Focus Your Uncertainty

Will bond yields go up, or down, or re­main the same? If you’re a TV pun­dit and your job is to ex­plain the out­come af­ter the fact, then there’s no rea­son to worry. No mat­ter which of the three pos­si­bil­ities comes true, you’ll be able to ex­plain why the out­come perfectly fits your pet mar­ket the­ory. There’s no rea­son to think of these three pos­si­bil­ities as some­how op­posed to one an­other, as ex­clu­sive, be­cause you’ll get full marks for pun­ditry no mat­ter which out­come oc­curs.

But wait! Sup­pose you’re a novice TV pun­dit, and you aren’t ex­pe­rienced enough to make up plau­si­ble ex­pla­na­tions on the spot. You need to pre­pare re­marks in ad­vance for to­mor­row’s broad­cast, and you have limited time to pre­pare. In this case, it would be helpful to know which out­come will ac­tu­ally oc­cur—whether bond yields will go up, down, or re­main the same—be­cause then you would only need to pre­pare one set of ex­cuses.

Alas, no one can pos­si­bly fore­see the fu­ture. What are you to do? You cer­tainly can’t use “prob­a­bil­ities.” We all know from school that “prob­a­bil­ities” are lit­tle num­bers that ap­pear next to a word prob­lem, and there aren’t any lit­tle num­bers here. Worse, you feel un­cer­tain. You don’t re­mem­ber feel­ing un­cer­tain while you were ma­nipu­lat­ing the lit­tle num­bers in word prob­lems. Col­lege classes teach­ing math are nice clean places, so math can’t ap­ply to life situ­a­tions that aren’t nice and clean. You wouldn’t want to in­ap­pro­pri­ately trans­fer think­ing skills from one con­text to an­other. Clearly, this is not a mat­ter for “prob­a­bil­ities.”

Nonethe­less, you only have 100 min­utes to pre­pare your ex­cuses. You can’t spend the en­tire 100 min­utes on “up,” and also spend all 100 min­utes on “down,” and also spend all 100 min­utes on “same.” You’ve got to pri­ori­tize some­how.

If you needed to jus­tify your time ex­pen­di­ture to a re­view com­mit­tee, you would have to spend equal time on each pos­si­bil­ity. Since there are no lit­tle num­bers writ­ten down, you’d have no doc­u­men­ta­tion to jus­tify spend­ing differ­ent amounts of time. You can hear the re­view­ers now: And why, Mr. Fin­kled­inger, did you spend ex­actly 42 min­utes on ex­cuse #3? Why not 41 min­utes, or 43? Ad­mit it—you’re not be­ing ob­jec­tive! You’re play­ing sub­jec­tive fa­vorites!

But, you re­al­ize with a small flash of re­lief, there’s no re­view com­mit­tee to scold you. This is good, be­cause there’s a ma­jor Fed­eral Re­serve an­nounce­ment to­mor­row, and it seems un­likely that bond prices will re­main the same. You don’t want to spend 33 pre­cious min­utes on an ex­cuse you don’t an­ti­ci­pate need­ing.

Your mind keeps drift­ing to the ex­pla­na­tions you use on tele­vi­sion, of why each event plau­si­bly fits your mar­ket the­ory. But it rapidly be­comes clear that plau­si­bil­ity can’t help you here—all three events are plau­si­ble. Fit­ta­bil­ity to your pet mar­ket the­ory doesn’t tell you how to di­vide your time. There’s an un­cross­able gap be­tween your 100 min­utes of time, which are con­served; ver­sus your abil­ity to ex­plain how an out­come fits your the­ory, which is un­limited.

And yet . . . even in your un­cer­tain state of mind, it seems that you an­ti­ci­pate the three events differ­ently; that you ex­pect to need some ex­cuses more than oth­ers. And—this is the fas­ci­nat­ing part—when you think of some­thing that makes it seem more likely that bond prices will go up, then you feel less likely to need an ex­cuse for bond prices go­ing down or re­main­ing the same.

It even seems like there’s a re­la­tion be­tween how much you an­ti­ci­pate each of the three out­comes, and how much time you want to spend prepar­ing each ex­cuse. Of course the re­la­tion can’t ac­tu­ally be quan­tified. You have 100 min­utes to pre­pare your speech, but there isn’t 100 of any­thing to di­vide up in this an­ti­ci­pa­tion busi­ness. (Although you do work out that, if some par­tic­u­lar out­come oc­curs, then your util­ity func­tion is log­a­r­ith­mic in time spent prepar­ing the ex­cuse.)

Still . . . your mind keeps com­ing back to the idea that an­ti­ci­pa­tion is limited, un­like ex­cus­abil­ity, but like time to pre­pare ex­cuses. Maybe an­ti­ci­pa­tion should be treated as a con­served re­source, like money. Your first im­pulse is to try to get more an­ti­ci­pa­tion, but you soon re­al­ize that, even if you get more an­ti­ci­pa­tion, you won’t have any more time to pre­pare your ex­cuses. No, your only course is to al­lo­cate your limited sup­ply of an­ti­ci­pa­tion as best you can.

You’re pretty sure you weren’t taught any­thing like that in your statis­tics courses. They didn’t tell you what to do when you felt so ter­ribly un­cer­tain. They didn’t tell you what to do when there were no lit­tle num­bers handed to you. Why, even if you tried to use num­bers, you might end up us­ing any sort of num­bers at all—there’s no hint what kind of math to use, if you should be us­ing math! Maybe you’d end up us­ing pairs of num­bers, right and left num­bers, which you’d call DS for Dex­ter-Sinister . . . or who knows what else? (Though you do have only 100 min­utes to spend prepar­ing ex­cuses.)

If only there were an art of fo­cus­ing your un­cer­tainty—of squeez­ing as much an­ti­ci­pa­tion as pos­si­ble into whichever out­come will ac­tu­ally hap­pen!

But what could we call an art like that? And what would the rules be like?