Category Archives: Motive

Reasoning about probability

There are many ways to approach the thorny issue of “reasonable doubt“.

Jury instructions may give guidance in this way:

“The State has the burden of proving the defendant guilty beyond a reasonable doubt. This means the State must prove each element of each charge beyond a reasonable doubt. In civil cases, it is only necessary to prove that a fact is more likely true than not or that its truth is highly probable. In criminal cases such as this, the State’s proof must be more powerful than that. It must be beyond a reasonable doubt. Proof beyond a reasonable doubt is proof that leaves you firmly convinced of the defendant’s guilt. There are very few things in this world that we know with absolute certainty, and in criminal cases the law does not require proof that overcomes every doubt. If, based on your consideration of the evidence, you are firmly convinced that the defendant is guilty of the crime charged, you must find her guilty. If, on the other hand, you think there is a real possibility that she is not guilty, you must give her the benefit of the doubt and find her not guilty.”

Estimates suggest that about 5% of people convicted and sentenced to death are innocent, meaning juries are regularly making mistakes, thinking a case for guilt has been proved beyond a reasonable doubt when this is not the case.

The reasons for these errors are undoubtedly complex and varied, but here I want to concentrate on fallacious reasoning about probability. Sometimes people talk about “too many coincidences”, when I hear that claim I immediately suspect fallacious reasoning.

How should a jury deliberate? Well, it would be good to reduce that error rate from 5% to a more acceptable rate, let’s say 1 in 1,000. That would be 500 times better than the current rate, and a significant improvement.

So let’s say we will convict if the chance of innocence is less than 0.1%, recognising that we cannot overcome every doubt. To put it another way, the probabilty of guilt should be more than 0.999.

But how can we estimate this probability in a rational way?

One thing to beware of is something known as the “prosecutors fallacy”.


At its heart the fallacy involves assuming that the prior probability of a random match is equal to the probability that the defendant is innocent. For instance, if a perpetrator is known to have the same blood type as a defendant and 10% of the population share that blood type, then to argue on that basis alone that the probability of the defendant being guilty is 90% makes the prosecutor’s fallacy (in a very simple form).

The basic fallacy results from misunderstanding conditional probability and neglecting the prior odds of a defendant being guilty before that evidence was introduced.

In other words, we must look at the “prior odds” of a defendant being guilty.

Let’s take a concrete example, the case of Jodi Arias. This may have looked like a simple case to a casual observer. Travis Alexander’s body was found dead in the shower at his home in June 2008. He had been shot in the head and stabbed repeatedly. Photographs recovered from a camera that was found in the washing machine showed Arias had visited Alexander on 4 June 2008, and pictures taken by the same camera showed Travis in the shower, around 5:30pm and then just a minute later, lying on the flood bleeding. Moreoever blood recovered from the scene contained a mixture of Arias’ DNA and Alexander’s DNA. However Arias when questioned first denied having visited Travis, then when shown the photographs claimed that intruders had appeared and shot and killed Alexander.

Finally she claimed that she had acted in self defence, that Alexander had become angry after she dropped his camera, and he had been shot after he assaulted her, then chased her, and she pointed a gun at him to keep him away ( explaining that she had squeezed the trigger without meaning to ). After he was shot, she claimed to be unable to remember very much about what happened, other than an overwhelming sense of fear.

The prosecution asserted that Arias’ account was untrue, and that Arias had travelled to Mesa with the intention of killing Alexander, evidenced by measures she took to keep the visit secret.

At first sight the defense case seems highly improbable. Why would Arias not have immediately told the police what happened if she acted in self defense? Why would Alexander become violent simply because she dropped his camera? And how if she was defending herself, could she have stabbed Alexander so many times, ultimately slashing his throat? And how could she have almost no memory of what happened after Alexander was shot?

Here there is a danger of what I would call a “lack of imagination”. The universe is full of events that are hard to comprehend, which may seem unusual, paradoxical and unlikely. For example, how did life start? Life is very complex, and it is hard to comprehend how such complex assemblies of atoms could come together by chance.

But we should also consider the prosecution version of events. The prosecution claimed that Arias had concealed her trip to Mesa, and there was circumstantial evidence to support this hypothesis. Travis was shot by a 0.25 caliber bullet, and  a 0.25 caliber gun had been stolen from Arias’ home seven days earlier. Secondly Arias had borrowed two gas cans from a friend, and bought a third gas can, and there was no record of her buying gas while in Arizona. Thirdly, Arias had turned off her mobile phone shortly before entering Arizona, perhaps in an effort to conceal the visit. Finally, when Arias was stopped by a policeman in Salt Lake City the day after Travis was killed, one of her licence plates was upside down, and the other was missing ( it was inside her car ). Could all this evidence of premeditated murder simply be a series of coincidences?

A reasonable person might easily conclude that this is overwhelming evidence of guilt. Firstly Arias’ denials, and secondly circumstances suggesting that she took measures to keep her visit to Mesa secret.

There is one big, massive problem here though. It can be expressed as a single word : why? Why would Arias want Alexander dead, and be prepared to risk ruining her life by being convicted of his murder?

In other words, the “prior odds” mentioned above are massively AGAINST Arias being guilty.

So, now to the question of how we could estimate the probability of guilt in the case, based only on the evidence given above.

There is no real doubt that Arias did kill Alexander. Firstly she testified that she killed him. Secondly her story that intruders appeared at the moment when Alexander was shot is not credible.

But is it possible that she was first attacked by Alexander? If there is a fight between two people, it’s reasonable to suggest that either could have started the fight, from that perspective, the chance that Arias is guilty is only 0.5.

The big issue here though is the improbability, before the evidence is considered, that Arias planned to murder Alexander. Planned murder is a very serious criminal offence, and very rare as well. Looking at women on death row in the United States, or the history of crime, there are almost no cases that could be said to be similar examples, where a woman has planned many days in advance to murder a man for no credible reason.

There was apparently no financial motive – although Arias did owe Alexander some money, it was not a large sum, and few people have even suggested that as a motive. Instead, the suggestion is that Arias may have acted due to feelings of jealousy or rejection. It is not unusual for men to murder women for this reason, especially at the end of a relationship. However cases of women murdering men for this reason seem much more unusual, and there seem to be no precedents for a woman who was not even living with the man at the time, and who had no reason to feel unreasonably rejected, to have embarked on murder.

From this perspective, the likelihood that Arias is guilty of murder planned a week or more ahead is very, very low, perhaps 1 in a million, or even 1 in a billion, perhaps even less, depending on your point of view.

So, the question then becomes, do the apparently improbable suspicious circumstances suggesting Arias concealed her trip to Mesa, combined with the apparent improbability of the defense case,  mean that it is very probable this is premeditated murder?

Let’s be generous to the prosecution here. Firstly, let’s say that the chance of such a suspicious event such as the theft of a gun of the correct caliber from Arias’s home a week before the murder is quite small. Perhaps 1 in 100. There is a problem here, in that the universe of possible “suspicious events” is very large. What if the theft had been two weeks before? That would presumably still be suspicious. What if the theft had been from the house next door, would that be suspicious? This consideration must tend to reduce the weight of this circumstance.

Now what about other circumstances? Well, I suggest that the other circumstances are really not at all conclusive. It is not unusual to switch a mobile phone off to save the battery. Paying for gas with cash is perhaps unusual ( which is what Arias claimed ). However having irregular license plates seems more likely to attract attention than be part of a plan of concealment, and the explanation Arias gave that pranksters were responsible seems more plausible to me.

So let’s take stock. Taking a view favorable to the defence:

Arias’ final story is in fact quite possible, with some imagination.

Likelihood that Arias planned the murder a week in advance for some very unusual reason : 1 in a billion.

Likelihood that the gun theft and other circumstances are just coincidences : 1 in a thousand.

Likelihood that Arias is guilty : only 1 in a thousand. Not nearly enough for a conviction.

Of course this process has been massively subjective. It is a matter of opinion how improbable the circumstances are, how improbable the defense case is, or how improbable it is that Arias is capable of premeditated murder planned a week in advance.

This is not the end of the matter though. There is a lot of evidence that has not yet been taken into account. The purpose of this article was to show the danger of believing the “too many coincidences” argument. We must not consider only circumstances that make the prosecution case seem likely, the general improbability of the prosecution case must also be taken into account.

I believe this is where juries mostly go wrong. There are numerous examples of defendants being convicted in spite of having a solid alibi. Many juries seem blind to exculpatory evidence or circumstances, and perhaps do not understand the idea of prior odds.

[ Please see here for a much more complete description of the evidence in this case ]

See also How juries are fooled by statistics a TED talk by Peter Donnelly.


Murder is:

1. Deliberately killing a particular person, without justification.

Example: a man is angry that another man has damaged his property. He takes a gun and shoots him.

2. Deliberately killing any person without justification.

Example 1: a terrorist plants a bomb in a shopping centre, it explodes killing several people.

Example 2: a man is angry that another man has damaged his property, he takes a gun a shoots a person, but it turns out to be someone else.

Murder may be:

3. Committing a crime, in the course of which someone is killed ( Felony murder ). Applies in some countries only.

Example: a man robs a bank, a police officer dies chasing after the robber.

Murder is not:

4. When a person kills in the belief that he is acting lawfully to defend himself and/or others.

Example 1: a man hears a burglar enter his home at night. He takes a gun and shoots the burglar.

Example 2: a man thinks he hears a burglar enter his home at night. He takes a gun and shoots the person, but it turns out the person is not a burglar.

Example 3: a police marksman shoots a terrorist in the belief that the terrorist is a danger to the public.

Example 4: a police marksman shoots an innocent man in the wrong belief that he is a danger to the public.

5. When a person kills someone without meaning to.

Example: a driver fails to see a pedestrian and runs him over.

In cases 4 and 5 there may still be a crime (manslaughter), if the killer was negligent in not acting with sufficient care, reckless behaviour, but it is not murder.

Note: the belief/intention of the killer is important, as well as the physical act, this idea is referred to by the Latin term “Mens Rea” meaning “the act is not culpable unless the mind is guilty”.

Reform / difficult cases


The Law Commission’s report on Partial Defences to Murder rejects the notion of creating a mitigatory defence to cover the use of excessive force in self-defence, but accepts that the “all or nothing” effect can produce unsatisfactory results in murder cases. For example, a battered woman or abused child using excessive force because they are physically at a disadvantage and not under imminent attack, would be denied a defence. Further, an occupant not sure if violence to defend their property against invasion is reasonable, may feel forced to do nothing. It was always possible the same set of facts could be interpreted as either self-defence or provocation where there was a loss of control resulting in death. Thus, the Commission recommends a redefinition of provocation to cover situations where a person acts lethally out of fear. This reflects the present view of psychiatrists that most people act in violent situations with a combination of fear and anger in their minds, and to separate the two emotions is not legally constructive.


Someone subjected to unlawful threats, and who kills out of fear of future violence, should be charged with manslaughter and not murder, where their actions were not entirely lawful. Sentencing should fully take into account the level of provocation and steps the accused person took to lawfully resolve the situation before killing out of fear.

See also What is Murder ?

Homicide classification

This is an attempt to classify homicides into different categories. Elements of section 5, mental illness, may contribute to the other categories.

1. Fights and disputes

A common type of homicide. An argument or dispute breaks out, leading to fighting. If weapons are to hand homicide becomes a real possibility. There is no rational motive – such as financial gain. There will likely be elements of self defense ( “he picked up a knife so I shot him” or “I thought he had a gun so I shot him”).

1.1. Fights between intimate partners, or ex-partners.

Common is for abusive, violent boyfriends to kill their partners, after being rejected, when the girlfriend is leaving.

Sometimes one partner kills the other for financial gain, typically during a divorce.

Sometimes women kill their partner in self defense.

Occasionally abusive, violent women kill their partners.

1.2. Other fights and disputes

Often alcohol or drug related, or disputes over property, noise, annoyance. Usually not premeditated.

Revenge killings. Honor kilings.

2. Homicide related to burglary, robbery, drug crime

During home invasions, robbery of stores or other properties.

Elimination or witnesses, homicide while evading capture following a robbery or other crime.

3. Other homicides for financial ( or similar gain )

Neglect or murder of step-children

4. Homicides for a political motive

Terrorism, political extremism.

5. Homicides due to mental illness / mental incapacity ( taken broadly )

Paranoia ( schiophrenia, or due to PTSD )

Depression ( murder-suicide, infanticide )

Extreme child neglect / bad parenting.

To be continued, first draft.

Jodi Arias’ motive for murder, according to the penalty retrial jury

Jodi premeditating murder?

Jen Wood of Trial Diaries has published an interview with the jury foreman in the penalty retrial. This statement particularly caught my eye:

We once again discussed how Jodi made phone calls just hours after murdering Travis and even went to see Ryan Burns. Most of us felt Jodi had to get rid of Travis Alexander so she could move on. Juror 17 agreed with this theory as a motive.

Is this a realistic motive for murder?

Firstly, it is not the motive offered by the prosecution, which was apparently that Jodi was jealous that Travis was not taking her to Cancun for a Pre-Paid-Legal conference.

Instead, the idea seems to be more: “Travis made Jodi miserable, and abused her, so she murdered him.”

I can see why they would come up with this theory, there was evidence that Jodi was miserable, and evidence that Travis was abusive, but I don’t think it has any precedent in the history of crime. Of course, the prosecution would not like this motive as it would concede that Jodi was abused.

In a way it has some truth : Jodi killed her abuser. Abused women sometimes kill their abusers to escape from them (with their children), or in self-defense when attacked.

However Jodi HAD escaped already, sitting in Yreka in complete safety. So like all the other motives for premeditated murder, it really doesn’t fit with the idea of murder premeditated by a week.

If Jodi wanted to move on, all she needed to do was to go and see Ryan!

It is not the fault of the retrial jury that they settled on such a preposterous and implausible motive, the alternatives are equally implausible. They must surely have been very puzzled. Their job of course was not to assess guilt, but accept the original verdict.

Jodi escaped death row, but it was apparently a chance event, a juror who didn’t see death as appropriate in this case. The difficulty for any innocent defendant in a penalty phase is the impossibility of showing remorse, this was picked up by the jury as an important factor, even though Juan may have been precluded from arguing it.

And that’s the memo. On to the appeal process to Free Jodi!

Good and bad

Some days I get a little depressed when I see so many injustices and feel so powerless. I need to have more faith when I am weak. There are many good people in the world, and a few very bad people. It’s truly odd how people sometimes can confuse the two. Bad people do not come from nowhere, they have a history. But people fail to understand this.

What is Murder ?

It seems to be that the general public, and indeed many people who should know better, often fail to understand the meaning of this ancient word.

Murder is the unlawful killing, with malice aforethought, of another human, and generally this premeditated state of mind distinguishes murder from other forms of unlawful homicide (such as manslaughter). (Wikipedia)

The key point that is often overlooked is “malice”. Malice implies some motive for personal gain, for example to eliminate a witness to an earlier crime, robbery, financial gain, to escape capture or to take revenge for some percieved wrong.

I believe people often only focus on the physical act  (“actus reus”) and forget the essential mental element (“mens rea”).

In law, the prosecution is generally not required to prove motive, but I sometimes wonder if this is a big mistake. If no rational, malicious motive can be established, then should we call a killing murder at all, but instead declare it to be manslaughter?

In the case of Oscar Pistorius, the South African authorities have opted to appeal the conviction for manslaughter, asserting that a murder verdict should have been returned. But it is abundantly clear that Pistorius had no malicious motive, he simply made an extremely tragic error, using force that was not justified, due to an irrational fear. There is no need for further analysis.

Similar considerations apply to women who have reacted with excessive, disproportionate force in situations where they have become terrified for psychological reasons. A person acting out of fear, should never be charged with murder, however unreasonable their actions may be, if a malicious motive is not evident.

That’s the memo.

See also Instrumental versus Expressive violence

Women don’t kill unless

Women (acting alone) don’t kill* (except to defend themselves or others) unless they have some MAJOR problem ( like drug addiction, severe depression or other severe mental illness, history of abuse ) or a strong MOTIVE ( typically financial or other material gain, or in crimes of passion, betrayal ).

Exclusions: Acts of War or Political Intrigue.

* By “kill” I mean kill another person or persons.

Counter-examples welcome here or here, but please check all conditions are satisfied.

List of non-counter-examples:

There was a comment:

Not at all true, women are just as evil as men when it comes to murder. See:…/8-sensational-female-murderers… ] Add to that Karla Homolka; Aileen Wuornos; Rosemary West; The “Blood Countess” Elizabeth Bathory; Lizzie Bordan; and Bonnie Parker of “Bonnie & Clyde” infamy.

Working through the list of 8:

1. Marie de Roux Manning : did not act alone, motive was financial or material gain.

Over the next two days, Marie cleaned out what valuables, cash, and stock certificates she could find at O’Connor’s home.

2. Constance Kent : is about as clear as mud, was 16 years old, and may have had the motive of competing against step-siblings.

3. Belle Gunness : financial motive.

4. Dagmar Overbye : financial motive ( paid to care for babies, murdered them instead ).

5.Jane Toppan : insane multiple poisoner. Found not guilty by reason of insanity, and was held in a mental institution for the rest of her life.

6. Mary Ann Cotton : murdered husbands, step-children ( motive, to favour her own interests ).

7. Amelia Dyer : another baby-farm murderer, financial motive.

8. Tillie Klimek : poisoned husbands for insurance money.

And the others:

1. Karla Homolka : didn’t act alone.

2. Aileen Wuornos : unusual serial self-defence claim, history of abuse.

3. Rosemary West : didn’t act alone, history of abuse.

4. The “Blood Countess” Elizabeth Bathory : a legend (died 1614). Witnesses may have been coerced : “All but one of the Countess’s servants testified against her–the one who refused had her eyes gouged out and her breasts removed before being burned at the stake.”

5. Lizzie Bordan : not clear : acquitted.

6. Bonnie Parker of “Bonnie & Clyde” infamy : didn’t act alone!

See also Instrumental versus Expressive violence and Psychopaths and Serial Killers.

The search for the Femme Fatale ( a.k.a. Witch )

Femme Fatale
Pretty witch
Pretty Witch

Over many centuries, women have been put on trial, accused of “witch-craft“, or in more recent times of being a “Femme Fatale” – having the ability to control men and to commit heinous crimes for no plausible reason. Debra Milke has spent 23 years on death row in Arizona. On the flimsiest evidence, people are still readily convinced that an instance of this elusive woman has been found. A woman who leads a blameless life, but then one day turns into a savage, calculating murderer for no good reason. The evidence is just some vague suspicion : the actual killer makes a suggestion, not repeated in court. A burglary with nothing taken, a gun is stolen.

Let’s be clear : “Femme Fatale” is simply the modern word for “Witch”. It serves to make discussion more plausible, but no less irrational. How many billions of women have lived on the planet? Not one “Femme Fatale” or “Witch” has ever been identified with certainty. It is extraordinary that the myth lives on. Harry Potter is fiction not fact. Every child knows this.

In a witch-hunt trial, the prosecution focus on tiny details, remote from the scene of the crime – a missing mark on a receipt, a telephone call placed at an odd hour, a mobile phone switched off, a mobile phone switched on. These tiny signs are interpreted as evidence of the accused’s guilt. If something does not fit, it is because the accused has cunningly manipulated or cleaned the crime scene, with infinite foresight.The accused is cunning and intelligent one moment, but makes stupid mistakes the next. A single phrase is picked out from thousands of pages of writing, taken out of context. If no mark can be found, an expert is brought in to find what is not there using some contaminated source. Detectives and Doctors are called by the prosecution to give any testimony that is needed.

No expense is spared. When evidence is disproven, a search for fresh evidence is conducted. Above all, the witch is required to prove her innocence beyond every doubt, an impossible task. She is thought to be a great liar, somehow she has an answer to everything, but every explanation is deemed to be pure invention. A hundred reasons for suspicion are laid against her, if a single one cannot be innocently explained, in that instant, she is doomed. The more she struggles, the more she explains, the more scorn is placed on her efforts, the more she incriminates herself in the mind of the mob. The burden of proof is reversed, the woman is guilty unless she can prove herself innocent. A succession of trials may be held. The general public become prejudiced, because they only have to believe in one bogus piece of evidence to become convinced of guilt, and often the innocent explanation is never heard – suppressed in the general condemnation “why would anyone want to defend this woman”.

The demeanour of the accused is confirmation, looking into the eyes allows a diagnosis to be made. If she cries, these are tears of self-pity, guilt, or an act. If she doesn’t cry, she is cold-hearted. These gentle women are often described as frightened rabbits, caught in the headlights of a rampaging lynch mob. No mercy is to be shown, the lack of a criminal record counts for nothing. The mob insists on the maximum penalty available – solitary confinement, life imprisonment with no parole, execution. Some even call for the woman to be executed then brought back to life, to be killed again and again, subjected to every imaginable torture.

In fact these cases can and should be easily resolved by simply checking that the woman is non-violent and gentle with no criminal record. That should be sufficient proof of innocence. It cannot be stressed too much – a woman of this type does not, cannot, never has and never will commit heinous murder for some implausible reason, such as “freedom from parental responsibility”, “revenge” or “jealousy”. If a woman of this type is alleged to have killed someone, it is either an accident, self-defense or simply not true, it is never murder.

The witch-hunters are quite sincere in their mistaken beliefs. They are consumed by the fear that the accused might escape punishment, even as they are aware of her charming appearance. I believe it is some kind of psychological imbalance – they know they must not be influenced by the pretty girl, but over-compensate, and ignore the obvious evidence in front of them. They genuinely do not want to believe, but they feel it is some civic or religious duty, and they really do believe. They are locked into a state of confirmation bias, oblivious to the lack of decisive evidence.

Any witness who might support the accused is attacked, threatened with death, perjury and slander charges, until nobody will testify for her out of fear. Anything can be twisted, because the end justifies the means, her guilt is never doubted.That is the tragedy. Once can forgive the family of the person who has died, grief clouds judgement. But people who administer justice should know better. In the internet age, the odds against the accused are even more staggering, with social media used to manipulate thousands of dedicated haters in an instant.

All the parties are losers – especially the accusing family, their faces twisted with mistaken hate, as they dedicate their lives to the futile hunt, refusing to even hear the accused. The prosecutor storms and rants, displaying any gruesome photographs available. He argues maybe this, perhaps that. The jury is cowed into the fear of error, openly weeping with horror, confusion, stress and exhaustion as they reach their verdict. Even the judge may weep openly in court, her face twisted with conflict, convinced of the witch’s guilt, but determined not to allow any avenue of escape.

You may not believe that the search for the Femme Fatale is still pursued using Witch-hunts in the Western world, but consider the following quotes:

“Death-row Debbie: No one wanted to believe she could kill her child” Paul Rubin, Wednesday, Apr 10 1991.

“We knew she was guilty of murder without physical evidence.” Edgardo Giobbi, Investigator, November 2007.

Raffaele Sollecito had probably given her that knife for reasons of self-defense, a knife which she could transport in her capacious purse.” Motivations report, Giancarlo Massei, March 2010.

“She was a diabolical, satanic, demonic she-devil. She was muddy on the outside and dirty on the inside. She has two souls, the clean one you see before you and the other.” Carlo Pacelli, September, 2011.

“The word “probable” (or “improbable”) occurs some 39 times in the course of the motivation.” Presiding Judge Dr. Hellman, Motivation report, December 2011.

“I really hate to be saying that she is guilty but sadly, she is as guilty as it gets.” Donald Trump, May 3, 2013.

“Alyce LaViolette, she had a motive to lie. I mean, um, maybe perhaps it was her reputation that she was interested in, or things like that.” Juan Martinez, closing argument, May 3, 2013.

“If you believe what the defendant is telling you, then all of these arguments then do begin to make sense.” Juan Martinez, closing rebuttal, May 4, 2013.

“I don’t have all the information, but I think she’s guilty.” Governor of Arizona, Jan Brewer, May 7, 2013.

God gives us big warning signs that something is very wrong with people. That witchcraft thing was it.” – Nancy Grace

On 8th May 2013, Jodi Arias was found guilty of premeditated first degree murder. The jury was not sequestered.The televised show trial broadcast nightly to millions of Americans was nothing less than pornography, thrilling the audience with the possible execution of an innocent Christian woman, the modern day version of the Christian martyrs slaughtered in the Colosseum. There was no attempt at fair, balanced coverage, the defense case was never fairly discussed in the live coverage. Cheerleaders for the prosecution were feted, the occasional supporter was mocked mercilessly, after showing just a few hand-picked seconds, while jurors followed the public mood on twitter in the jury room.

Please see also:

“Men, it has been well said, think in herds; it will be seen that they go mad in herds, while they only recover their senses slowly, and one by one.” Extraordinary Popular Delusions and the Madness of Crowds, Charles Mackay, 1841.

Extraordinary Claims Require Extraordinary evidence – Carl Sagan.

A version of this article was also published at ground report in June 2013

See also: