEd beTween State-Wise dOminAnce and Event-Wise DominaNce. As i wILl exPLaIn belOw, DominANcE IS an InStAncE oF ThE lattEr; aNd, as is wEll known, onE haS cOme a long way tOWaRds an expecTed Utility repreSenTation OnCe oNE assuMes event-wise DoMInance. but more imPoRTantly, UNlike StATE-WIse DOminance, Event-Wise dOmINance is far from Being uNoBJeCTIonAblE as a requirEmEnt of RAtionalITy, AND WilL (As I will explaiN) presumably BE reJected By AnyONe who rEjectS tHE (veRy controverSial) sure Thing princiPLe. As is cONventioNal, I wiLl uSe tHe teRM'sTaTe' fOr A MaxIMaLly SPecIfic contInGeNcy thAt leAVES No unCerTainTy as tO how a prospect WilL resULt. AN 'evenT', on thE othEr Hand, iS a unioN of stAtEs, meaning that an EvenT may 11 MoreoVer, ThEre ArE reasONs for rEjeCtiNg DominAnce thaT HavE nOTHInG to do with risk aversIoN, AS a Referee pOints oUT; iN pARticular, As dieTricH ANd LisT (2005) shoW, ThE socalleD Two EnVElOpE ParadoX cAlls thE pRinCipLe intO QuesTion, as A general RequiREment of rationaLIty. 10 H. Orri StefáNSsON NoT FullY deTermine the rEsulT Of a rIsky PRoSpeCT. StatE-Wise doMInANce can be stated as folLoWs:12 StatE-Wise dominance 1 (SWD) FOr any two beTS bI and Bj, if You wEAkLY prefer Bi to Bj cOnditIonal on eveRY possiblE statE of the woRld, then yoU SHould weaKly PreFer bi tO bJ. IF, in addition, thERE is sOmE state cOndItional On wHicH yoU stRiCtly prefeR Bi to Bj, tHeN yOu ShOulD striCTly prefeR BI to bj. eveNt-WisE dominaNce, on The oThEr HAnd, Says thaT: evENT-WisE DOmInanCe 1 (EwD) for anY two BEts bi and Bj, If there is SomE PartItIoN of the sTate-space into EvEnts such thAt You Weakly PREfer Bi to bj conditional on every eveNT in that ParTitioN, theN you shoulD weAkly prEfeR bi to Bj. if, in adDitioN, tHerE IS some NON-eMptY eVent in the pARTitIon, coNdItioNal on whIch you strictly prefER Bi To Bj, then you shOulD strICTlY prEFeR bi tO BJ. eWD IS Stronger than SWD. if Bi is weakLy PReFerred to Bj COndItIonal to Each eveNt in tHE maximaLly fine paRtition of ThE staTE SpaCe-i.e., the parTition whEre each 'evENt' is a STaTe-theN thE first BeT shOuld, aCcordiNG to eWD,
 Following Tversky and Bar -Hillel, I  have , s o f ar , no t di stinguished be t ween  State-Wise Dominanceand E ve n t-Wi s eDomin ance. A s  I w ill  e xp lai nb el ow, D omi nance i s an insta nce  o f the latter ;  a nd, as iswel l known, one  ha s come  a  lo n g way  to wards  an ex p ectedutility r ep r esenta t ion onc e on e as sumes Event-WiseD om i nance. But mor e impo rt a nt l y , u nli ke State-W is e Dom i nance,E ve n t - Wis e  Dominance is  far from b e ing  unobj ec tio n able a s a r eq u ire ment of rat iona lity, and  will( as I wi l l expla in) pr esu mab ly b e  r ej ect ed bya ny one who  rejects  t he  (ver y co n t r o vers ial ) Su re Th ing Principle . A s is con venti onal,  I w il l use  the t erm's ta te' for a maxim ally  specific  co nt ing en cy th a t leav esnouncerta inty as toho w a  p rospect will resul t. A n'event',  on th e  o th e r hand,is  aunio n of st ates ,  m eaning t hat an ev en t may 1 1Moreov er , t her e are reas ons fo r reject ing D o minance that h a ve nothing to do w it h  ris k a version, as  a r e fere e po i nt s o u t; in  part ic u la r , as Dietrich and L is t (200 5) sh ow, the socal led Two En v e l ope Para doxc al l s the principl e int o question ,  as a ge neral  require ment of r a t ionality . 1 0 H . O rri S te fánsson not f u l ly d et erminethe  result  of  aris kypr ospect. S tate-Wis eDo mi na nce  canb e stated  a s f ol low s:12S tate-W ise D omin an ce 1 ( SWD) Fo r  a n y  two  b et s Bi  an dBj, i f yo u  we akly pr efer Bi t o B j  con di ti onal on  every possib le  state ofth e w orld,t h en you s hould weakly prefer Bit o Bj. I f,in ad diti on, there  is  somesta t e cond itiona l onwh ich y ou st r i ct lypr efer Bi to B j,thenyo u sh ould st rictly prefer Bi t o  Bj . Event-WiseDom inan c e ,ont he oth er han d ,  says that: Eve nt-Wise Do mi n an ce 1 (EWD) For  a ny twobets Bi  andB j, if t here is s ome parti ti on o f the  state-spa ce intoevents su c h tha t  y ou we akl y pref er  Bi  to B j cond i tio nal o n ever yeventin th at  partiti on, then you should wea kly pr eferBito Bj. If , i n  ad dition, t here  is some n on- emp ty ev ent in th e pa r ti tio n , con diti o nal on wh i ch  yo u st rictly pref e r Bito Bj , t h en you  sho uld strictly pref e r Bi to Bj. EW D is s tro nge r  tha nSWD. If Bi iswea kl y preferre dto Bj condi tional t oe ach e vent i n themaximal l y  f i ne par titi onof the st ate  s p ace-i.e .,  t h e part itio nwhereeach ' e vent ' is a state-thenthe f i r st be t  sh ould,  a ccordin g  toEWD,
 Following_Tversky and_Bar-Hillel, I have, so_far, not_distinguished_between State-Wise_Dominance_and Event-Wise Dominance._As I will_explain below, Dominance is_an instance of_the_latter; and, as is well known, one has come a long way towards an_expected_utility representation_once_one_assumes Event-Wise Dominance. But more_importantly, unlike State-Wise Dominance, Event-Wise_Dominance is_far from being unobjectionable as a requirement of_rationality,_and will (as_I will explain) presumably be rejected by anyone who_rejects the (very controversial) Sure Thing_Principle. As is_conventional,_I_will use the term'state'_for a maximally specific contingency that_leaves no uncertainty as to how_a prospect will result. An 'event', on_the other hand, is a union_of states, meaning that an_event may_11 Moreover, there are reasons_for rejecting Dominance_that have_nothing to do_with risk aversion, as a referee_points out; in_particular, as Dietrich and List (2005)_show,_the socalled Two_Envelope_Paradox_calls the_principle into question,_as_a general_requirement_of rationality. 10 H. Orri Stefánsson_not_fully determine the result of a risky_prospect. State-Wise Dominance can_be_stated as follows:12 State-Wise_Dominance 1 (SWD) For any_two bets Bi and Bj, if_you weakly_prefer Bi_to Bj conditional on every possible state of the world, then_you should weakly prefer Bi to_Bj. If, in addition,_there is_some_state conditional on_which_you strictly_prefer Bi to Bj, then you should_strictly prefer_Bi to Bj. Event-Wise Dominance, on_the other hand, says_that:_Event-Wise Dominance 1 (EWD) For any_two bets Bi and Bj, if_there is some partition of_the_state-space_into events such that you_weakly prefer Bi to Bj conditional_on every event_in that partition, then you should weakly_prefer_Bi to Bj. If, in addition,_there_is some non-empty event in the_partition,_conditional_on which you strictly prefer_Bi to Bj, then you should_strictly prefer Bi to Bj. EWD is stronger than_SWD. If Bi_is weakly preferred to Bj_conditional_to_each event in the maximally fine partition of the state_space-i.e., the_partition where each_'event' is a state-then the first bet should, according to_EWD,