The Probability of The Fallacies of Weak Induction Discussion
I’m working on a philosophy question and need an explanation and answer to help me learn.
Human beings are for some reason very bad at inductive reasoning. Our instinctive estimate of a probability often does not match the mathematically correct estimate. Here are some of the most common errors that people are prone to make.
- The Conjunction Fallacy. The probability of two propositions A and B both being true is the probability of A being true times the probability of B being true. In other words, A & B is less likely to be true than either A or B on their own. Yet experiments have shown that most people believe the reverse.
- Gambler’s Fallacy. This is the fallacy of believing that probabilities that are in fact independent (like spins of a roulette wheel) are in some mysterious way dependent, hence that bad luck will be balanced out by good luck.
- Estimating Coincidences. People are prone to underestimate coincidences, especially when the number of cases is very large. Hence they often interpret things as miraculous or “spooky” which are in fact perfectly predictable
- Generalising from a small sample. It is always risky to generalise from a small sample. (This follows from the law of large numbers.) Statisticians usually recommend a sample of no fewer than 400.
- Generalising from a unrepresentative sample. A sample should not only be sufficiently large but also representative (these are not necessarily the same thing). The only safe way of obtaining a representative sample is through “randomisation”.
- Self-selecting polls. Polls which only volunteers take part in (such as TV call-ins or focus groups) are for obvious reasons not representative of the population as a whole, and therefore of little or no value.
- P conditional on Q is not the same as Q conditional on P. Pick an Exeter student at random, and there is a 4/5 chance that he or she will be British. But pick a British person at random, and there isn’t a 4/5 chance that he or she studies at Exeter.
- Base-rate fallacy. When estimating the probability of P given some piece of evidence E, you have to take into account the probability of P on its own (or the “base-rate” of P). If this is very low, it is unlikely that E will make much difference. Failure to grasp this is known as the “base rate fallacy.”
- Confusing Correlation and Causation. The fact that P and Q are correlated (i.e. often occur together) does not necessarily mean that P causes Q. Q might cause P. Or they might both be caused by some third thing R.
- Confirmation Bias. If we have a hypothesis or a fixed belief, we tend to focus on evidence that confirms it, and ignore evidence that goes against it. This is how stereotypes are perpetuated in the face of contradictory evidence.
Prompt
Identify a news story or current event that demonstrates a fallacy of weak induction. Identify the fallacy and explain how it can be avoided. This is a similar discussion to one you have already done, but focuses on inductive rather than deductive fallacies. Remember, fallacies are mistakes in reasoning that should be recognized and avoided. For your responses, express ways in which a similar but more logical argument can be made to express a similar point or try to reframe one of your peer’s arguments to express a similar point but avoids fallacious reasoning.
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