The Mathematical Murder of Innocence

by Michael Carter

  Suddenly I realised that I had just stated the right answer. “That’s it, of course!” I exclaimed. “Contrary to what you say, those marks are not specific to Mrs Richardson’s case. They are to be expected each time we get a cot death. This means that any parent who suffers the same bad luck has a good chance of also being accused of being a murder suspect, because there is a good chance of there being these same marks on the baby’s face. Your reasoning would have been correct if, and only if, those marks would be truly specific to Mrs Richardson’s case.”

  Goodwin looked non-plussed but did not say anything.

  “Do you agree, Professor?” I asked. “Are those marks uniquely specific to Mrs Richardson, or do you not admit that we might see them in any cot death case?”

  “It’s possible,” he finally admitted. “But I still think unlikely.” He was not going to back down easily.

  “But again,” I asked, “can you prove to the court that we will not get these marks each time there is a cot death?”

  “No, I can’t prove it,” he conceded.

  “So, I ask you again,” I said, “with these revised figures, in your expert opinion, is the probability of the accused’s children dying of natural causes greater or lesser than the probability of her intentionally killing them both?”

  “Only if your assumptions on the gene effect were correct,” replied Goodwin, “which I repeat I don’t believe, only in that case would we have the possibility of a higher probability of deaths from natural causes.”

  “But do you confirm that you cannot prove that my assumptions are wrong? For example, you cannot prove that there is not a gene that increases the probability of S.I.D.S.?”

  “No. I don’t believe it, but I cannot prove it.”

  “Therefore, by extension, you cannot prove statistically that these deaths were murder?” I asked.

  There was silence for two seconds. “No,” he finally said.

  “So, do you retract your initial testimony that you can prove that the cause of death was intentional killing?”

  Again, silence for a few seconds. “I maintain my conviction that this was murder. But I need to revisit my statistical analysis to counter your arguments. So today, no, I do not have the proof that the court needs,” said Goodwin.

  The judge looked to the far-left rear of the court with a small smile on his face, nodding slightly. Then he turned to me. “Thank you, Mr Fielding. Nicely done. Does the prosecution wish to re-examine this witness? I personally would advise caution given the fact that he has formally retracted his proof.”

  Scott had a heated discussion with his junior and with the solicitor from the Crown Prosecution Team.

  “No, my Lord,” he said. “And as this was our last witness, I will close by saying that this is the case for the Crown.”

  The judge turned towards the witness stand. “Professor Goodwin, you are free to go.” He then turned to the defence. “Mr Dawkins, in light of this, how do you wish to proceed?”

  Dawkins discussed with his team, then he stood up. “Given the empty state of the prosecution’s case, we prefer to stop here and say that this is also the case for the defence. I should thus like to make an application to you, my Lord.”

  “I understand,” said the judge nodding. “We shall now break for lunch. I wish to meet with counsel at 2pm. Jury keepers, please keep the jury ready in their room until I call you.”

  We all stood as the judge marched out. Then our keepers promptly led us out of the courtroom.

  Chapter Eleven

  Once back in our jury room, this time there was some backslapping and forthcoming comments of congratulations.

  Even business suit (David was his name) spontaneously said, “I thought at one point that you were all over the place, but the way you finally brought it all together was just excellent. Bravo!”

  One of the previous evening’s detractors was (slightly) less aggressive. “Still didn’t understand a bloody word you said; but it must have been good otherwise his nibs wouldn’t have backed down, would he?”

  But Mrs die-hard (Beth, actually) was not to be detracted. “What ’ave you gone and done? This woman’s suffering from that F.D… wotsits disease, she shook the life out of ’er first child, they found smovering marks on ’er poor second baby’s mouth, that’s good enough for me. She’s killed twice, so we’d better stop trying to find excuses for ’er, before she kills again. You and all your big words and your big ideas. You confused the professor, you confused the judge, and you confused me! You even forced that poor man to say black when ’e was saying white.”

  David came to my help. “Calm down, Beth. You’re entitled to your opinion; but in a court of law opinion won’t do. You have to be convinced beyond any reasonable doubt. Young Martin here has shown there’s so much doubt in this case that you can drive a double decker bus through it. Personally, I’m now convinced it’s natural causes. When my wife got pregnant the first time, she had a miscarriage. For her next pregnancy, she spent three months lying in bed. Why? Because the doctor told her that if she has already had a first miscarriage, then there is a high risk of her having a second. Well, why can’t it be the same thing for cot deaths? Can you imagine a poor mother that has lost two babies for tragic natural reasons, then being put into prison for murder despite being innocent? How terrible that would be?”

  It seemed that most people agreed with David.

  Hilary, our foreperson, decided to intervene. “Look, everybody, this isn’t yet the time for jury deliberation. I suggest we eat our lunch and wait for our next instructions from the judge, OK?”

  Hunger pangs decided that this was a good proposal, so we attacked the day’s offering. There were ample portions of quiche Lorraine (I remember my dad quoting the title of a book called Real Men Don’t Eat Quiche, which apparently split the world into doers and poseurs; to which my mum countered that ‘real men eat quiche and don’t read that book’.) There was also some limp lettuce, Heinz salad dressing, a modest cheese board and some French baguettes (or rather English bread shaped into long loaves imitating the shapes of baguettes).

  “If you don’t eat the bread, then this is almost your Montignac diet,” joked Stephanie.

  “More like food for the real food,” I countered.

  “By the way, well done again. As the French would say, it was certainly gale force and coming in far above our heads!”

  “That’s anatomically impossible.”

  While we were all waiting and drinking our second cups of weak coffee out of not very ecological plastic cups, served from the rather tired thermos, the judge was talking to counsel. This is what I later gleaned of the discussion from my same sources.

  “Mr Dawkins,” asked the judge, “you wished to make an application to me?”

  “Yes, my Lord. I wish to make a half time submission of no case to answer. There is either no evidence left in the prosecution’s case, or whatever remaining evidence there is, it’s insufficient to support a conviction.”

  “Mr Scott?”

  “The prosecution has rested its case, my Lord. I have nothing more to say. This is your decision.”

  “This is a trial for murder, Mr Dawkins,” said the judge. “As such, before I can decide on your application, I require you to reconfirm to me that the defence does not wish to present any witnesses, and that you also rest your case?”

  “I confirm, my Lord.”

  “Very well, in that case I fully agree to this submission.” The judge turned to the court clerk. “Please bring in the jury.”

  “Members of the jury,” said the judge solemnly, “the defence has made an application called a ‘submission of no case to answer’. The prosecution has not opposed this application. Furthermore, the defence has reconfirmed that they also rest their case.

  “So, under the Criminal Procedure Rules Part 25.9 brackets 2, paragraph (e), I have
decided to direct you, the jury, to acquit the defendant on the grounds that the prosecution’s evidence is insufficient for any reasonable court to convict.

  “I do this because after this morning’s retraction by the expert witness, the prosecution’s case is weak, with virtually no evidence left, and what is left is certainly insufficient to convict. I would go further; we have seen that a more rigorous analysis of the information fully exonerates the defendant of any crime.

  “For the sake of clarity, and to clear up any doubt in the jury, or indeed in the public at large,” here the judge cast his eye over the journalists on the public benches, “I wish to go through rapidly all the accusations we originally heard from the prosecution, and to give you a summary of the evidence and arguments you have heard that refute this.”

  The judge glanced down at his notes. “First, the suspicious marks around the baby’s mouth. The pathologist himself admitted to the court that he did not believe at the time that this was anything other than a natural death, and he agreed that they could have been due to the resuscitation effort. Concerning the retrospective speculation that the first child Andrew might have been shaken, although the defence chose to rest their case before bringing in an eye expert to formally contest this, the prosecution’s own paediatric expert, who agreed he is not an eye specialist, confirmed there was an open disagreement between himself and the more qualified expert on this issue. In any case, this previous death is formally not part of this court’s remit.

  “Next, the order of the telephone calls. The police officer handling the investigation confirmed to the court that a person trained in advanced first aid should be able to determine when someone has died. This lightens markedly the question mark as to why the defendant did not call an ambulance before calling her husband.

  “Next, the diagnosis of F.D.I.A., that is, a syndrome where a mother might deliberately harm one of her children. We only have one expert’s diagnosis, without ever having interviewed the patient. We do not have any second opinion. Together this renders the diagnosis at best insufficient, at worse suspect.

  “Furthermore, the defence has pointed out that many of the preceding suspicions may be an attempt to fit a narrative ex-post to support a theory of murder, a theory originally suggested by a dubious analysis of statistics, rather than there being clear evidence on its own. The defence suggested there was a circular argument – F.D.I.A. syndrome is one of the only credible reasons for the mother to commit murder if the statistics are to be believed; and once you believe in the F.D.I.A. diagnosis, it makes the apparent statistical analysis all the more credible. Then the rather loose medical arguments seem to be forcibly retrofitted to support all this, even going against other medical experts’ opinions. With a circular argument, once you break it, in this case the statistics seem manifestly to be wrong, then all the other arguments fail.

  “Finally, for the statistical evidence, this depended on only one expert witness, and he formally retracted himself this morning. Thanks to Mr Fielding’s intervention, we detect several flaws in his original argument:

  “There are millions of births happening. The sheer number of events allows even very unlikely ‘bad-luck’ events to eventually happen, just like the ‘good-luck’ counter example, one out of the 50 million people who buys a lottery ticket will win the lottery.

  “Our expert made a mistake in assuming that the average for a population applied to each individual in that population. His own statistics showed us incredible variations were possible, some conditions gave forty times more likelihood of a cot death than others. He used the worst possible combination, and squared it to get his one in 72 million. Even using his own flawed logic, if we square the probability that is forty times larger, I calculate we get down to odds of one in only 45,000, not much considering the millions of births. I understand this error made by our expert witness is called the ‘ecological fallacy’.

  “Our expert witness did not compare the probabilities of two hypotheses of rare events – cot death and murder, once the rare event of double deaths had already happened. He only analysed the stand-alone probability of double cot deaths, which was also a mistake. I am given to understand this is called the ‘prosecutor’s fallacy’.

  “We have now understood that random results do not mean random causes, therefore the cause of cot deaths may not be random.

  “As such there may be triggers due to the environment and/or due to genes. Our expert witness eventually confirmed that he did not do anywhere near enough searches to eliminate genes as a cause.

  “Hence, we may well have statistical dependence rather than statistical independence, which would be the equivalent of having a weighted dice. In which case, you cannot simply square the stand-alone probability: since the first cot death could indicate a dramatic increase in probability for a second cot death.

  “Given these possibilities, Mr Fielding came up with a credible scenario where you could find anything between one cot death in the UK every two years, right up to six cot deaths every year. The possibility of this scenario was confirmed, even if unwillingly, by the expert.

  “And Mr Fielding points out that Mrs Richardson is in court precisely because she is one of the unlucky ones to whom this tragedy has happened.

  “That is why, ladies and gentlemen of the jury, I direct you to find a verdict of not guilty to exonerate the defendant.

  “Finally, we need a unanimous verdict. Please put any thoughts of a majority verdict out of your minds unless I give you further instructions.”

  Way to go, judge! I thought. You must have suddenly remembered your O-level in maths. That was just an incredible summary!

  We went off to the jury room. The jury keeper stood right outside the door. He obviously did not expect us to take long. Hilary had us all sit down.

  “We have been directed to find a verdict of not guilty. Is there any reason to disagree?” she asked.

  Most people were shaking their heads. Even Beth said nothing; she just looked down at the table.

  “Hands up for not guilty, then,” said Hilary. All hands went up – those of us twelve official jurors, as well as those of the two substitutes just for good measure. “So, we return a unanimous verdict of not guilty.”

  “Looks like we’ll be going home earlier than expected,” said David. “Two days for a murder trial! Before we go back into the courtroom, I’m curious to know how we would have voted if Martin hadn’t destroyed Professor Goodwin’s bad statistics. Personally, it’s only after listening to Martin that I made the parallel with my wife’s miscarriages: that cot deaths are probably statistically dependent and not independent. At the time, although I thought the medical proof was a bit iffy, I was blinded by that one in 72 million statistic. I was sure at that point she was guilty. Be honest, what did you others think?”

  Different people round the table nodded their agreement, and added their comments: “I agree,” said one.

  “No way did I think it could it be an accidental death with a one to 72 million chance against it,” said another.

  “That was exactly my reasoning too,” said a third.

  “Me too, she was guilty as sin until Martin waded in,” said a fourth.

  “God forgive me, I thought she was guilty too,” another said.

  “Me too,” yet another said; and so on.

  “Let’s have an unofficial straw poll just for curiosity,” said David. “When the defence sat down, just before Martin gave his list of questions to the judge, who had already decided she was guilty? Hands up!”

  Thirteen hands went slowly and somewhat embarrassingly up, including the two substitutes.

  “You too, Stephanie?” I asked.

  “Yes, sorry, at first I thought she was guilty,” she replied. “Professor Sir Michael Goodwin is so well known. He’s got more initials after his name then there are letters in the alphabet. And in my line of business when a med
ical professor speaks, his word is gospel. And how can you not vote guilty if you are told the odds of natural deaths are 72 million to one?! Even if you just can’t believe a mother would do that to her children.”

  “Eleven to one would have led to a majority vote of guilty,” said David. “That poor lady would have spent most of the rest of her life in prison. Not only did she have the tragedy of losing her two sons, each of us would have contributed to the second tragedy of wrongfully convicting her. We have so narrowly escaped a travesty of justice. Thanks, Martin, for not letting us do that! What luck the judge let you cross-examine that professor.”

  “Even if I hadn’t been allowed to cross-examine,” I said, “I wouldn’t have let you leave this jury room until I had convinced each one of you of Goodwin’s manifest errors.”

  “Manifest to you, perhaps,” said David, “but not to us. It would have been Twelve Angry Men all over again!”

  “Twelve Angry Men and Women!” added Hilary. “I hope you would have succeeded Martin. Thank you for stopping me sending an innocent woman to prison. Now let’s just hope she can begin to piece her life back together after all that has happened to her.”

  “For those who did at least some maths at school,” I said, “I would have hassled you with Bayes’ theorem derived from simple first principles. This shows that the probability of two cot deaths is irrelevant; the only statistic that counts is the ratio of the probability of double murder to that of double cot deaths. That’s the crux of the prosecutor’s fallacy. Even you would have understood it, David!”

  “Thanks, Martin,” he replied sarcastically, but with a chortle.

  “Hang on,” I added in my enthusiasm, “I worked out the Bayes’ equation for this situation late last night.”