Michael Graham Richard

Image: MiG 19. Public Domain.

The base-rate fallacy happens when available statistical data is ignored in favor of specific data to make a probability judgment.

The C.I.A. gives this example to illustrate the problem:

During the Vietnam War, a fighter plane made a non-fatal strafing attack on a US aerial reconnaissance mission at twilight. Both Cambodian and Vietnamese jets operate in the area. You know the following facts:

(a) Specific case information: The US pilot identified the fighter as Cambodian. The pilot’s aircraft recognition capabilities were tested under appropriate visibility and flight conditions. When presented with a sample of fighters (half with Vietnamese markings and half with Cambodian) the pilot made correct identifications 80 percent of the time and erred 20 percent of the time.

(b) Base rate data: 85 percent of the jet fighters in that area are Vietnamese; 15 percent are Cambodian.

Question: What is the probability that the fighter was Cambodian rather than Vietnamese?

A common procedure in answering this question is to reason as follows: We know the pilot identified the aircraft as Cambodian. We also know the pilot’s identifications are correct 80 percent of the time; therefore, there is an 80 percent probability the fighter was Cambodian. This reasoning appears plausible but is incorrect. It ignores the base rate–that 85 percent of the fighters in that area are Vietnamese. The base rate, or prior probability, is what you can say about any hostile fighter in that area before you learn anything about the specific sighting.

The correct way to do this is to use Bayesian reasoning:

If we suppose that there are 100 enemy fighter planes total, that means that 85 are Vietnamese and 15 are Cambodian.

From paragraph (a), we know that the eye-witness identifies correctly enemy planes 80% of the time, so out of 85 Vietnamese planes, he would identify 68 correctly (85 * 0.80 = 68) and erroneously identify 17 (85 * 0.20 = 17).

Out of the 15 Cambodian aircrafts, he would identify correctly 12 of them (15 * 0.80 = 12) and be mistaken about 3 (15 * 0.20 = 3).

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Photo by Charles R. Kaiser, original here. Creative Commons license.

The planning fallacy is simply the human tendency to underestimate task-completion times. Finding real-world examples of this cognitive bias is easy, from the smallest everyday task to huge governmental undertakings.

One side effect of badly estimating task-completion times is cost overruns; if something is going to take longer than planned, you often have the option of throwing more resources at it in the hope that it will be done on time. One example of this is the Canadian gun registry program:

The project which was meant to cost approximately $119 million ended up costing over a billion dollars to implement. Documents obtained by the Canadian Broadcasting Corporation now estimate the program cost at $2 billion.

The way I see it, part of the cause of this problem is the fact that humans are very goal-oriented, and so when we try to visualize what is involved in executing a task, we focus on what is most important with regard to reaching goals. This can often mean that we overlook less important parts of the process that are nonetheless time-consuming.

What’s important to reach goals and what’s time-consuming are rarely in perfect overlap.

An example might be someone who’s thinking about going to the store to get some food. That person might try to estimate the time it will take by visualizing getting in the car, driving to the store, picking up pasta boxes, some fresh vegetables, etc. But there are many other elements in the process of getting food at the store that aren’t as important from a goal perspective but that can take quite a bit of time; waiting at red lights on the road to the store, walking around the store to locate the items that we want to buy, waiting for minutes in line to pay for items, walking to and from a vehicle in the parking lot, etc.

For repetitive tasks such as going to the store, we usually avoid the problem by using our past experience as a guide. How long does it usually take to go the store? That’s usually a good estimate.

But for one-off tasks, we can’t rely on past experience and so we should be particularly careful about the planning fallacy, especially if the task is complex and requires concerted actions by many people.

This might all seem very obvious, and yet this is still a frequent problem at all levels, from individuals to corporations and governments. We all pay for wasted resources and cost overruns via higher product prices and higher taxes.

Source: Planning Fallacy at Wikipedia

See also: Rationality Resources

This one is fairly simple. The conjunction fallacy occurs when it is assumed that multiple 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:

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 likely?

1. Linda is a bank teller.
2. Linda is a bank teller and is active in the feminist movement.

85% of those asked chose option 2.

The “and” in number two is very important, because it is the addition of those two conditions that make it both more specific and less likely than number 1.

This can be proven mathematically:

Translation: Conditions A & B, when taken together as they are in the middle of the equation, are less probable than A or B when taken alone, as in the extremities of the equation.

So if we go back to our example, this means that if there is a 50% chance that Linda is a bank teller and a 95% chance that she is active in the feminist movement, choice #1 has a 50% probability of being true and choice #2 has a 47.5% probability of being true (0.5 * 0.95 = 0.475).

Tversky and Kahneman argue that most people get this problem wrong because they use the representativeness heuristic to make this kind of judgment: Option 2 seems more “representative” of Linda based on the description of her, even though it is clearly mathematically less likely.

This representativeness heuristic makes us see things that are more specific as more likely, which can partly explain why good fiction (and good lies) contain many specific and telling details. Mathematically, a simpler, more general proposition has more chances of being true, but seen through our biased mental lens, more detailed and specific propositions seem more probable.

This heuristic pattern has probably evolved with time because it is usually considered harder to make up specific details than general ones, so looking for these extra specificities was a good way to assess the veracity of someone’s claims.

Source:

• Conjunction Fallacy at Wikipedia
• Conjunction Fallacy at Overcoming Bias

See also: Rationality Resources

Also known as the Gambler’s Fallacy, the Monte Carlo Fallacy is simple: It’s the belief that the likelihood of a random event is influenced and/or predicted by other independent events.

For example: Someone who flips a fair coin 10 times and gets “heads” on all tries, who then thinks that the likelihood of getting “tails” is now higher than a 50% chance.

It is not.

Each coin flip is independent, and the odds the same (50% for each side) each time, even if a whole sequence of coin tosses can be described as low probability (the odds of getting 11 “heads” in a row are 0.00048828125, or (1/2)^11, but the odds of getting “heads” once you already have 10 “heads” are 0.5).

The gambler’s fallacy often takes one of these forms:

* A particular outcome of a random event is more likely to occur because it has happened recently (”run of good luck”);
* A particular outcome is more likely to occur because it has not happened recently (”law of averages” or “it’s my turn now”).

Similarly

* A particular outcome is less likely to occur because it has happened recently (”law of averages” or “exhausted its luck”);
* A particular outcome is less likely to occur because it has not happened recently (”run of bad luck”).

A more subtle version of the fallacy is that an “interesting” (non-random looking) outcome is “unlikely” (eg that a sequence of “1,2,3,4,5,6″ in a lottery result is less likely than any other individual outcome). Even apart from the debate about what constitutes an “interesting” result, this can be seen as a version of the gambler’s fallacy because it is saying that a random event is less likely to occur if the result, taken in conjunction with recent events, will produce an “interesting” pattern.

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