Amanda Knox Trial: Crazy Numbers

A very important day in the Amanda Knox appeal trial being held in Perugia, Italy.

Knox and her former boyfriend Raffaele Sollecito have been found guilty and sentenced to 26 and 25 years of prison respectively for the murder of British Erasmus student Meredith Kercher, at the cottage the two girls shared with two other roommates.

Amongst many troubling indices of guilt were a large kitchen knife found in the drawer of Raffaele's flat, a five-minute walk from the girls' cottage, and a small piece of Meredith's bra, the part of the clasp containing two hooks, which had been cut or torn off and separated from the rest of the bra during the attack on the unfortunate student.

The knife was tested for DNA, and while a sample of Amanda's was found on the handle, a tiny amount attributed to Meredith was found on the blade. As for the bra hooks, analysis in the forensic lab of the Scientific Police of Rome found a mixture of DNA coming from two people: a larger portion from Meredith and a small amount clearly identifiable as Raffaele's.

No other DNA of Raffaele was found in the room where Meredith was stabbed. Apart from the bra hooks, the clear evidence against him consists of a bloody footprint attributed to him found on the bathmat, and incontrovertible proof that he lied several times, in particular about his alibi.

Electropherograms (DNA graphs) of the sample found on the knife blade have been made public, and can be easily compared to available electropherograms of DNA known to be Meredith's. Although the peaks in the knife DNA are much lower, indicating a very tiny sample, the two graphs are obviously identical, with peak pairs located in precisely the same positions.

Amanda Knox's father, Curt Knox, and her mother, Edda Mellas, have commented in public at great length on the subject of the DNA found on the knife. Criticizing the work of the forensic biologist from Rome, Patrizia Stefanoni, the Knox/Mellas family has repeated in every media venue across the United States such messages as "the DNA on the knife has only a 1% chance of belonging to Meredith" or "the DNA on the knife could belong to half of Italy".

These statements are mathematical nonsense. It is quite undermining to their efforts at proving their daughter's innocence via a media blitz to make statements which are so mathematically wrong. The DNA on the knife corresponds at all thirteen genetic loci with that of Meredith Kercher. The chance that a different person produced that DNA sample is 1 in trillions or quadrillions - far more than the earth's population. If genetic analysis is used to identify human beings, it is because a complete sample (usually considered to be thirteen clear genetic loci, each one consisting of a pair of peaks) is considered just about 100% certain.

To say that the knife DNA has a "1% chance of belonging to Meredith" is simply a flagrant misuse of "numberspeak" in order to influence a public assumed to be either too ignorant to notice, or simply to have no access to the documents (electropherograms) that prove the opposite.

What the Knox/Mellas family should have said, and would have said loud and clear all along if they had been correctly advised from a mathematical point of view, is that the DNA from the knife blade clearly belongs to Meredith, but there is a clear possibility of that electropherogram being the result of contamination. This is, indeed, what Amanda Knox's lawyers held in court. The suggestion was dismissed, however, by the judge and jury in the court of first instance, because it was never explained how and where contamination might have occurred. The knife was collected by gloved investigators and packaged in a new unused envelope before being transmitted to the Rome laboratory for analysis, and Meredith had never set foot in Raffaele's house, so it seems extremely unlikely that any contamination occurred during the collection.

Raffaele further complicated his own situation by reacting with a completely unlikely story when he learned about Meredith's DNA on his knife. Instead of saying "That's impossible, she was never at my house" - or preserving a wise silence - he spun a tale about how it was normal that her DNA was on his knife because once he pricked her with it by accident while they were cooking together. Although he had once or twice cooked at the flat the girls' shared, he and Amanda both denied having ever taken the knife there, so his story sounded horribly like a lie.

Nevertheless, Raffaele and Amanda have had a break today. As a gesture of objectivity, the judge in their appeal trial handed the knife, the bra clasp, and all of the documents concerning them to a pair of objective, court-appointed experts from a university in Rome. Their report was handed in to the Court today, and leaked - already yesterday - to a number of sources.

The conclusions are that contamination may have occurred.

For the knife, it is pointed out in the report that given the tiny quantity of DNA on the blade, it should not have been analysed in the same laboratory where other samples of Meredith's DNA were already analysed, as the earlier samples can easily contaminate the later tinier ones. Proper protocol would have indicated taking the tiny knife sample to a different lab for analysis, but this was not done.

For the bra clasp, the report explains that there were any number of possibilities for contamination due to faulty collection procedures. It furthermore specifies that Dr. Stefanoni erred in attributing the DNA on the hooks to just two people, as there are clearly further contributors to the mix of DNA on the hooks, with more than one male. As no other male has been identified - neither the third accused perpetrator of the murder, Rudy Guede, nor Meredith's boyfriend, nor any other known person, this presence could be indicative of contamination.

There is a more evidence against Amanda Knox and Raffaele Sollecito: their own lies, mixed traces of Amanda's blood or DNA and Meredith's about the murder cottage, a painfully obvious effort at staging a faked burglary. Acquittal is far from certain. But the experts findings in the report turned in today will help, removing any proof of premeditation - such as bringing the knife from Raffaele's place to the cottage - and any actual guilty trace of Raffaele in the murder house, apart from a fuzzily outlined footprint.

The news reports that Amanda is singing and dancing today.

The experts' report will be presented in court on July 25.

Dominique Strauss-Kahn: recommended strategy

When people are in a situation where they have to make tough decisions, taking a number of factors into account and evaluating the risks, they generally proceed by a combination of imagination, instinct and principle.

Actuaries, however, who deal with risk evaluation professionally, are used to placing monetary values on things which are generally considered to escape measurement in financial terms, such as the risk of accidental death.

What would make a lot of sense, and certainly makes quite an interesting exercise, would be to use an actuary-style approach when selecting strategy, except in terms of a unit of measure that corresponds to human feelings rather than currency.

There is no such unit of measure in our language: apparently it isn’t a concept that is used enough to have justified the creation of an actual word. For today, let’s use the expression catastrophe points.

You measure all the bad things that can happen to you in catastrophe points. The measurements are subjective, since obviously different people are not necessarily going to assign the same number of points to different catastrophes. One person might think it worse to lose a job than a lover, for example, while another might feel just the opposite. These measurements are individual, subjective figures, but when a person is deciding on a strategy in a difficult situation, they can be really helpful and shed quite a new light.

As an exercise in the use of catastrophe points in choosing strategy, let’s amuse ourselves by considering the case of Dominique Strauss-Kahn, currently under house arrest due to an accusation of attempted rape and sequestration against a hotel maid in New York.

From information leaked by police and prosecutors, Strauss-Kahn is said to have emerged naked from the shower in his luxury suite at the Sofitel to find the maid on her way to clean his bedroom, under the mistaken impression that he was not in the hotel. What is he accused of having done? Grabbed the woman, pressed his private parts against her mouth, tried to pull off her stockings, grabbed her again as she fled up the corridor to the bathroom, and prevented her from leaving the suite by closing the door which she had left open, as maids generally do while cleaning.

We don’t yet really have enough information to come to a clear conclusion about what actually happened in that hotel suite on that day. Why did the woman enter an occupied hotel room at all? How did she get out? Perhaps Strauss-Kahn didn’t intend to actually rape her; he may be aware within himself that he wouldn’t go beyond a certain point in forcing an unwilling woman. It’s hard to tell for now; we will learn more as the case unfolds. But it does seem pretty clear that Strauss-Kahn actually did much of what he is accused of doing. Yet he doesn’t appear to feel any trace of guilt or remorse. This may be as much a sign of mental trouble as his repeated aggressive sexual approaches towards women. Or else, maybe it just comes from a sense of entitlement due to his wealth and position, or from a profound conviction of his own irresistible charm.

Under the assumption - which seems pretty clear - that Strauss-Kahn does not feel real guilt or remorse for his acts, and that he doesn’t feel any particular inner or moral pressure to confess, he is in a perfect position to make a numerical assessment of the gains and losses of the strategies open to him. The goal of this post is to help him do that, while getting in a little practice about how one might think this way in front of one’s own personal dilemmas.

In order to help Mr. Strauss-Kahn with the task of choosing an optimal strategy, we’re going to have to make a guess at the values in terms of catastrophe points that certain negative events would have for him. This is obviously the point where our little exercise loses validity, since a person can only really make that evaluation for him- or herself. However, as we’ve said, something of Strauss-Kahn’s personality has filtered out recently through the news, and we think we can make a stab at a realistic assessment as follows.

First of all, we have to note that Strauss-Kahn is in possession of a considerable fortune (largely belonging to his wife) estimated at about 50 million dollars. Therefore, the loss of a million dollars will be worth many less catastrophe points for him than it would be for most of us. We can safely say that DSK would be more than happy to pay a couple of million dollars to stay out of prison for a year.

But he isn’t just risking prison: he stands to lose much more, in terms of his career, and also in terms of the difficult-to-measure advantage of “face”, something of little importance to many people, but of tremendous importance to those who choose to engage in public life. The major losses that DSK is facing in his present situation are: loss of money, loss of freedom (i.e. prison), loss of face and loss of career.

Let’s assign catastrophe points to these losses as we might imagine that DSK measures them.

Money: loss of $1,000,000 = 1 catastrophe point

Prison: loss of 1 year of freedom = 2 catastrophe points

Career: loss of (possibility of) important public office = 10 catastrophe points

Face: loss of face because guilty of sex attack = 3 catastrophe points

...........loss of face because proven to be a liar = 5 catastrophe points

...........loss of face because of illegally buying his way out = 8 catastrophe points

Admittedly, these quantities are selected more or less intuitively: we imagine that DSK regrets the impossibility of running for president more than he feels guilty, that he feels less ashamed that people should think of him as a sex attacker (i.e. sex bomb) than that they should think of him as a liar, etc. But when using our method in your own strategies, you’ll be able to choose the numbers that really make sense to you.

Now let’s go over the DSK’s possible strategies and evaluate the risks and losses associated with each one. Naturally, our risk evaluations are also guesses, but they seem fairly probable. Note that the victim in the case is a witness and not a plaintiff, therefore DSK cannot make any legal offer to negotiate with her; in fact he cannot even contact her as she is presently being sequestered in order to prevent any possibility of witness tampering. Any effort to influence her via her family in Africa, say, would be highly illegal, yet difficult to prove or to punish given the international nature of the situation.

I. Deny, deny, deny.

Strategy: Go to court and plead innocent.

Risk: guilty verdict, probability 90%.

Loss if successful: if DSK is acquitted, no loss.

Losses if unsuccessful:

..........freedom (say 5 years)

..........any possibility of a career in public life

..........money (say $1,000,000 in damages)

II. Cards on the table.

Strategy: Go to court and plead guilty, express remorse.

Risk: None. Guilty verdict certain.

Losses:

..........freedom (say 3 years)

..........any possibility of a career in public life.

..........face: guilty plus liar (denying crime until guilty plea)

..........money (say $1,000,000 in damages)

III. Sneaky sneaky.

Strategy: secretly offer money to the victim’s family

Risk: truth may come out: 70% (hard to hide)

Loss if strategy successful:

..........money (say $2,000,000)

Loss if strategy fails:

..........face (illegally buying his way out)

..........Has to return to strategy II (can hardly plead innocent after this)

Now, DSK wants to choose the best strategy based purely on the possible risks, gains and losses. Which strategy is the wisest?

To answer the question, we count up the numerical result of each strategy, using the “expected losses” formula given by the sum of the probability of each outcome multiplied by the catastrophe points of that outcome.

Strategy I:

....If successful: 0 (10%=0.1)

....If unsuccessful: 21 (90%=0.9)

....Expected result: .1x0 + .9x21 = 18.9 catastrophe points

Strategy II:

....25 (100%=1.0)

....Expected result: 1x25 = 25 catastrophe points

Strategy III:

....If successful: 2 (30%=0.3)

....If unsuccessful: 33 (70%=0.7)

....Expected result: .2x3 + .7x33 = 23.7 catastrophe points

So, it looks like DSK’s best -- or least catastrophic! -- option is to go to trial and deny everything. We’ll wager that’s what he’ll choose to do, because given his character, a guilty plea involves too much loss of face, and an effort at secret negotiation involves too high a risk.

Top lawyer Ivan Fisher has expressed the opinion that pleading not guilty is a bad strategy, that if Strauss-Kahn confessed to having a psychological compulsion to attack women, expressed remorse, and sought professional help, he would garner widespread sympathy and probably less if any prison time. That’s a very interesting analysis, in that Fisher is clearly equating a “bad strategy” with a strategy that will lead to a severer sentence. In other words, Fisher is assigning a lot of catastrophe points to a prison term, and not so many to the loss of face involved in confessing to psychological problems, to needing help, to doing wrong. But that assessment corresponds to a defence lawyer’s professional task, not to Dominique Strauss-Kahn’s mindset. If DSK pleads not guilty, if he goes on declaring his innocent throughout the trial, then whether he wins or loses he’ll go on claiming innocence till the day he dies. It looks like that’s may just the most important thing for him, in the end.

News Flash!

Today, June 6, 2011, Strauss-Kahn pled not guilty at his arraignment in New York. According to news reports, he pronounced only those two words and nothing else. We’ll see what the future holds, but it’s a fact that his attitude today bears out our analysis.

Dominique parody song