Prosecutors Fallacy

The arguer relies on the base rate (prior probability) of an action taking place.

• ex. - a lottery winner is accused of cheating, based on the improbability of winning. At the trial, the prosecutor calculates the (very small) probability of winning the lottery without cheating and argues that this is the chance of innocence. The logical flaw is that the prosecutor has failed to account for the large number of people who play the lottery. While the probability of any singular person winning is quite low, the probability of any person winning the lottery, given the number of people who play it, is very high.

• ex. - DNA is found at a crime scene, and it is run through a database of 20,000 men. A match is found, and it is found that the probability that 2 DNA samples match by pure chance is only 1 in 10,000. This does not mean the probability that the suspect is innocent is 1 in 10,000. Since 20,000 men were tested, there were 20,000 opportunities to find a match by chance. Even if none of the men in the database left the crime-scene DNA, a match by chance to an innocent is more likely than not. The chance of getting at least one match among the records is 86%.

• ex. - Suppose there is a one-in-a-million chance of a match given that the accused is innocent. The prosecutor says this means there is only a one-in-a-million chance of innocence. But if everyone in a community of 10 million people is tested, one expects 10 matches even if all are innocent. The defense fallacy would be to reason that "10 matches were expected, so the accused is no more likely to be guilty than any of the other matches, thus the evidence suggests a 90% chance that the accused is innocent." :)

• Always be suspicious of the reasons why you know something. Get in the habit of making Flash analyzations about your assumptions and where they come from

  • ex. - belief in God. logically, you should not base knowledge of what the apostles did, since if the proof upon which that was built (ie. the Bible) is fallible, then the logic for the apostles' actions is immediately shakey. This illustrates the importance of having high confidence in the logic upon which you base further logic (and so on)
    • this visualization can be thought of as asking the question "why? why? why? why? why? why? why? why? why?" in order to arrive at the root reason of why something is in the first place.

• Be skeptical anytime 2 different people have used the same methods to arrive at entirely different conclusions

  • Most religions have the same method of reasoning, yet they all arrive at different conclusions.