The Amanda Knox Test: How an Hour on the Internet Beats a Year in the Courtroom

Note: The quan­ti­ta­tive el­e­ments of this post have now been re­vised sig­nifi­cantly.

Fol­lowup to: You Be the Jury: Sur­vey on a Cur­rent Event

All three of them clearly kil­led her. The jury clearly be­lieved so as well which strength­ens my ar­gu­ment. They spent months ex­am­in­ing the case, so the idea that a few min­utes of in­ter­net re­search makes [other com­menters] cer­tain they’re wrong seems laughable

- lord­weiner27, com­ment­ing on my pre­vi­ous post

The short an­swer: it’s very much like how a few min­utes of philo­soph­i­cal re­flec­tion trump a few mil­len­nia of hu­man cul­tural tra­di­tion.

Wield­ing the Sword of Bayes—or for that mat­ter the Ra­zor of Oc­cam—re­quires courage and a cer­tain kind of ruth­less­ness. You have to be will­ing to cut your way through vast quan­tities of noise and fo­cus in like a laser on the sig­nal.

But the tools of ra­tio­nal­ity are ex­tremely pow­er­ful if you know how to use them.

Ra­tion­al­ity is not easy for hu­mans. Our brains were op­ti­mized to ar­rive at cor­rect con­clu­sions about the world only in­so­far as that was a nec­es­sary byproduct of be­ing op­ti­mized to pass the ge­netic ma­te­rial that made them on to the next gen­er­a­tion. If you’ve been read­ing Less Wrong for any sig­nifi­cant length of time, you prob­a­bly know this by now. In fact, around here this is al­most a ba­nal­ity—a cached thought. “We get it,” you may be tempted to say. “So stop sig­nal­ing your tribal alle­giance to this web­site and move on to some new, non­triv­ial meta-in­sight.”

But this is one of those things that truly do bear re­peat­ing, over and over again, al­most at ev­ery op­por­tu­nity. You re­ally can’t hear it enough. It has con­se­quences, you see. The most im­por­tant of which is: if you only do what feels epistem­i­cally “nat­u­ral” all the time, you’re go­ing to be, well, wrong. And prob­a­bly not just “sooner or later”, ei­ther. Chances are, you’re go­ing to be wrong quite a lot.

To bor­row a Yud­kowskian turn of phrase: if you don’t ever—or in­deed of­ten—find your­self need­ing to zig when, not only other peo­ple, but all kinds of in­ter­nal “voices” in your mind are loudly shout­ing for you to zag, then you’re ei­ther a na­tive ra­tio­nal­ist—a born Bayesian, who should per­haps be de­duc­ing gen­eral rel­a­tivity from the fall of an ap­ple any minute now—or else you’re sim­ply not try­ing hard enough.

Oh, and an­other one of those con­se­quences of hu­mans’ not be­ing in­stinc­tively ra­tio­nal?

Two in­tel­li­gent young peo­ple with pre­vi­ously bright fu­tures, named Amanda and Raf­faele, are now seven days into spend­ing the next quar­ter-cen­tury of their lives be­hind bars for a crime they al­most cer­tainly did not com­mit.

“Al­most cer­tainly” re­ally doesn’t quite cap­ture it. In my pre­vi­ous post I asked read­ers to as­sign prob­a­bil­ities to the fol­low­ing propo­si­tions:

1. Amanda Knox is guilty (of kil­ling Mered­ith Kercher)
2. Raf­faele Sol­lecito is guilty (of kil­ling Mered­ith Kercher)
3. Rudy Guédé is guilty (of kil­ling Mered­ith Kercher)

I also asked them to guess at how closely they thought their es­ti­mates would match mine.

Well, for com­par­i­son, here are mine (re­vised):

1. Neg­ligible. Small. Hardly differ­ent from the prior, which is dom­i­nated by the prob­a­bil­ity that some­one in what­ever refer­ence class you would have put Amanda into on Jan­uary 1, 2007 would com­mit mur­der within twelve months. Some­thing on the or­der of 0.001 0.01 or 0.1 at most.
2. Ditto.
3. About as high as the other two num­bers are low. 0.999 0.99 as a (prob­a­bly weak) lower bound.

Yes, you read that cor­rectly. In my opinion, there is for all in­tents and pur­poses zero Bayesian ev­i­dence that Amanda and Raf­faele are guilty. Need­less to say, this differs markedly from the con­sen­sus of the jury in Peru­gia, Italy.

How could this be?

Am I re­ally sug­gest­ing that the es­ti­mates of eight ju­rors—among whom two pro­fes­sional judges—who heard the case for a year, along with some­thing like 60% of the Ital­ian pub­lic and prob­a­bly half the In­ter­net (and a sig­nifi­cantly larger frac­tion of the non-Amer­i­can In­ter­net), could be off by a min­i­mum of three or­ders of mag­ni­tude (prob­a­bly sig­nifi­cantly more) such a large amount? That most other peo­ple (in­clud­ing most com­menters on my last post) are off by no fewer than two?

Well, dear reader, be­fore get­ting too in­cre­d­u­lous, con­sider this. How about av­er­ag­ing the prob­a­bil­ities all those folks would as­sign to the propo­si­tion that Je­sus of Nazareth rose from the dead, and call­ing that num­ber x. Mean­while, let y be the cor­rect ra­tio­nal prob­a­bil­ity that Je­sus rose from the dead, given the in­for­ma­tion available to us.

How big do you sup­pose the ra­tio x/​y is?

Any­one want to take a stab at guess­ing the log­a­r­ithm of that num­ber?

Com­pared to the prob­a­bil­ity that Je­sus rose from the dead, my es­ti­mate of Amanda Knox’s cul­pa­bil­ity makes it look like I think she’s as guilty as sin it­self.

And that, of course, is just the cen­tral one of many sub-claims of the hugely com­plex yet widely be­lieved propo­si­tion that Chris­ti­an­ity is true. There are any num­ber of other equally un­likely as­ser­tions that Amanda would have heard at mass on the day af­ter be­ing found guilty of kil­ling her new friend Mered­ith (source in Ital­ian) -- as­ser­tions that are as­signed non-neg­ligible prob­a­bil­ity by no fewer than a cou­ple billion of the Earth’s hu­man in­hab­itants.

I say this by way of pream­ble: be very wary of trust­ing in the ra­tio­nal­ity of your fel­low hu­mans, when you have se­ri­ous rea­sons to doubt their con­clu­sions.

The Lawful­ness of Mur­der: In­fer­ence Pro­ceeds Back­ward, from Crime to Suspect

We live in a lawful uni­verse. Every event that hap­pens in this world—in­clud­ing hu­man ac­tions and thoughts—is ul­ti­mately gov­erned by the laws of physics, which are ex­cep­tion­less.

Mur­der may be highly ille­gal, but from the stand­point of physics, it’s as lawful as ev­ery­thing else. Every phys­i­cal in­ter­ac­tion, in­clud­ing a homi­cide, leaves traces—changes in the en­vi­ron­ment that con­sti­tute in­for­ma­tion about what took place.

Such in­for­ma­tion, how­ever, is—cru­cially—lo­cal. The fur­ther away in space and time you move from the event, the less en­tan­gle­ment there is be­tween your en­vi­ron­ment and that of the event, and thus the more difficult it is to make le­gi­t­i­mate in­fer­ences about the event. The sig­nal-to-noise ra­tio de­creases dra­mat­i­cally as you move away in causal dis­tance from the event. After all, the hy­poth­e­sis space of pos­si­ble causal chains of length n lead­ing to the event in­creases ex­po­nen­tially in n.

By far the most im­por­tant ev­i­dence in a mur­der in­ves­ti­ga­tion will there­fore be the ev­i­dence that is the clos­est to the crime it­self—ev­i­dence on and around the vic­tim, as well as de­tails stored in the brains of peo­ple who were pre­sent dur­ing the act. Less im­por­tant will be ev­i­dence ob­tained from per­sons and ob­jects a short dis­tance away from the crime scene; and the im­por­tance de­cays rapidly from there as you move fur­ther out.

It fol­lows that you can­not pos­si­bly ex­pect to re­li­ably ar­rive at the cor­rect an­swer by start­ing a few steps re­moved in the causal chain, say with a per­son you find “sus­pi­cious” for some rea­son, and work­ing for­ward to come up with a plau­si­ble sce­nario for how the crime was com­mit­ted. That would be priv­ileg­ing the hy­poth­e­sis. In­stead, you have to start from the ac­tual crime scene, or as close to it as you can get, and work back­ward, let­ting your­self be blown by the winds of ev­i­dence to­ward one or more pos­si­ble sus­pects.

In the Mered­ith Kercher case, the winds of ev­i­dence blow with some­thing like hur­ri­cane force in the di­rec­tion of Rudy Guédé. After the mur­der, Kercher’s bed­room was filled with ev­i­dence of Guédé′s pres­ence; his DNA was found not only on top of but ac­tu­ally in­side her body. That’s about as close to the crime as it gets. At the same time, no re­motely similarly in­crim­i­nat­ing ge­netic ma­te­rial was found from any­one else—in par­tic­u­lar, there were no traces of the pres­ence of ei­ther Amanda Knox or Raf­faele Sol­lecito in the room (and no, the sup­posed Sol­lecito DNA on Mered­ith’s bra clasp just plain does not count—nor, while we’re at it, do the 100 picograms [about one hu­man cell’s worth] of DNA from Mered­ith allegedly on the tip of a knife han­dled by Knox, found at Sol­lecito’s apart­ment af­ter the two were already sus­pects; these two things con­sti­tut­ing pretty much the en­tirety of the phys­i­cal “ev­i­dence” against the cou­ple).

If, up to this point, the po­lice had rea­sons to be sus­pi­cious of Knox, Sol­lecito, and Guédé, they should have cleared Knox and Sol­lecito at once upon the dis­cov­ery that Guédé -- who, by the way, was the only one to have fled the coun­try af­ter the crime—was the one whom the DNA matched. Un­less, that is, Knox and Sol­lecito were speci­fi­cally im­pli­cated by Guédé; af­ter all, maybe Knox and Sol­lecito didn’t ac­tu­ally kill the vic­tim, but in­stead maybe they paid Guédé to do so, or were oth­er­wise in­volved in a con­spir­acy with him. But the prior prob­a­bil­ities of such sce­nar­ios are low, even in gen­eral—to say noth­ing of the case of Knox and Sol­lecito speci­fi­cally, who, tabloid press to the con­trary, are known to have had ut­terly be­nign dis­po­si­tions prior to these events, and no rea­son to want Mered­ith Kercher dead.

If Amanda Knox and Raf­faele Sol­lecito were to be in in­ves­ti­ga­tors’ thoughts at all, they had to get there via Guédé -- be­cause oth­er­wise the hy­poth­e­sis (a pri­ori un­likely) of their hav­ing had homi­ci­dal in­tent to­ward Kercher would be en­tirely su­perflu­ous in ex­plain­ing the chain of events that led to her death. The trail of ev­i­dence had led to Guédé, and there­fore nec­es­sar­ily had to pro­ceed from him; to fol­low any other path would be to fatally side­track the in­ves­ti­ga­tion, and vir­tu­ally to guaran­tee se­ri­ous—very se­ri­ous—er­ror. Which is ex­actly what hap­pened.

There was in fact no in­fer­en­tial path from Guédé to Knox or Sol­lecito. He never im­pli­cated ei­ther of the two un­til long af­ter the event; around the time of his ap­pre­hen­sion, he speci­fi­cally de­nied that Knox had been in the room. Mean­while, it re­mains en­tirely un­clear that he and Sol­lecito had ever even met.

The hy­pothe­ses of Knox’s and Sol­lecito’s guilt are thus seen to be com­pletely un­nec­es­sary, do­ing no ex­plana­tory work with re­spect to Kercher’s death. They are noth­ing but ex­tremely bur­den­some de­tails.

Epistemic Ruth­less­ness: Fol­low­ing the Strong Signal

All of the “ev­i­dence” you’ve heard against Knox and Sol­lecito—the chang­ing sto­ries, sus­pi­cious be­hav­ior, short phone calls, wash­ing ma­chine ru­mors, etc. -- is, quite liter­ally, just noise.

But it sounds so sus­pi­cious, you say. Who places a three-sec­ond phone call?

As hu­mans, we are pro­grammed to think that the most im­por­tant kinds of facts about the world are men­tal and so­cial—facts about what hu­mans are think­ing and plan­ning, par­tic­u­larly as re­gards to other hu­mans. This ex­plains why some peo­ple are ca­pa­ble of won­der­ing whether the pres­ence of (only) Rudy Guédé′s DNA in and on Mered­ith’s body should be bal­anced against the pos­si­bilty that Mered­ith may have been an­noyed at Amanda for bring­ing home boyfriends and oc­ca­sion­ally for­get­ting to flush the toi­let—that might have led to re­sent­ment on Amanda’s part, you see.

That’s an ex­treme ex­am­ple, of course—cer­tainly no one here fell into that kind of trap. But at least one of the most thought­ful com­menters was severely both­ered by the length of Amanda’s phone calls to Mered­ith. As—I’ll con­fess—was I, for a minute or two.

I don’t know why Amanda wouldn’t have waited longer for Mered­ith to pick up. (For what it’s worth, I my­self have some­times, in a state of ner­vous­ness, di­aled some­one’s num­ber, quickly changed my mind, then di­aled again a short time later.) But—as coun­ter­in­tu­itive as it may seem—it doesn’t mat­ter. The er­ror here is even ask­ing a ques­tion about Amanda’s mo­ti­va­tions when you haven’t es­tab­lished an ev­i­den­tiary (and that means phys­i­cal) trail lead­ing from Mered­ith’s body to Amanda’s brain. (Or even more to the point, when you have es­tab­lished a trail that led de­ci­sively el­se­where.)

Maybe it’s “un­likely” that Amanda would have be­haved this way if she were in­no­cent. But is the de­gree of im­prob­a­bilty here any­thing like the im­prob­a­bil­ity of her hav­ing par­ti­ci­pated in a sex-orgy-kil­ling with­out leav­ing a sin­gle piece of phys­i­cal ev­i­dence be­hind? While some­one else left all kinds of traces? When you had no rea­son to sus­pect her at all with­out look­ing a good dis­tance out­side Mered­ith’s room, far away from the im­por­tant ev­i­dence?

It’s not even re­motely com­pa­rable.

Think about what you’re do­ing here: you are in­vok­ing the hy­poth­e­sis that Amanda Knox is guilty of mur­der in or­der to ex­plain the fact that she hung up the phone af­ter three sec­onds. (Re­mem­ber, the ev­i­dence against Guédé is such that the hy­poth­e­sis of her guilt is su­perflu­ous—not needed—in ex­plain­ing the death of Mered­ith Kercher!)

Maybe that’s not quite as bad as in­vok­ing a su­per­in­tel­li­gent de­ity in or­der to ex­plain life on Earth; but it’s the same kind of mis­take: ex­plain­ing a strange thing by pos­tu­lat­ing a far, far stranger thing.

“But come on,” says a voice in your head. “Does this re­ally sound like the be­hav­ior of an in­no­cent per­son?”

You have to shut that voice out. Ruth­lessly. Be­cause it has no way of know­ing. That voice is de­signed to as­sess the mo­ti­va­tions of mem­bers of an an­ces­tral hunter-gather band. At best, it may have the abil­ity to dis­t­in­guish the cor­rect mur­derer from be­tween 2 and 100 pos­si­bil­ities -- 6 or 7 bits of in­fer­en­tial power on the ab­solute best of days. That may have worked in hunter-gath­erer times, be­fore more-closely-causally-linked phys­i­cal ev­i­dence could hope to be eval­u­ated. (Or maybe not—but at least it got the genes passed on.)

DNA anal­y­sis, in con­trast, has in prin­ci­ple the abil­ity to uniquely iden­tify a sin­gle in­di­vi­d­ual from among the en­tire hu­man species (de­pend­ing on how much of the genome is looked at; also ig­nor­ing iden­ti­cal twins, etc.) -- that’s more like 30-odd bits of in­fer­en­tial power. In terms of epistemic tech­nol­ogy, we’re talk­ing about some­thing like the differ­ence in lo­co­mo­tive effi­cacy be­tween a horse­drawn car­riage and the Star­ship En­ter­prise. Our an­ces­tral en­vi­ron­ment just plain did not equip our knowl­edge-gath­er­ing in­tu­itions with the abil­ity to han­dle weapons this pow­er­ful.

We’re talk­ing about the kind of power that al­lows us to re­duce what was formerly a ques­tion of hu­man so­cial psy­chol­ogy—who made the de­ci­sion to kill Mered­ith? -- to one of physics. (Or chem­istry, at any rate.)

But our minds don’t nat­u­rally think in terms of physics and chem­istry. From an in­tu­itive point of view, the equa­tions of those sub­jects are for­eign; whereas “X did Y be­cause he/​she wanted Z” is fa­mil­iar. This is why it’s so difficult for peo­ple to in­tu­itively ap­pre­ci­ate that all of the chat­ter about Amanda’s “sus­pi­cious be­hav­ior” with var­i­ous con­vinc­ing-sound­ing nar­ra­tives put forth by the pros­e­cu­tion is to­tally and ut­terly drowned out to oblivion by the sheer strength of the DNA sig­nal point­ing to Guédé alone.

This ra­tio­nal­ist skill of fol­low­ing the strong sig­nal—mer­cilessly block­ing out noise—might be con­sid­ered an epistemic ana­log of the in­stru­men­talshut up and mul­ti­ply”: when much is at stake, you have to be will­ing to jet­ti­son your in­tu­itive feel­ings in fa­vor of cold, hard, ab­stract calcu­la­tion.

In this case, that means, among other things, think­ing in terms of how much ex­plana­tory work is done by the var­i­ous hy­pothe­ses, rather than how sus­pi­cious Amanda and Raf­faele seem.

Con­clu­sion: The Amanda Knox Test

I chose the ti­tle of this post be­cause the par­allel struc­ture made it sound nice. But ac­tu­ally, I think an hour is a pretty weak up­per bound on the amount of time a skil­led ra­tio­nal­ist should need to ar­rive at the cor­rect judg­ment in this case.

The fact is that what this comes down to is an ut­terly straight­for­ward ap­pli­ca­tion of Oc­cam’s Ra­zor. The com­plex­ity penalty on the pros­e­cu­tion’s the­ory of the crime is enor­mous; the ev­i­dence in its fa­vor had bet­ter be over­whelming. But in­stead, what we find is that the ev­i­dence from the scene—the most im­por­tant sort of ev­i­dence by a huge mar­gin—points with liter­ally su­per­hu­man strength to­ward a mun­dane, even typ­i­cal, homi­cide sce­nario. To even con­sider the­o­ries not di­rectly sug­gested by this ev­i­dence is to en­gage in hy­poth­e­sis priv­ileg­ing to the ex­treme.

So let me say it now, in case there was any doubt: the pros­e­cu­tion of Amanda Knox and Raf­faele Sol­lecito, cul­mi­nat­ing in last week’s jury ver­dict—which ap­par­ently was unan­i­mous, though it didn’t need to be un­der Ital­ian rules—rep­re­sents noth­ing but one more gi­gan­tic, dis­as­trous ra­tio­nal­ity failure on the part of our species.

How did Less Wrong do by com­par­i­son? The av­er­age es­ti­mated prob­a­bil­ity of Amanda Knox’s guilt was 0.35 (thanks to Yvain for do­ing the calcu­la­tion). It’s pretty rea­son­able to as­sume the figure for Raf­faele Sol­lecito would be similar. While not par­tic­u­larly flat­ter­ing to the defen­dants (how would you like to be told that there’s a 35% chance you’re a mur­derer?), that num­ber makes it ob­vi­ous we would have voted to ac­quit. (If a 65% chance that they didn’t do it doesn’t con­sti­tute “rea­son­able doubt” that they did...)

The com­menters whose es­ti­mates were clos­est to mine—and, there­fore, to the cor­rect an­swer, in my view—were Daniel Bur­foot and jen­marie. Con­grat­u­la­tions to them. (But even they were off by a fac­tor of at least ten!)

In gen­eral, most folks went in the right di­rec­tion, but, as Eliezer noted, were far too un­der­con­fi­dent—ev­i­dently the re­sult of an ex­or­bitant level of trust in ju­ries, at least in part. But peo­ple here were also widely mak­ing the same ob­ject-level mis­take as (pre­sum­ably) the jury: vastly over­es­ti­mat­ing the im­por­tance of “psy­cholog­i­cal” ev­i­dence, such as Knox’s in­con­sis­ten­cies at the po­lice sta­tion, as com­pared to “phys­i­cal” ev­i­dence (only Guédé′s DNA in the room).

One thing that was in­ter­est­ing and rather en­courag­ing, how­ever, is the amount of up­dat­ing peo­ple did af­ter read­ing oth­ers’ com­ments—most of it in the right di­rec­tion (to­ward in­no­cence).

[EDIT: After read­ing com­ments on this post, I have done some up­dat­ing of my own. I now think I failed to ad­e­quately con­sider the pos­si­bil­ity of my own over­con­fi­dence. This was pretty stupid of me, since it meant that the fo­cus was taken away from the ac­tual ar­gu­ments in this post, and ba­si­cally to­ward the is­sue of whether 0.001 can pos­si­bly be a ra­tio­nal es­ti­mate for any­thing you read about on the In­ter­net. The qual­i­ta­tive rea­son­ing of this post, of course, stands. Also, the fo­cus of my ac­cu­sa­tions of ir­ra­tional­ity was not pri­mar­ily the LW com­mu­nity as re­flected in my pre­vi­ous post; I ac­tu­ally think we did a pretty good job of com­ing to the right con­clu­sion given the in­for­ma­tion pro­vided—and as oth­ers have noted, the lev­el­head­ed­ness with which we did so was im­pres­sive.]

For most fre­quenters of this fo­rum, where many of us reg­u­larly speak in terms of try­ing to save the hu­man species from var­i­ous global catas­trophic risks, a case like this may not seem to have very many grand im­pli­ca­tions, be­yond serv­ing as yet an­other ex­am­ple of how ba­sic prin­ci­ples of ra­tio­nal­ity such as Oc­cam’s Ra­zor are in­cred­ibly difficult for peo­ple to grasp on an in­tu­itive level. But it does catch the at­ten­tion of some­one like me, who takes an in­ter­est in less-com­monly-thought-about forms of hu­man suffer­ing.

The next time I find my­self dis­cussing the “hard prob­lem of con­scious­ness”, think­ing in vivid de­tail about the spec­trum of hu­man ex­pe­rience and won­der­ing what it’s like to be a bat, I am go­ing to re­mem­ber—whether I say so or not—that there is most definitely some­thing it’s like to be Amanda Knox in the mo­ments fol­low­ing the an­nounce­ment of that ver­dict: when you’ve just learned that, in­stead of head­ing back home to cel­e­brate Christ­mas with your fam­ily as you had hoped, you will be spend­ing the next decade or two—your twen­ties and thir­ties—in a prison cell in a for­eign coun­try. When your de­ceased friend’s rel­a­tives are watch­ing with satis­fac­tion as you are led, sob­bing and wailing with des­per­a­tion, to a van which will trans­port you back to that cell. (Ever thought about what that ride must be like?)

While we’re busy elimi­nat­ing hunger, dis­ease, and death it­self, I hope we can also find the time, some­where along the way, to get rid of that, too.

(The As­so­ci­ated Press re­ported that, ap­par­ently, Amanda had some trou­ble go­ing to sleep af­ter the mid­night ver­dict.)

I’ll con­clude with this: the noted math­e­mat­i­cian Serge Lang was in the habit of giv­ing his stu­dents “Hunt­ing­ton tests”—named in refer­ence to his con­tro­versy with poli­ti­cal sci­en­tist Sa­muel Hunt­ing­ton, whose en­trance into the U.S. Na­tional Academy of Sciences Lang waged a suc­cess­ful cam­paign to block on the grounds of Hunt­ing­ton’s in­suffi­cient sci­en­tific rigor.

The pur­pose of the Hunt­ing­ton test, in Lang’s words, was to see if the stu­dents could “tell a fact from a hole in the ground”.

I’m think­ing of adopt­ing a similar prac­tice, and call­ing my ver­sion the Amanda Knox Test.

Postscript: If you agree with me, and are also the sort of per­son who en­joys pur­chas­ing warm fuzzies sep­a­rately from your utilons, you might con­sider donat­ing to Amanda’s defense fund, to help out her fi­nan­cially dev­as­tated fam­ily. Of course, if you browse the site, you may feel your (prior) es­ti­mate of her guilt tak­ing some hits; per­son­ally, that’s okay with me.