From Wiki:
The conjunction fallacy is a logical fallacy that occurs when it is assumed that specific conditions are more probable than a single general one.
The most oft-cited example of this fallacy originated with Amos Tversky and Daniel Kahneman [1]:
- Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.
- Which is more probable?
- Linda is a bank teller.
- Linda is a bank teller and is active in the feminist movement.
85% of those asked chose option 2 [2]. However, mathematically, the probability of two events occurring together (in "conjunction") will always be less than or equal to the probability of either one occurring alone.
Thus is the brain seduced by detail. All writers know this fact. Which works best: "Dick wore a hat." or "Dick wore a green felt hat with a pheasant-feather hatband."
One of my favorite sites to visit, Overcoming Bias, wonderfully discusses When not to use probabilities. He says:
The laws of probability are laws, not suggestions, but often the true Law is too difficult for us humans to compute. If P != NP and the universe has no source of exponential computing power, then there are evidential updates too difficult for even a superintelligence to compute - even though the probabilities would be quite well-defined, if we could afford to calculate them.
So sometimes you don't apply probability theory. Especially if you're human, and your brain has evolved with all sorts of useful algorithms for uncertain reasoning, that don't involve verbal probability assignments.
Those algorithms are "gut feelings." Often wrong, often accurate. There is one thing that I know for certain: the more time I have to think about how to hit a tennis ball, the more likely I am to blow the shot. He also says:
In general a rationalist tries to make their minds function at the best achievable power output; sometimes this involves talking about verbal probabilities, and sometimes it does not, but always the laws of probability theory govern.
If all you have is a gut feeling of uncertainty, then you should probably stick with those algorithms that make use of gut feelings of uncertainty, because your built-in algorithms may do better than your clumsy attempts to put things into words.
