Amanda Knox: post mortem

Continuing my interest in tracking real-world predictions, I notice that the recent acquittal of Knox & Sollecito offers an interesting opportunity - specifically, many LessWrongers gave probabilities for guilt back in 2009 in komponisto’s 2 articles:

Both were interesting exercises, and it’s time to do a followup. Specifically, there are at least 3 new pieces of evidence to consider:

  1. the failure of any damning or especially relevant evidence to surface in the ~2 years since (see also: the hope function)
  2. the independent experts’ report on the DNA evidence
  3. the freeing of Knox & Sollecito, and continued imprisonment of Rudy Guede (with reduced sentence)

Point 2 particularly struck me (the press attributes much of the acquittal to the expert report, an acquittal I had not expected to succeed), but other people may find the other 2 points or unmentioned news more weighty.

2 Probabilities

I was curious how the consensus has changed, and so, in some spare time, I summoned all the Conscientiousness I could and compiled the following list of 54 entries based on those 2 articles’ comments (sometimes inferring specific probabilities and possibly missing probabilities given in hidden subthreads), where people listed probabilities for Knox’s guilt, Sollecito’s guilt, and Guede’s guilt:

Knox Sollecito Guede LWer
.20 .20 .70 badger
.05 .10 .90 mattnewport
.20 .25 .90 AngryParsley
.05 .05 .95 tut
.05 .05 .95 bentarm
.85 .60 .20 bgrah449
.01 .01 .99 kodos96
.01 .01 .99 Daniel_Burfoot
.40 .40 .90 nerzhin
.45 .45 .60 Matt_Simpson
.33 .33 .90 Cyan
.50 .50 .95 jimmy
.05 .05 .99 Psychohistorian
.40 .40 .90 Threads
.50 .50 .80 Morendil
.15 Eliezer_Yudkowsky
.20 .35 .98 LauraABJ
.10 .10 .90 curious
.20 .20 .96 jpet
.06 .06 .70 saliency
.80 .60 .95 Mario
.20 .20 .95 Yvain
.70 Shalmanese
.05 .05 .95 gelisam
.05 .05 .90 Mononofu
.90 .90 .90 lordweiner27 (changed mind)
.50 .50 .99 GreenRoot
.99 .99 .99 dilaudid
.13 .15 .97 Jack
.05 .05 .90 wedrifid
.01 .01 .90 Nanani
.35 .35 .95 imaxwell
.01 .01 .99 jenmarie
.25 .25 .75 Jawaka
.41 .38 .99 magfrump
.40 .20 .60 gwern
.08 .10 .95 loqi
.25 .25 .50 JamesAndrix
.90 .85 .99 Unknowns
.35 .35 .90 Sebastian_Hagen
.90 .90 .99 brazil84
.30 .30 .40 ChrisHibbert
.02 .02 .98 wnoise
.50 .40 .90 John_Maxwell_IV
.10 .10 k3nt
.01 .01 .99 Sinai
.00 .00 1.0 KayPea
.00 .00 .60 MerleRideout
.15 .10 .80 TheRev
.01 .01 .99 komponisto
.30 pete22
.01 SforSingularity
.00 .00 .90 AnnaGilmour
.05 .05 .95 Seth_Goldin
.60 .60 .95 bigjeff5

It’s interesting how many people assign a high-probability to Knox being guilty; I had remembered LW as being a hive of Amanda fans, but either I’m succumbing to hindsight bias or people updated significantly after those articles. (For example, Eliezer says .15 is too high, but doesn’t seem otherwise especially convinced; and later one reads in Methods of Rationality that "[Hagrid] is the most blatantly innocent bystander to be convicted by the magical British legal system since Grindelwald's Confunding of Neville Chamberlain was pinned on Amanda Knox.")

EDIT: Jack graphed the probability against karma:

2.1 Outliers

If we look just at >41% (chosen to keep contacts manageable), we find 12 entries out of 54:

Knox Sollecito Guede LWer
.45 .45 .60 Matt_Simpson
.50 .40 .90 John_Maxwell_IV
.50 .50 .80 Morendil
.50 .50 .95 jimmy
.50 .50 .99 GreenRoot
.60 .60 .95 bigjeff5
.70 Shalmanese
.80 .60 .95 Mario
.85 .60 .20 bgrah449
.90 .85 .99 Unknowns
.90 .90 .90 lordweiner27
.90 .90 .99 brazil84
.99 .99 .99 dilaudid

I have messaged each of them, asking them to comment here, describing if and how they have since updated, and any other thoughts they might have. (I have also messaged the first 12 commenters or so, chronologically, with <41% confidence in Knox’s guilt, with the same message.) The commenters:

AngryParsley / Cyan / Daniel_Burfoot / Eliezer_Yudkowsky / GreenRoot / John_Maxwell_IV / LauraABJ / Mario / Matt_Simpson / Morendil / Psychohistorian / Shalmanese / Threads / Unknowns / badger / bentarm / bgrah449 / bigjeff5 / brazil84 / dilaudid / jimmy / kodos96 / lordweiner27 / mattnewport / nerzhin / tut

I look forward to seeing their retrospectives, or indeed, anyone's retrospectives on the matter.

Allknowing and most merciful Bayes;
We have erred, and strayed from thy ways like biased sheep.
We have followed too much the devices and desires of our own hearts.
We have offended against thy axiomatic laws.
We have left undone those updates which we ought to have done;
And we have done those updates which we ought not to have done;
And there is no calibration in us.
But thou, O Bayes, have mercy upon us, miserable wannabes.
Spare thou them, O Bayes, who confess their faults.

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Over the summer, Eliezer suggested (approximately, I am repeating this from memory) the following method for making an important decision:

  1. write down a list of all of the relevant facts on either side of the argument.
  2. assign numerical weights to each of the facts, according to how much they point you in one direction or another.
  3. burn the piece of paper on which you wrote down the facts, and go with your gut.

This was essentially the method I used in coming to my (probably slightly low) estimate of the probability that Knox and Sollecito were innocent. It just felt like they were innocent, and I saw essentially no reason to suspect they were guilty. I will note that the 'pro-guilt' site that komponisto linked to was just horribly devoid of anything that I might consider evidence (if anything, that site did more to convince me of Knox's innocence than the pro-innocence site), and I did spend probably about 10 minute trying to find some evidence that they had missed, but completely failed.

On a different not, as I said at the time, 0.95 and 0.05 were just proxies for "pretty damn sure" and "pretty damned unlikely" - I have very little idea what 5% probability feels like, and I'm sure that if arbitrary scientific convention had settled on some different number for significance, I'd have picked that one instead. I have made some progress since a year ago on calibrating my estimates of small probabilities, but I absolutely do not think that I would be wrong approximately 1 time in 20 when making predictions to which I assign a probability of 0.95.

This is a better summary of what I said than what I actually said, so I hereby declare your distorted version to be my true teaching.

I have very little idea what 5% probability feels like

???

1d20!!!

Despite the fact that my opinion on the case has hardly changed at all, these posts -- and thinking about the case in general -- were a tremendous learning experience for me. Some of the lessons include:

  • Less Wrong is good at getting the right answer. Believe it or not, the strong survey consensus in favor of innocence -- prior to my second post -- came as something of a pleasant surprise to me. You don't find this in many other places, despite the fact that the case is a no-brainer. I had assumed there would be more wishy-washiness and probabilities close to 50% than there turned out to be. (There was some of this, but less than I expected.)

  • People in general are bad at getting the right answer. As shown by the original verdict, not to mention all the numerous pro-guilt commentators on internet forums and elsewhere. What's surprising about that? Not much, perhaps, but I would say that one thing that is important about it is that it shows that huge, glaring errors of judgement are not restricted to Far Mode. Even on a mundane question such as this, people are susceptible to strange cognitive biases that can severely distort their assessment of evidence.

  • Confidence should depend on how much you know. I erred twice during the original sequence of posts on the case: once when I implied that participants in my survey ought to have come up with numbers like mine (0.001), and then again when I reacted to the indignation that followed by downgrading my own confidence. In truth, because (even before the verdict) I had followed the case more than most LW readers, my level of confidence should have been higher than most readers'. For someone who spends ten minutes reading the two sites I linked to, 0.9 probability of innocence (as opposed to 0.99) is perfectly reasonable; whereas someone like me should expect to be more confident, even if only on account of the meta-information that any additional information not on those sites isn't particularly relevant.

(More comments possibly to be added later...)

See my added comment. I did not assign a probability of 15%. I said that if you assigned a probability higher than 15%, it meant you had a really major problem with crediting the opinions of other people and the authority of idiots. My probability that Knox and Sollecito were guilty was "that's privileging the hypothesis", i.e., "I see no real evidence in its favor so same as prior probability", i.e., "really damned' low".

The Knox thread was one of the first steps in my getting interested in predictions in general. It was a slow process and is still ongoing, but it has had me spend time on various calibration exercises, on PredictionBook, on the Crowdcast instance dedicated to the Good Judgment project, on Inkling Markets because I saw a few arbitrage opportunities there that sounded like fun. I'm not as into predictions as gwern appears to be, but they're growing on me.

All that and I'm still not very sure what to think of the Knox case. Yes, if our predictions were being scored I'd be getting a non-trivial penalty from my 50% chance of her guilt - that is, if we take the outcome of the appeals process as an arbitration of the prediction, and judge, for the purposes of scoring, that she was "in fact" innocent. (I'm not saying I have much doubt now about her innocence: I'm saying that we won't ever know for sure, and part of the point of these prediction exercises is to allow us to better deal with that permanent uncertainty.)

On the other hand, some of the people listed above would be taking a much more serious hit. One thing I've learned from my various exercises is that you can't expect to be right all the time - sometimes, with minimal knowledge of the relevant facts, a 50% prediction is in fact not so bad.

Then again, some of us were also apparently very confident in the answer that "in fact" turned out to be the correct one. Then again, we all get lucky from time to time - that too is the nature of the beast...

My intention is to continue to learn, to continue to get better at predicting, to become better calibrated and more discriminating over time.

(I'm not saying I have much doubt now about her innocence: I'm saying that we won't ever know for sure, and part of the point of these prediction exercises is to allow us to better deal with that permanent uncertainty.)

One of the unfortunate things about living when we do is that it seems unlikely there will be any future oracles developed which reveal definitive answers to ancient crimes.

I refer, of course, to DNA evidence, which gave us an astonishing oracle to ask questions about old crimes, revealing a shockingly high lower bound on the justice system's error rates. If we had been around and recorded predictions about various death row inmates, then the Innocence Project's &etc. results would've been an assessment of our calibration worth writing home about!

I want to see the regression of LW karma (or the log of LW karma) on probability-Amanda-is-guilty!

You ought to leave Eliezer out of the equation, or assign him a Karma value equal to Yvain's, or else he'll dominate the regression.

Doesn't look like there's any sort of function you can use, but there are almost no points in the top right corner of your graph. Almost nobody with high karma on LW assigned a substantial probability that Knox was guilty.

Strange thing about this is, if I've calculated it right, the average probability estimate of Guede's guilt is only ~87%. It seems to me that if this were your real probability estimate of his guilt, and you were on the jury at the guy's trial, you would be obligated to vote innocent. If you operate on the basis that a 13% chance of innocence is not a reasonable doubt, about thirteen out of every hundred people who go to jail will be innocent. That is (let me check) more than one in ten, which strikes me as rather a lot. I think my own estimate of Guede's guilt is above 99%, so I would vote guilty, but I'm surprised the average here is so low.

If you operate on the basis that a 13% chance of innocence is not a reasonable doubt, about thirteen out of every hundred people who go to jail will be innocent.

That's if everyone who went to jail had a 13% chance of innocence. Presumably much of the time it would be lower.

Well, I haven't looked at those estimates for a few months, but I'd imagine that a lot of the margin in the outside view of Guede's case comes from uncertainties introduced by the media handling of the case or by an imperfect view of the evidence. Neither of those factors would, presumably, apply to a jury.

That being said, I wouldn't be all that surprised if thirteen out of a hundred prisoners in Europe and the US were innocent of some of the charges that put them in jail. It's higher than my own estimate would be, but within the same order of magnitude.

I updated my 60% guilt for Knox/Sollecito almost immediately after reading the follow-up article. As I noted on that page, my 60% judgement was a clear case of anchoring. I started with the pro-guilt evidence and only managed an 80% guilt after reading only their evidence. That I was then only able to re-adjust down to 60% was absurd. Since I was (and still am) fairly weak as a rationalist, I probably should have withheld any kind of assessment until after I had read the pro-innocence website, rather than try to make an early assessment and update it with the evidence I knew would be coming.

I didn't put a number on my update at the time, I just went from "There isn't enough evidence to convict" to "Why were they still suspects?". If I had to put a number on it, I'd say this was a <5% chance of guilt.

Since the acquittal, given the judge's statements about the DNA evidence and the handling thereof (I didn't read the full assessment by the independent expert), I'd have to adjust it now to <1%.

ETA: I just went through the independent analysis, and the conclusions were even stronger than I thought they were.

I thought that the conclusions were of the nature: "this DNA cannot be conclusively matched to anyone".

In fact, they were of the nature: "There is no organic material present."

They did find a few grains of starch on the bra clasp, but that was it. How did the Scientific Police screw it up that badly? They got a shakey DNA match where no DNA existed!

I have to update my assessment yet again, to the lowest I'm willing to put a number on, and that's <0.1% chance that either of them are guilty. There is literally zero evidence that either of them were involved.

Amazing job putting this together.

I had remembered LW as being a hive of Amanda fans, but either I’m succumbing to hindsight bias or people updated significantly after those articles.

My .13 probability in the first thread definitely went down following further discussion and, in particular, komponisto's second post. In the last year I've been comfortable using "She's definitely innocent" talking about the case with non-LWers.