Guess Again

In Bead Jar Guesses, I made a slightly clumsy at­tempt at carv­ing out a kind of guess based on so lit­tle in­for­ma­tion that even a ra­tio­nally-sup­posed, very small prob­a­bil­ity of some out­come doesn’t con­fer a com­men­su­rate level of sur­prise when that out­come oc­curs. Here are sev­eral cat­e­gories of prob­a­bil­ity as­sign­ment (in­clud­ing a re-state­ment of the bead jar thing) that I think might be worth con­sid­er­ing sep­a­rately. (I’m open to chang­ing their names if other peo­ple have bet­ter ideas.)

Bewil­der­ment: You don’t even have enough in­for­ma­tion to un­der­stand the ques­tion. What is your prob­a­bil­ity that any given shren is a dark­ling? What is your prob­a­bil­ity that Sa­faitic is some­times recorded in bous­tro­phe­don? What is your prob­a­bil­ity that 你有鼻子? (Ig­nore ques­tion 1 if you have read Elce­nia, es­pe­cially if you’ve seen more than is cur­rently pub­lished; ig­nore ques­tion 2 if you know what ei­ther of those funny words mean; ig­nore ques­tion 3 if you can read Chi­nese.) In this case, you might find your­self in a situ­a­tion where you have to make a guess, but even if you were then told the an­swer it wouldn’t tell you much in the ab­sence of fur­ther con­text.1 You would have no rea­son to be sur­prised by such an an­swer, no mat­ter what prob­a­bil­ity you’d as­signed.

Bead Jar: You un­der­stand the ques­tion, but have no in­for­ma­tion about any­thing that causally in­ter­acts with the an­swer. To guess, you have to grasp at the flim­siest of straws in the word­ing of the ques­tion and the mo­ti­va­tions of the asker, or much broader be­liefs about the gen­eral kind of ques­tion. What is your prob­a­bil­ity that Omega will pull out a red bead? What’s your prob­a­bil­ity that I’m mak­ing the peace sign as I type this ques­tion with the other hand? What’s your prob­a­bil­ity that the fruit on the tree in my best friend’s back­yard is deli­cious? Like Bewil­der­ment ques­tions, Bead Jar guesses come with no sig­nifi­cant chance of sur­prise. Even if you have a tiny prob­a­bil­ity that the bead is lilac, it should not sur­prise you.

Bingo: You un­der­stand the ques­tion and you know some­thing about what causes the an­swer, but the mechanism by which those con­di­tions come about is known to be ran­dom (in a prac­ti­cal epistemic sense, not nec­es­sar­ily in the sense of be­ing phys­i­cally un­de­ter­mined). You can have an ex­cel­lent, well-cal­ibrated prob­a­bil­ity. Here, there are two var­i­ants: one where the out­comes have mostly com­men­su­rate like­li­hood (the prob­a­bil­ity that you’ll draw any given card from a deck) or one where the out­comes have a va­ri­ety of prob­a­bil­ities (like the prob­a­bil­ity that you draw a card with a skull, or one with a star). You shouldn’t be sur­prised no mat­ter what hap­pens in the first case (un­less the out­come is some­how spe­cial to you—be sur­prised if a per­sonal friend of yours wins the lot­tery!), but in the sec­ond case, sur­prise might be war­ranted if some­thing es­pe­cially un­likely hap­pens.

1About 56 of shrens are dark­lings, de­pend­ing on pop­u­la­tion fluc­tu­a­tions; Sa­faitic is in­deed some­times recorded in bous­tro­phe­don; and 有 (I hope).