Reason for a New Age

The Strength of Evidence

Posted by publius2point0 on 2010/03/21


In my time on the internet, I have met many a person who is a denialist or conspiracist and argued with them. Generally, their rather odd beliefs seem to come from a basic misunderstanding of how evidence works. I often get the feeling that many people don’t, in fact. This is why OJ Simpson was able to go free most likely.

Say that you are on the jury for a murder trial. George is the defendant, accused of murdering Janet in her apartment.

One eye witness says that he saw a brown-haired man running from the scene of the crime. George is, indeed, brown haired. The defending attorney, however, points out that most men have brown hair and so this is meaningless. He also will point out that eye-witness testimony is wrong a significant amount of the time.

The detective who pursued the case takes the stand and points out that George owed money to Janet and so had a motive for killing her. The defending attorney, however, points out that almost everyone owes money to someone, and almost never does it lead to murder.

The detective also points out that the angle of the wound indicates that the attacker was a person of George’s general height. But of course, all that really tells us is that the criminal was probably male, since most men are George’s general height.

None of these items of evidence is particularly compelling. All of them could be tossed away for being too non-specific to be of any practical value. But that’s if you are taking them as individual elements.

Let’s say that 50% of all people (in modern America) have brown hair. For a woman to be murdered in her own home, it’s most likely that she knew her attacker. Say, 90% of the time, it will have been someone she knew. Janet probably knew maybe two dozen people, at most, who would know her and care enough to kill her. 90% of the time, the murderer is going to be one of those two dozen, not some unknown stranger. Of those, only one dozen will have brown hair. Only half of everyone she knows will be male, so there’s only six people of those she knows who probably killed her. Of those, only one had a motive. If I know that 90% of the time two people who know each other have no reasonable motive to kill one another, our six possibilities are strongly cut down to just George.

Does this mean that George killed her? Of course not. But, the evidence is actually fairly decent–probably something around 85% just from what we have (depending on how much weight you want to give to inaccuracies of testimony and so forth).

People have a tendency to not combine information into a cumulative whole, though. If I say that 50% of everyone has brown hair, many people will say that this still leaves half the population of the world. They say that it’s meaningless because the number of people that it leaves as possibilities is so large that it’s silly to give it weight. And so they throw it away. They find out that the attacker was probably male. Again, this is 50% of everyone on the planet. That it is only a “probably” simply makes that statistic worse, meaningless, and so they throw it away.

Most evidence, in life, doesn’t work based on a smoking gun. You use subtle clues to chip away and slowly reduce down to a single possible answer. Being able to point out that it’s possible that there was a different man with brown hair, that a tall woman or a different grip couldn’t have produced the same wound, and so on and so forth doesn’t disprove anything because evidence isn’t taken on an item by item basis. The question isn’t what is the odds that a woman would be tall, but rather, what are the odds that a tall woman would have brown hair, a motive to kill Janet, and not have been discovered by the police in their investigation? Is that really more likely than that it was George who did it?

http://en.wikipedia.org/wiki/Prosecutor%27s_fallacy

http://en.wikipedia.org/wiki/Conjunction_fallacy

http://en.wikipedia.org/wiki/Neglect_of_probability

http://en.wikipedia.org/wiki/Base_rate_fallacy

http://en.wikipedia.org/wiki/Subadditivity_effect

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