In the situation known as the “cable guy paradox” the expected utility principle and the “avoid certain frustration” principle (ACF) seem to give contradictory advice about what one should do. This article tries to resolve the paradox by presenting an example that weakens the grip of ACF: a modified version of the cable guy problem is introduced in which the choice dictated by ACF loses much of its intuitive appeal

Sesardić, Neven

English

PhilPapers

Thought ISSN 2161-2234OR IG INAL ART ICLEAvoid Certain Frustration—Or Maybe Not?Neven Sesardic´In the situation known as the cable guy paradox, the expected utility principle and the avoid certainfrustration (ACF) principle seem to give contradictory advice aboutwhat one should do.This articletries to resolve the paradox by presenting an example that weakens the grip of ACF: a modifiedversion of the cable guy problem is introduced in which the choice dictated by ACF loses much ofits intuitive appeal.Keywords cable guy paradox; decision theory; expected utility; certain frustration; Alan HájekDOI:10.1002/tht3.390In the situation known as the cable guy paradox (Hájek 2005), the expected utilityprinciple and the avoid certain frustration (ACF) principle seem to give contradictoryadvice about what one should do. Although Alan Hájek, the father of the cable guyparadox, ultimately rejects the advice derived from ACF, he concedes that something ofa paradox still remains.This article tries to remove the lingering appearance of a paradox by presenting anexample that weakens the grip of ACF: a modified version of the cable guy problem willbe introduced in which the choice dictated by ACF loses much of its intuitive appeal.Let us first recall the original paradox.The cable guywill come to your home tomorrowsometime after 8 a.m. and before 4 p.m. Your friend proposes a bet, on even money, onwhether the cable guy will come in the morning (between 8 and 12) or in the afternoon(between 12 and 4). You can choosewhich option youwant to bet on. Since the probabilityof MORNING or AFTERNOON is the same (one half) and since your potential gain andloss are also the same (the assumption is that nothing else matters but money), it seemsyou should be indifferent between the two options. This answer is based on the expectedutility principle.Then Hájek introduces an alternative argument (which he in the end rejects) in favorof AFTERNOON. If you bet onMORNING, there will inevitably be somemoment in themorning (before the cable guy arrives) when you will be aware that some of “your” timehas elapsed, and consequently the probability of AFTERNOON will at that moment behigher than the probability of MORNING. Since it is certain that at some point you willbe frustrated with your choice if you chooseMORNING, but it is not certain that you willbe frustrated with your choice if you choose AFTERNOON, there is a suggestion that youCorrespondence to: E-mail: sesardic@gmail.comThought (2018) © 2018 The Thought Trust and Wiley Periodicals, Inc. 1Neven Sesardic´ Avoid Certain Frustrationε1 MORNING  –  ε1 ε2 AFTERNOON  –  ε2 Figure 1: The cable guy problemmodified.should bet on AFTERNOON. This suggestion is based on ACF, which Hájek formulatesin the following way:Avoid Certain Frustration (ACF) Principle: Suppose you now have a choice betweentwo options. You should not choose one of these options if you are certain that arational future self of yours will prefer that you had chosen the other one – unlessboth your options have this property. (Hájek 2005, p. 114)Hájek notes that the choice to bet on MORNING “falls squarely under the purview”of ACF, which conflicts with what is recommended by the principle of expected utility(namely, that one should be indifferent between the two choices). One way to solvethe paradox would be to put ACF itself in question by constructing a counterexamplein which all of Hájek’s conditions for applying ACF are satisfied but where there is noimperative to ACF. This is what I will attempt to do.Let us first change the conditions of the bet. Let us divide the entire period between8 a.m. and 4 p.m. into the following four temporally consecutive subintervals: ε1 (thetrillionth-of-a-second interval after 8 a.m.), MORNING − ε1 (the rest of the morning),ε2 (the trillionth-of-a-second interval after 12 noon), and AFTERNOON − ε2 (the restof the afternoon).Or, to put it in more exact terms:ε1 = (8, 8+ε]MORNING − ε1 = (8+ε, 12]ε2 = (12, 12+ε]AFTERNOON – ε2 = (12+ε, 4)The division is shown in Figure 1 (not drawn to scale), which represents the wholeperiod between 8 a.m. and 4 p.m.Now in the new version of the cable guy problem, the choice is between betting on oneof the two time periods in the figure that are represented by white and gray, respectively.Your options now are betting either onW (thewhite segment) or onG (the gray segment):Betting on W means you win if the cable guy arrives during ε1 or during (AFTER-NOON – ε2), and you lose otherwise.Betting on G means you win if the cable guy arrives during (MORNING – ε1) orduring ε2, and you lose otherwise.The difference between this and the original cable guy scenario is that now your firstoption includes betting on a time that consists of two noncontiguous intervals: ε1 and(AFTERNOON – ε2). However, the intervals W and G are still of the same duration2 Thought (2018) © 2018 The Thought Trust and Wiley Periodicals, Inc.Neven Sesardic´ Avoid Certain Frustration(exactly 4 hours each), so according to the expected utility principle you should againbe indifferent between the two choices.ACF, however, clearly favors G, because choosingW would lead to certain frustrationof your future rational self (during the initial interval ε1). For, whether the cable guyarrives during ε1 or not, there will certainly be an interval, during ε1, when you will regretchoosingW, since you will realize that some of “your” time has elapsed without the cableguy coming and that consequently your chance of winning just became (be it even veryslightly) lower than .5.Although it is indeed certain that a rational future self of yours will regret the choiceofW, let us look at how another rational future self of yours would feel at a still later time.If you choose G, what is the probability that a later self of yours will at some future timeregret that choice? Obviously, this probability is equal to the probability that the cableguy does not arrive during the interval (8, 8+ 2ε]. Explanation: a future self will regretchoosing G just as long as the cable guy has not yet arrived and the remaining portion ofG time ahead is shorter than the remaining portion ofW time. If after 8 o’clock the shortperiod of the duration 2ε expires without the cable guy arriving, then a future self wouldregret choosing G.Since 2ε is an extremely small part of the whole time periodwithinwhich the cable guycan arrive, the probability that the guy will not come during that period is very high. Sothe probability that a “post-2ε” rational future self of yours will be frustrated if you chooseG is very, very high (although lower than unity). And the probability that a rational laterself of yours will regret making choice G in this kind of scenario can be made as close tounity as we like—by making the interval 2ε smaller and smaller.Now back to ACF. ACF is based on the idea that, other things being equal, a judgmentof one’s later rational self (during ε1) should carry more weight (because it is based onmore comprehensive evidence) than the judgment of one’s earlier rational self (before8 a.m.). But why shouldn’t we then extend this reasoning and also take into account ajudgment of an even later rational self (after ε1), especially since this self is also expectedto be frustrated with a very high probability? Admittedly, choosing W entails that one’searly future rational self—during ε1—will certainly regret one’s decision. Choosing G,however, entails that one’s later future rational self will regret one’s decision with theprobability that can bemade as close to unity as desired (bymaking ε smaller and smaller).The probabilities of frustration in the cases of the two decisions can be made as close toone another as you like.But then it is unclear why one should followACF.There is nothing obviously irrationalabout going against ACF and betting on W, with its certain frustration of one’s earlierfuture self, rather than betting on G, with its frustration of one’s later future self with aprobability that can be made as close to certainty as we please.Hájek was not convinced by my argument, though. This is his response (personalcommunication):But in a way [your example] only strengthens my paradoxical reasoning. Supposeyou bet on G. You will certainly be glad for a little while, during period ε1. You willThought (2018) © 2018 The Thought Trust and Wiley Periodicals, Inc. 3Neven Sesardic´ Avoid Certain Frustrationenjoy watchingW dwindle, for a short time. Then yes, very probably you will begin aperiod of frustration as we enter the gray region, and G begins to dwindle. So youwill experience:(i) gladness certainly, and(ii) frustration (only) very probably.On the other hand, if you bet on W, you will experience:(i) frustration certainly, and(ii) gladness (only) very probably.So there are now two reasons to prefer G toW!1. CERTAIN gladness is better than PROBABLE gladness.2. PROBABLE frustration is better than CERTAIN frustration.My argument based on ACF only gave you one reason to do so!Note that Hájek stresses that he does not ultimately advocate ACF—indeed theconclusion of his paperwas to reject it—nor the reasoning in the above passage.However,he offers both as prima facie plausible, and finds it surprising that they must be rejected.I disagree with Hájek’s response, but I think it is very useful because it helps us probedeeper into the core of the cable guy paradox.His two reasons for preferring G overW are: on one hand, certain gladness (the resultof choosing G) is better than merely probable gladness (the result of choosing W), andon the other hand, merely probable frustration (the result of choosing G) is better thancertain frustration (the result of choosingW).The reasoning would be convincing if certain and probable frustration—or certainand probable gladness—associated with the two respective decisions were quantitativelythe same. But they are not.Take frustration first. Recall that here we are talking about the frustration of one’sfuture self if a part of one’s time elapses without the cable guy arriving, which proportion-ately decreases one’s chances of winning the bet. Now it is obvious that the (certain) frus-tration resulting from choosing W will be very small. The worst case scenario would bethat your future self would realize toward the end of theminuscule interval ε1 that almostone trillionth of a second of “your” time has elapsed, and that consequently your chancesof winning the bet would have diminished only by a practically negligible amount.If you choose G, though, your future frustration will indeed not be certain but it willbe practically indistinguishable from certainty. In addition, this frustration will not becontainedwithin the very narrow range ε, as in the choice ofW. On the contrary, choosingG you will risk a much larger frustration, that is, realizing with regret that a much higherproportion of your time than ε has elapsed without the cable guy coming. (At the limitthere is a probability of around 1/2 that you will go through successive and ever largerlevels of frustration until almost your entire time expires without the cable guy arriving.)4 Thought (2018) © 2018 The Thought Trust and Wiley Periodicals, Inc.Neven Sesardic´ Avoid Certain FrustrationBriefly, if choosing betweenW and G comes down to choosing between the certaintyof a virtually zero frustration and the high probability (very closely approaching certainty)of amuch larger frustration, it is far from clear that choosing G is preferable.Ditto for gladness. Is Hájek right that certain gladness is better than merely probablegladness? Again, no. When a certain but tiny gladness is pitted against a much largergladness that is virtually (though not actually) certain, an argument could be made forchoosing the latter. Let me stress I do not want to defend that other argument. I merelyuse it to show that the reasoning in favor of ACF that Hájek finds prima facie plausibleloses its force on closer inspection.Contra Hájek, two out of three possible reasons favor choosing interval W overinterval G. First, in the case of choosing W potential frustration would be smaller andpotential gladness greater (than if one chose G). Second, deferring to the judgment ofone’s later rational self (in the spirit of Van Fraassen’s reflection principle) also supportschoosingW, because an almost certain frustration expected by one who chose G wouldhappen after a certain frustration expected by one who choseW. (Andmutatis mutandisfor gladness). Third, the only reason apparently favoring interval G is that the futurefrustration is certain for one who chooses W, though not for one who chooses G. But,to repeat, the difference between certainty and a probability that we can make as close tocertainty as we like should not carry much weight.So should one always follow ACF? Perhaps not.AcknowledgmentsI would like to thank Nathan Cofnas, Rafael De Clercq, Alan Hájek, andMatej Sušnik foruseful comments on earlier drafts of this paper.ReferenceHájek, A. “The Cable Guy Paradox.” Analysis 65 (2005): 112–119.Thought (2018) © 2018 The Thought Trust and Wiley Periodicals, Inc. 5

Avoid Certain Frustration—Or Maybe Not?

https://philpapers.org/archive/SESACF.pdf

Avoid Certain Frustration—Or Maybe Not?

Abstract

Similar works

Full text

Available Versions

PhilPapers