Explicit Bayes as a counter for 'worrying'

One of the pos­si­ble hu­man uses of ex­plicit Bayesian rea­son­ing is that mak­ing up ex­plicit prob­a­bil­ities and do­ing the Bayesian calcu­la­tion lets us sum­ma­rize the rele­vant con­sid­er­a­tions in one place. This can counter a men­tal loop of ‘wor­ry­ing’ by bounc­ing back and forth be­tween fo­cus­ing on in­di­vi­d­ual con­sid­er­a­tions.

One ex­am­ple comes from a woman who was a test sub­ject for an early ver­sion of the Bayes in­tro at the same time she was dat­ing on OKCupid, and a 96% OKCupid match can­celed their first date for coffee with­out ex­pla­na­tion. After bounc­ing back and forth men­tally be­tween ‘maybe there was a good rea­son he can­celed’ ver­sus ‘that doesn’t seem like a good sign’, she de­cided to try Bayes. She es­ti­mated that a man like this one had prior odds of 2 : 5 for de­sir­a­bil­ity vs. un­de­sir­a­bil­ity, based on his OKCupid pro­file and her past ex­pe­rience with 96% matches. She then es­ti­mated a 1 : 3 like­li­hood ra­tio for de­sir­able vs. un­de­sir­able men flak­ing on the first date. This worked out to 2 : 15 pos­te­rior odds for the man be­ing un­de­sir­able, which she de­cided was un­fa­vor­able enough to not pur­sue him fur­ther.

The point of this men­tal ex­er­cise wasn’t that the num­bers she made up were ex­act. Rather, by lay­ing out all the key fac­tors in one place, she stopped her mind from bounc­ing back and forth be­tween

knows-req­ui­site(Con­di­tional prob­a­bil­ity): vi­su­al­iz­ing \(\mathbb P(\text{cancel}|\text{desirable})\) and vi­su­al­iz­ing \(\mathbb P(\text{cancel}|\text{undesirable})\), which were pul­ling her back and forth as ar­gu­ments point­ing in differ­ent di­rec­tions.
!knows-req­ui­site(Con­di­tional prob­a­bil­ity): switch­ing be­tween imag­in­ing rea­sons why a good prospect might’ve can­celed, ver­sus imag­in­ing rea­sons why a bad prospect might’ve can­celed.
By com­bin­ing both ideas into a like­li­hood ra­tio, and mov­ing on to pos­te­rior odds, she sum­ma­rized the con­sid­er­a­tions and was able to stop un­pro­duc­tively ‘wor­ry­ing’.

Wor­ry­ing isn’t always un­pro­duc­tive. Pay­ing more at­ten­tion to an in­di­vi­d­ual con­sid­er­a­tion like “Maybe there were rea­sons a good dat­ing prospect might’ve can­celed any­way?” might cause you to ad­just your es­ti­mate of this con­sid­er­a­tion, thereby chang­ing your pos­te­rior odds. But you can get the illu­sion of progress by switch­ing your at­ten­tion from one already-known con­sid­er­a­tion to an­other, since it feels like these con­sid­er­a­tions are pul­ling on your pos­te­rior in­tu­ition each time you fo­cus on them. It feels like your be­liefs are chang­ing and cog­ni­tive work is be­ing performed, but ac­tu­ally you’re just go­ing in cir­cles. This is the ‘un­pro­duc­tive wor­ry­ing’ pro­cess that you can in­ter­rupt by do­ing an ex­plic­itly Bayesian calcu­la­tion that sum­ma­rizes what you already know into a sin­gle an­swer.

(She did send him a re­jec­tion no­tice spel­ling out her nu­mer­i­cal rea­son­ing; since, if he wrote back in a way in­di­cat­ing that he ac­tu­ally un­der­stood that, he might’ve been worth a sec­ond chance.)

(He didn’t.)

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