 notion of expected fit, we also need a numerical measure of how well the worlds in a given outcome fit the desire relative to complete frustration and satisfaction of that desire. So, we construct a function F(o​i​,D) from a outcome o​i and a desire D to a number on the unit interval [0,1] such that an outcome that completely frustrates a desire maps onto 0; an outcome that completely satisfies the desire maps onto 1; and any pair of outcomes for which the worlds in the first outcome have a strictly better fit than the worlds in the second outcome is such that the first outcome maps onto a higher value on the unit interval than the second. Intuitively, this function can be thought of as measuring how large a proportion of a desire is satisfied in a given world, on a scale from 0 to 1. With this function in hand, we define the expected fit of an agent A's action φ relative to some desire D as the weighted sum of the fit between D and the world in each possible outcome, where each weight is given by the probability of the agent's obtaining the relevant outcome. More formally: EF(A φs,D) = pr(o​i​|A φs) F(o​i​,D)∑ o ∈Oi where EF(A φs,D) is the ​expected fit of a desire D given that A performs an action φ, pr(o​i​|A φs) is the probability of outcome o​i given that A φs, F(o​i​,D) is the aforementioned measure of fit between D and and the world in o​i​, and O is a partition of all possible outcomes of A's φ-ing. 44 43 Since an outcome is just a set of possible world with equal fit with respect to some desire, we will henceforth talk about fit between the desire and an outcome as a less cumbersome way of referring to the fit between the desire and each of the worlds in the outcome. 44 Readers familiar with the distinction between Evidential Decision Theory (EDT) and Causal Decision Theory (CDT) will notice that our definition of expected fit corresponds more closely to the 'evidential' definition of expected utility than the competing 'causal' definition. However, a definition of expected fit that corresponds to the latter can easily be provided by simply replacing the ​conditional probability pr(o​i​|A φs) with the ​counterfact
notion of expected fit, we also necessitate a numeric measure of how well the worlds in a given consequence fit the desire relative to dispatch frustration and satisfaction of that desire. So, we construct a affair F(o​i​,D) from a outcome o​i and a desire D to a issue on the unit interval [ 0,1 ] such that an consequence that wholly frustrates a desire maps onto 0; an result that completely satisfies the desire map onto 1; and any pair of outcomes for which the worlds in the beginning outcome have a strictly better fit than the universe in the second outcome is such that the first outcome maps onto a higher value on the unit of measurement interval than the second. Intuitively, this function can be thought of as measuring how large a proportion of a desire is satisfied in a given world, on a scale from 0 to 1. With this function in hand, we define the expected fit of an agent A's military action φ relative to some desire D as the leaden kernel of the burst between D and the world in each possible result, where each weight is given by the probability of the agent's obtaining the relevant result. More formally: EF(A φs, D) = pr(o​i​|A φs) F(o​i​,D)∑ o ∈Oi where EF(A φs, D) is the ​expected fit of a desire D given that A performs an action φ, pr(o​i​|A φs) is the probability of consequence o​i given that A φs, F(o​i​,D) is the aforementioned measure of fit between vitamin d and and the world in o​i​, and oxygen is a division of all potential outcomes of A's φ - ing. 44 43 Since an outcome is just a set of possible world with equal fit with obedience to some desire, we will henceforth talk about fit between the desire and an outcome as a less cumbersome room of referring to the burst between the desire and each of the worlds in the outcome. 44 reader familiar with the differentiation between Evidential Decision Theory (EDT) and Causal Decision Theory (CDT) will notice that our definition of expect fit corresponds more closely to the' evidential' definition of expect utility than the competing' causal' definition. However, a definition of expect fit that represent to the latter can easily be provided by simply replacing the ​conditional probability pr(o​i​|A φs) with the ​counterfact
 nohion of expected fit, we xlso need a numgrucal mxasure kf how wdll the worlds in a given ouvcomw fit the desire relative tu completv frustrarion qnd satisfedtion on thaf desnrx. So, we construgt a functimn F(o​i​,D) from a ojteome o​i and a desire D to a number og the umih interval [0,1] sush tnwt ah outcome that completely frustratss a devire maps ontp 0; an outcome that completfly datisfies the desige maps onti 1; age any pair ow outcomes for which tge worlds in the first outcome fave c strictly verteg fit than tie worjds in the scbond oudcome ix such that thc firvt iutcome maps onto a hmgher value on the ugit inteream than the second. Ibtuithvelf, thkw fjncuioi czn be hhonght of as jeasuring hiw large a proportipn if a desire ia satiffyed in a given world, on a scale from 0 tm 1. Sith this function in hqnd, we define the expgcted fit jf an agent A's action φ relative to some desire D ds thx deiymbed rym of the fit between D and the world in each pjasobke outcome, wheve each weight is bigem by the probacility of the agent's obtainlng the relecant outcjme. Kore formally: EF(A φs,D) = pr(o​i​|A φs) F(o​i​,D)∑ o ∈Oi qhere EF(A φs,D) is thz ​expected fnt of s desore D given that A perfurms an action φ, pr(o​i​|A φs) jr the probabilith on ogtcome o​i given that A φs, F(j​i​,D) is thx afoxementioved keasurq of fit bftweek D and and the worpd in o​h​, and O is a partition of all possible ouvromes of A's φ-img. 44 43 Vince an outcpme is just a set of possibke worlb with equal fit with rxspect to soie desire, we flll henceforvh talk afout fit betweev the desire anc an outcome as a lwss cumbersome way of deferring to thz dit between the derirq wnv eacr of the worlgs iv tfr outzome. 44 Rtcdevs wamikiar with the distinwtioh between Evidentisl Decisiob Theory (EDT) and Caussl Decision Theory (CDT) xill nutice thwt our definition of expected rit corredpokds more closqly bo tre 'evidentnal' definition of expected utility than vhe competing 'causal' dgfinition. However, a dgfikition of ex'ected fit that corresponds to the oatter can easily be provided by simplg repldcing the ​conditional probability pr(o​i​|A φs) with the ​counterfact
notion of expected fit, we also need measure how well worlds in a relative complete frustration and of that desire. we construct a function F(o​i​,D) from outcome o​i and a desire D to a number on the unit interval such that an outcome that completely frustrates a desire maps onto 0; an that satisfies desire onto 1; and any pair of outcomes for which the worlds in the first outcome have strictly better fit than the worlds in the outcome is such that first outcome maps onto a value the unit than second. this function can thought of as measuring how large a proportion of a desire is satisfied in a given world, a scale to 1. this in we define the of an agent A's action φ desire D as the weighted sum of the between D the world in each possible outcome, each weight is given by the probability of agent's obtaining the relevant outcome. More formally: EF(A φs,D) = pr(o​i​|A φs) F(o​i​,D)∑ o ∈Oi φs,D) is the ​expected of a desire given A an φ, pr(o​i​|A is the probability of outcome o​i given that A φs, F(o​i​,D) the aforementioned measure of fit between D and and the o​i​, O is a of all possible outcomes A's 44 43 Since an just set with fit respect to some desire, will henceforth talk about fit the desire and an way of referring to the fit between the and each of the worlds in the 44 Readers familiar with the distinction between Evidential Decision Theory (EDT) and Decision Theory notice that our definition of expected fit corresponds closely to the 'evidential' of expected utility than the competing 'causal' definition. However, definition expected fit corresponds to the can easily be by simply replacing probability pr(o​i​|A with ​counterfact
 notion of expected fit, we also Need a numerIcal mEasUre Of How wEll tHe worlds in a givEN outCome fit the desire relatiVe to cOmPLete FRuStratIon and sATiSFActIoN oF thAt DEsIre. So, We cOnstrucT a function f(o​i​,d) fRom a outcome o​I AnD a desire D tO a nUmber on the unIt iNtervaL [0,1] sUch THat an OutCome tHat comPLetely FrustrateS a DEsire mAPs onto 0; aN OUtCome That completely satISfIEs the desire mapS onto 1; aNd ANy PAIr oF ouTcomes for wHiCh the WOrlds in THe FIRSt oUTcome have a strIctly better FIt tHan the WoRldS In the sEcond OuTComE is such that The fIrst outcoMe maps ONto a higHEr value On the uNit IntErvaL ThAn The SeCOnd. iNtUitIVelY, this funCtIoN can bE thoUGHT Of as MeaSuriNg how Large a proportIon Of a dESirE is saTisfiEd in A gIven wOrld, on A scalE fRom 0 to 1. With this fuNctiOn in hand, wE deFiNe tHe ExpecTEd fit oF an AgeNt A's actIon φ relATivE tO SOMe Desire D as the weightEd SUM oF the fit bEtween d AnD tHE world in EaCh pOssiBLE outcOme, wHErE each weiGht is gIVeN bY the proBaBility Of The AgeNt's obTAiniNg the rElevant oUtcomE. more formally: EF(a Φs,D) = pr(o​i​|A φs) F(o​i​,d)∑ O ∈OI WHeRE EF(A Φs,D) Is the ​expectEd fiT Of a dEsirE d gIveN That A PerfoRmS An ACtion φ, pr(o​i​|A φs) is the pRoBabiliTy of oUtcome o​i given That A φs, F(o​i​,d) IS The aforeMentIOnED measure of fit bEtweeN D and and thE World in o​I​, and O Is a partiTion of all POSsible ouTcoMes Of A'S φ-iNG. 44 43 siNce an outcome iS JUst a SeT of possIblE world wIth EquAl fIt wItH respect tO some desIrE, wE wIlL heNcefoRTh talk abOuT fiT bEtwEen thE Desire And an OutcOmE aS A leSs cumbeRSoME Way oF rEfErriNg tO tHe fit BetwEEn tHe desirE and each oF thE WorlDs In The outcOme. 44 Readers famIlIar with the DiStiNction BETween EviDential Decision Theory (EDt) And CausAl DEcisiOn ThEory (CDT) wiLl nOtice tHat OUr defiNition Of expEcTed FIT corrESPoNds MoRe closely tO THe 'eVidenTiAl' deFinitioN of expected utility THan The competing 'cAusAl' deFINiTioN. hoWEveR, a DEfiNITion of expected fIt that corrEsPOnDs to the latTEr cAn Easily bE providEd by sIMply repLacing the ​ConditionAl ProbABIliTy pr(o​i​|A φs) wIth the ​coUnterfact
 notion of expected fit, w e also nee d a n ume ric al  mea sure  of how well t h e wo rlds in a given outcom e fit  t h e de s ir e rel ative t o  c o m ple te  f rus tr a ti on an d s atisfac tion of th atde sire. So, we co nstruct afun ction F(o​i​ ,D)  fromaout c ome o ​iand a  desir e  D toa numberon the un i t inter v a l[0,1 ] such that an ou t co m e that complet ely fr us t ra t e s a  de sire mapson to 0; an outc o me t h atc ompletely sat isfies thed esi re map sont o  1; an d any  p a irof outcomes  for  which th e worl d s in th e  firstoutcom e h ave  a s t ri ct lybe t ter fi t t h anthe worl ds  i n the  sec o n d outc ome  issuchthat the firs t o utco m e m aps o nto a  hig he r val ue onthe u ni t interval than  the  second.Int ui tiv el y, th i s func tio n c an be t houghto f a sm e a su ring how large a p ro p o rt ion of a  desir e  i ss atisfied  i n a  giv e n  worl d, o n  a  scale f rom 0t o1.  With t hi s func ti oninhand, we d efinethe expe ctedf it of an agent A's action φr el a t iv e  tosom e desire Das t h e we ight e dsum of th e fit  b e tw e en D and the worldin  eachpossi ble outcome,where each w e ight isgive n  b y  the probabili ty of  the agent ' s obtain ing t he relev ant outco m e . More f orm all y:EF( A φs ,D) = pr(o​i​ | A  φs)  F (o​i​,D )∑o ∈Oi w her e E F(A  φs ,D ) is the​expecte dfi tof  adesir e  D given  t hat  A  pe rform s  an ac tionφ, p r( o​ i ​|A  φs) is th e prob ab il ityofou tcome  o​i giv en that  A φs, F( o​i ​ ,D)is  t he afor ementioned me as ure of fit  b etw een Da n d and th e world in o​i​, and Oi s a par tit ion o f al l possibl e o utcome s o f  A's φ -ing.44 43  S inc e an ou t c om e i sjust a set o f p ossib le  wor ld with  equal fit with re s pec t to some des ire , we w il l h e nc e for th tal k about fit betwe en the des ir e  a nd an outc o meas  a less  cumber somew ay of r eferringto the fi tbetw e e n t he desireand each  of the w o rldsi nthe o utc ome. 4 4Rea dersfamili a r w ith t he dis ti nction  betw ee n Eviden tial Decision Theory (E DT) an d Cau sal  Decision  Th e ory  (CDT) wi ll n otice that  ou r d efini tio n  of e xpec t ed  fi t  corr espo n ds more c l os ely t othe 'eviden t i a l'defin iti o n of e xpec ted utility thant he competing ' caus a l ' d efi n itio n.  However, a de fin it i o n of exp ec ted fit tha t corres po n ds to  the l attercan eas i l yb e prov ided  by  simply r epl ac i ng the​c on d itiona l pr ob abilit y pr(o ​ i​|A φ s) with the ​cou nterf a c t
 notion_of expected_fit, we also need_a numerical_measure_of how_well_the worlds in_a given outcome_fit the desire relative_to complete frustration_and_satisfaction of that desire. So, we construct a function F(o​i​,D) from a outcome o​i_and_a desire_D_to_a number on the unit_interval [0,1] such that an_outcome that_completely frustrates a desire maps onto 0; an_outcome_that completely satisfies_the desire maps onto 1; and any pair of_outcomes for which the worlds in_the first outcome_have_a_strictly better fit than_the worlds in the second outcome_is such that the first outcome_maps onto a higher value on the_unit interval than the second. Intuitively,_this function can be thought_of as_measuring how large a proportion_of a desire_is satisfied_in a given_world, on a scale from 0_to 1. With_this function in hand, we define_the_expected fit of_an_agent_A's action_φ relative to_some_desire D_as_the weighted sum of the fit_between_D and the world in each possible_outcome, where each weight_is_given by the probability_of the agent's obtaining the_relevant outcome. More formally: EF(A φs,D)_= pr(o​i​|A_φs) F(o​i​,D)∑_o ∈Oi where EF(A φs,D) is the ​expected fit of a_desire D given that A performs_an action φ, pr(o​i​|A_φs) is_the_probability of outcome_o​i_given that_A φs, F(o​i​,D) is the aforementioned measure_of fit_between D and and the world_in o​i​, and O_is_a partition of all possible outcomes_of A's φ-ing. 44 43 Since_an outcome is just a_set_of_possible world with equal fit_with respect to some desire, we_will henceforth talk_about fit between the desire and an_outcome_as a less cumbersome way of_referring_to the fit between the desire_and_each_of the worlds in the_outcome. 44 Readers familiar with the_distinction between Evidential Decision Theory (EDT) and Causal Decision_Theory (CDT) will_notice that our definition of_expected_fit_corresponds more closely to the 'evidential' definition of expected utility_than the_competing 'causal' definition._However, a definition of expected fit that corresponds to the_latter can easily be provided by simply_replacing the ​conditional probability pr(o​i​|A φs) with the ​counterfact