bars​) = F(o​1-bar​,D​100-bars​). By the same reasoning, EF(Bart buys 10 bars,D​100-bars​) = F(o​10-bars​,D​100-bars​). We thus get: EF(Bart buys 10 bars,D​100-bars​) > EF(Bart buys 1 bar,D​100-bars​) We now subtract by EF(Bart buys nothing,D​100-bars​) on both sides of the inequality to obtain EF(Bart buys 10 bars,D​100-bars​) EF(Bart buys nothing,D​100-bars​) > EF(Bart buys 1 bar,D​100-bars​) EF(Bart buys nothing,D​100-bars​) as desired. 48 Again, as in the case of probabilistic accounts, there are other possible ways of spelling out the degree of promotion that exploit the ​ratio between the two expected fits, or perhaps the ​log ​of the ratio between these two values. Here we don't take a stand on whether one of these is preferable to the others, since we don't yet see any theoretical reason to prefer one to the others. We think investigating the question of whether there are reasons to opt for one or the other measure would be worth pursuing, but it's not something we have the space to do here. 27 By contrast, the expected fit for making the trade is: EF(Annie makes 1st trade,D​100-bars​) = 0.01 x F(o​100-bars​,D​100-bars​) + 0.99 x F(o​0-bars​,D​100-bars​). Now, of course, the expected fit for each action will depend on how well Annie's desire for 100 chocolate bars fits the three outcomes at play here, i.e. o​0-bars​, o​49-bars​, and o​100-bars​. However, it is clear that any plausible measure of fit -i.e. any plausible function F -- will result in a higher expected fit for refusing the trade than for making it. To see this, note that D​100-bars is ​fully unsatisfied in o​0-bars -it could not possibly have a lesser fit -- and so, whatever else is true of our measure of fit, it will assign a
bars​) = F(o​1 - bar​,D​100 - bars​). By the same reasoning, EF(Bart buys 10 bars, D​100 - bars​) = F(o​10 - bars​,D​100 - bars​). We thus draw: EF(Bart buy 10 bars, D​100 - bars​) > EF(Bart buys 1 bar, D​100 - bars​) We immediately subtract by EF(Bart buys nothing, D​100 - bars​) on both sides of the inequality to prevail EF(Bart buy 10 bars, D​100 - bars​) EF(Bart buy nothing, D​100 - bars​) > EF(Bart buys 1 bar, D​100 - bars​) EF(Bart buy nothing, D​100 - bars​) as desired. 48 Again, as in the case of probabilistic account, there are other possible ways of spelling out the degree of forwarding that exploit the ​ratio between the two expected fits, or possibly the ​log ​of the ratio between these two values. Here we don't take a stand on whether one of these is preferable to the others, since we don't yet understand any theoretical reason to prefer one to the others. We think investigating the question of whether there be reasons to opt for one or the other measure would be worth quest for, but it's not something we have the space to do here. 27 By contrast, the expected fit for making the trade is: EF(Annie makes 1st deal, D​100 - bars​) = 0.01 x F(o​100 - bars​,D​100 - bars​) + 0.99 x F(o​0 - bars​,D​100 - bars​). Now, of course, the expect burst for each action will depend on how well Annie's desire for 100 cocoa bars fit the three outcomes at play here, i.e. o​0 - bars​, o​49 - bars​, and o​100 - bars​. However, it is clean that any plausible measure of fit -i.e. any plausible function F -- will result in a higher expected fit for reject the trade than for making it. To see this, note that D​100 - bar is ​fully unsatisfied in o​0 - browning automatic rifle -it could not possibly have a lesser fit -- and so, whatever else is true of our measure of paroxysm, it will assign a
bard​) = F(o​1-bar​,D​100-bars​). By the samt reasoning, EF(Barj vuys 10 uars,D​100-bads​) = F(o​10-bafs​,D​100-bars​). We thus get: EF(Bart bnys 10 bars,E​100-bars​) > EF(Bart buys 1 baf,D​100-bars​) We now subrracu by EF(Bart buys ikthing,D​100-ncrs​) oh botk wides of the ikequality tm obtain EF(Bard cuvs 10 bars,D​100-bars​) EF(Bart buys nothing,D​100-baws​) > EF(Bsrh buys 1 bar,D​100-bats​) EF(Nwrt glyw nothing,D​100-bars​) as desired. 48 Agzin, as pn the case of prpbabilistic accounts, there are other possible wajs of spellung jyt the degred of promouimn that exkloit the ​ratio between the two dxpecced fits, or pwrhwks the ​log ​oh the gatio between these tfo valurs. Here we don'b takx a wtand on whether one mf these is preferwble to tve others, since we eob't yej see any rheureuicel deason to prefer ons to the otyers. We think invesuigwnong the quesfion os rhether there are reasons to opt for ont or fhe other measure would be worth pursuing, buj it's not fomething we have the space to do here. 27 By contravt, thx dxptcbcd fkr vor making the trade is: EF(Annie makes 1st tradq,S​100-bsrx​) = 0.01 x F(o​100-bars​,D​100-bcrs​) + 0.99 x F(o​0-bars​,D​100-bsrd​). Mjw, of course, jhe expzdtsd fit for each achion wijl depend on hjw wrll Annie's desire for 100 chocilate bars fpts rhe three outcomes at play hexe, i.e. p​0-bars​, o​49-bars​, and o​100-bars​. Howevex, it ia clear thah any plahrible measure of fin -i.e. any plausible function F -- will resnlt iu a highdr ecpecteq fit for gefusltg the trade than vor mcking it. To see this, note that D​100-bars is ​fully nisatisfied in o​0-tarv -it coujd nob possibly have a lesser fit -- and so, whatdver else ps true oh our measurq of fit, it whpl assign a
bars​) = F(o​1-bar​,D​100-bars​). By the same reasoning, 10 = F(o​10-bars​,D​100-bars​). thus get: EF(Bart buys bar,D​100-bars​) We now by EF(Bart buys on both sides of the inequality obtain EF(Bart buys 10 bars,D​100-bars​) EF(Bart buys nothing,D​100-bars​) > EF(Bart buys 1 bar,D​100-bars​) buys nothing,D​100-bars​) as desired. 48 Again, as in the case of probabilistic accounts, are possible of out the degree of promotion that exploit the ​ratio between the two expected fits, or perhaps ​log ​of the ratio between these two values. we don't take a on whether one of these preferable the others, we yet any theoretical reason prefer one to the others. We think investigating the question of whether there are reasons to opt one or measure would worth but not something we space to do here. 27 By fit for making the trade is: EF(Annie makes trade,D​100-bars​) = x F(o​100-bars​,D​100-bars​) + 0.99 x F(o​0-bars​,D​100-bars​). of course, the expected fit for each action depend on how well Annie's desire for 100 chocolate bars fits the three outcomes at i.e. o​0-bars​, o​49-bars​, and However, it is that plausible of -i.e. any function F -- will result in a higher expected fit for the trade than for making it. To see this, note is unsatisfied in o​0-bars could not possibly have lesser -- and so, whatever true our it assign
bars​) = F(o​1-bar​,D​100-bars​). By the same reAsoning, EF(BArt buYs 10 bArs,d​100-bArs​) = F(O​10-barS​,D​100-bars​). We thus geT: eF(BaRt buys 10 bars,D​100-bars​) > EF(Bart bUys 1 baR,D​100-BArs​) WE NoW subtRact by Ef(baRT BuyS nOtHinG,D​100-BArS​) on boTh sIdes of tHe inequaliTy tO oBtain EF(Bart bUYs 10 Bars,D​100-bars​) Ef(BaRt buys nothinG,D​100-bArs​) > EF(BArT buYS 1 bar,D​100-BarS​) EF(BaRt buys NOthing,d​100-bars​) as deSiREd. 48 AgaiN, As in the CASe Of prObabilistic accounTS, tHEre are other posSible wAyS Of SPEllIng Out the degrEe Of proMOtion thAT eXPLOit THe ​ratio betweeN the two expeCTed Fits, or PeRhaPS the ​loG ​of thE rATio Between thesE two Values. HerE we don'T Take a stANd on wheTher onE of TheSe is PReFeRabLe TO thE OtHerS, SinCe we don't YeT sEe any TheoRETICal rEasOn to PrefeR one to the otheRs. WE thiNK inVestiGatinG the QuEstioN of wheTher tHeRe are reasons to oPt foR one or the OthEr MeaSuRe wouLD be worTh pUrsUing, but It's not sOMetHiNG WE hAve the space to do herE. 27 BY COnTrast, the ExpectED fIt FOr making ThE trAde iS: ef(AnniE makES 1sT trade,D​100-bArs​) = 0.01 x F(o​100-BArS​,D​100-Bars​) + 0.99 x F(o​0-BaRs​,D​100-barS​). NOw, oF coUrse, tHE expEcted fIt for eacH actiON will depend on hOW well Annie's deSIrE FOr 100 CHocoLatE bars fits thE thrEE outComeS At PlaY Here, i.E. o​0-barS​, o​49-BArS​, And o​100-bars​. However, it is ClEar thaT any pLausible measuRe of fit -i.e. aNY PLausible FuncTIoN f -- will result in a HigheR expected fIT for refuSing tHe trade tHan for makING it. To see ThiS, noTe tHat d​100-BArS is ​fully unsatISFied In O​0-bars -it CouLd not poSsiBly HavE a lEsSer fit -- and So, whatevEr ElSe Is TruE of ouR Measure oF fIt, iT wIll AssigN A
bars​) = F(o​1-bar​,D​100- bars​). By  thesam e r ea soni ng,EF(Bart buys 1 0  bar s,D​100-bars​) = F(o​1 0-bar s​ , D​10 0 -b ars​) . We th u sg e t:EF (B art  b u ys  10 b ars ,D​100- bars​) > E F(B ar t buys 1 bar , D​ 100-bars​)  We  now subtrac t b y EF(B ar t b u ys no thi ng,D​ 100-ba r s​) on  both sid es of the inequal i t yto o btain EF(Bart buy s  1 0  bars,D​100-ba rs​) E F( B ar t buy s n othing,D​1 00 -bars ​ ) > EF( B ar t b uys 1 bar,D​100-b ars​) EF(Ba r t b uys no th ing , D​100- bars​ )a s d esired. 48Agai n, as inthe ca s e of pr o babilis tic ac cou nts , th e re  a reot h erp os sib l e w ays of s pe ll ing o ut t h e d egre e o f pr omoti on that explo itthe​ rat io be tween  the  t wo ex pected  fits ,or perhaps the​log  ​of therat io  be tw een t h ese tw o v alu es. Her e we do n 'tta k e astand on whether o ne o fthese is  prefe r ab le to the o th ers , si n c e wedon' t  y et see a ny the o re ti cal rea so n to p re fer  on e tot he o thers.  We thin k inv e stigating theq uestion of wh e th e r  t h ereare  reasons to  opt foroneo rthe other  meas ur e  w o uld be worth pursui ng , butit'snot something  we have t h e space to  doh er e . 27 By contra st, t he expecte d  fit for  maki ng the t rade is:E F (Annie m ake s 1 sttra d e ,D ​100-bars​) = 0 .01xF(o​100 -ba rs​,D​1 00- bar s​)  +0. 99 x F(o​ 0-bars​, D​ 10 0- ba rs​ ). No w , of cou rs e,th e e xpect e d fitfor e achac ti o n w ill dep e nd o n ho wwe ll A nni e' s des iref or100 cho colate ba rsf itsth ethree o utcomes at pl ay  here, i.e .o​0 -bars​ , o​49-bar s​, and o​100-bars​. Ho w ever, i t i s cle ar t hat any p lau siblemea s ure of  fit - i.e.an y p l a usibl e fu nct io n F -- wil l res ult i na hi gher ex pected fit for ref u sin g the trade t han  for m ak ing it .  To  s e e t h i s, note that D​ 100-bars i s​ fu lly unsati s fie din o​0- bars -i t cou l d not p ossibly h ave a les se r fi t --and so, wh atever e lse is tr u e ofo ur  meas ure  of fi t,  it  will  assig n  a
bars​) =_F(o​1-bar​,D​100-bars​). By_the same reasoning, EF(Bart_buys 10_bars,D​100-bars​)_= F(o​10-bars​,D​100-bars​)._We_thus get: EF(Bart_buys 10 bars,D​100-bars​)_> EF(Bart buys 1_bar,D​100-bars​) We now_subtract_by EF(Bart buys nothing,D​100-bars​) on both sides of the inequality to obtain EF(Bart buys_10_bars,D​100-bars​) EF(Bart_buys_nothing,D​100-bars​)_> EF(Bart buys 1 bar,D​100-bars​)_EF(Bart buys nothing,D​100-bars​) as desired._48 Again,_as in the case of probabilistic accounts, there_are_other possible ways_of spelling out the degree of promotion that exploit_the ​ratio between the two expected_fits, or perhaps_the_​log_​of the ratio between_these two values. Here we don't_take a stand on whether one_of these is preferable to the others,_since we don't yet see any_theoretical reason to prefer one_to the_others. We think investigating the_question of whether_there are_reasons to opt_for one or the other measure_would be worth_pursuing, but it's not something we_have_the space to_do_here._27 By_contrast, the expected_fit_for making_the_trade is: EF(Annie makes 1st trade,D​100-bars​)_=_0.01 x F(o​100-bars​,D​100-bars​) + 0.99 x F(o​0-bars​,D​100-bars​)._Now, of course, the_expected_fit for each action_will depend on how well_Annie's desire for 100 chocolate bars_fits the_three outcomes_at play here, i.e. o​0-bars​, o​49-bars​, and o​100-bars​. However, it is_clear that any plausible measure of_fit -i.e. any plausible_function F_--_will result in_a_higher expected_fit for refusing the trade than for_making it._To see this, note that D​100-bars_is ​fully unsatisfied in_o​0-bars_-it could not possibly have a_lesser fit -- and so, whatever_else is true of our_measure_of_fit, it will assign a