The Black Swan: Second Edition: The Impact of the Highly Improbable: With a New Section: On Robustness and Fragility: 2 (Incerto)

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There have been plenty of other heroes along the way – head of recruitment Steve Walsh has crafted an outstanding scouting network so essential to the building of this history-making squad; fans’ favourite midfielder Andy King, meanwhile, has become the first player to win the top three divisions with the same club, and now prepares for a final-day trip to Stamford Bridge – the ground on which he used to be a ball boy in Ranieri’s Chelsea days.

The ... Swan: The Impact of the Highly Improbable," 2007 book by author Nassim Nicholas Taleb Crossword Clue There have been four standout players in Wes Morgan, N’Golo Kante, Riyad Mahrez and Jamie Vardy, but it goes without saying that this team is so much greater than the sum of its parts. Leicester’s lineup is an electrical circuit that needs all of its components to power on; Ranieri its master technician. At the heart of the Supreme Court’s ruling is the idea that courts can reject a defendant’s explanation even in cases where the evidence does not refute this explanation. While rejecting the story by referring to a ‘smoking gun’ (i.e. refuting evidence) may be the ideal, other responses are possible too. The Supreme Court distinguishes three categories. First, some explanations can be rejected because they ‘did not become plausible’. I argued that whether an explanation needs to ‘become plausible’ during the criminal proceedings depends on its inherent plausibility at the time it is offered—its prior probability. If an explanation with a low prior probability does not become probable by means of the evidence, then the explanation fails to create a reasonable doubt. Second, some explanations are ‘incredible’. Whether an explanation offered by a defendant is probable partially depends on evidence about the credibility of the defendant. Finally, some explanations are so ‘highly improbable’ that the court does not have a duty to respond to them. I argued that what distinguishes these explanations from explanations that the court should respond to is that their improbability is obvious. When an explanation is obviously improbable, the court would not serve the goals of making its decision understandable by offering a response. A duty to respond would then only reduce the efficiency of the decision process. There are two reasons why an explanation can be improbable: due to the evidence in the case (likelihood) or due to its prior probability. If an explanation is improbable due to the likelihood, it conflicts with (reliable) evidence that was already brought forward in court. In such cases the court can point to that evidence when justifying its decision to reject the explanation. Yet the Supreme Court’s ruling is about cases in which courts cannot point to such evidence. So, the court presumably describes situations in which an explanation is improbable because of its low prior probability. The prior probability of an explanation is its probability before any evidence is observed. The lower the prior probability of an explanation is, the stronger the evidence has to be to make that explanation probable. If the evidence is not strong enough (in terms of the likelihood) then the prior probability will not be raised sufficiently to create a reasonable doubt. In that case, the explanation has not become ‘plausible’. When reasoning about which story to accept, rejecting one story and accepting the other often means finding ‘discriminating evidence’, i.e. evidence that fits better with one story than another ( Van Koppen, 2011, pp. 52–55). In Bayesian terms this means evidence where the likelihood ratio strongly favors one story over the other. Such evidence discriminates between the two explanations because we would expect the evidence much more if one explanation were true than if the other was. If the likelihood ratio is sufficiently much greater than 1, the probability of one explanation will be high and the probability that the alternative explanation is true will be low. In such a cases the court can point to the discriminating evidence as a reason why it rejects the alternative explanation.The court’s position is understandable if we look at it in the context of Dutch criminal law. First, whenever a defendant offers an alternative explanation, the court can only convict him if it provides a justification for rejecting this explanation in its ruling. 5 Second, the proof standard in the Netherlands states that a defendant can only be convicted if the court has to be convinced based on the admissible evidence. 6 So, at first sight, when the court has to justify why it is convinced of the guilt of the defendant, it should also do so by referring to the admissible evidence. When a conviction involves the court rejecting the defendant’s story, this would then also require the court referring to some piece of evidence that refutes this alternative explanation. The notion of credibility can easily be expressed in Bayesian terms. Whether a story is credible depends on the answer to the following question: ‘given that a witness testifies to fact X, what is the probability of X?’ ( Goldman, 1999, 4.2–4.4). To put it in terms of a formula, we are interested in P(Defendant’s explanation | Defendant offers this explanation in this way). So, the fact that this defendant offers this explanation, and at this moment, can count as evidence about whether that explanation is true.

But they can never, ever take this stupid, staggering achievement away – and that’s the greatest feeling of all. Just don’t call it a fairy tale. If the phrase has proved a worn cliché over the last six months anyway, now it’s simply not true. The Collins Dictionary defines ‘fairy tale’ as being “a highly improbable account”– but this has happened. This is very real. They know that much of their success this campaign has been down to other sides failing miserably, and that next season offers them all a shot at redemption; Manchester City and Chelsea with incoming managers, Manchester United too if Jose Mourinho gets his way, Arsenal in what might be Arsene Wenger’s final season at the club, and even Liverpool where Jurgen Klopp now has a full summer of fine-tuning ahead. Mauricio Pochettino’s Tottenham, who ran them so close, are built to last.Suppose that the defendant’s story is weak and that the prosecution’s case is strong. This means that if no further evidence or arguments were adduced, the defendant would most likely lose the case and be found guilty beyond a reasonable doubt. So, if the defendant tells a story that is initially improbable, he risks losing the case if no new evidence confirms his story. The defendant may then have a burden to introduce new arguments or evidence that would make the court decide in his favor or he risks losing the case. 9