Beware the fisherman who's casting out his line
Into a dried up river bed
But don't try to tell him 'cause he won't believe you
Throw some bread to the ducks instead, it's easier that way
Feel like an alien, a stranger in an alien place
Saturday 11 January 2014
Song of the Day - Heathaze
Beware the fisherman who's casting out his line
Into a dried up river bed
But don't try to tell him 'cause he won't believe you
Throw some bread to the ducks instead, it's easier that way
Feel like an alien, a stranger in an alien place
Friday 3 January 2014
Probability in TV and Economics
In TV, nothing proves how clever you are than spouting off probabilities. "I estimate a 75.2% chance of destruction!" cries Mr Spock when encountering some new alien, or perhaps "There's a 30% chance he's guilty" from a university boffin on a show like Numb3rs. There's just one problem with this: it's complete and utter bollocks.
The problem is that in real world complex situations, there is basically no way of accurately estimating probabilities. In situations where the rules are simple and known, probabilities can often be calculated, but when you move to a situation where a lot of information is hidden, estimated probabilities are more or less meaningless.
If we go back to Mr. Spock and his attempts to estimate how likely James T is to get everyone killed, the following might be major stumbling blocks:
1. Often, the knowledge of the enemy is very limited. If your overall probabilities involve decisions by living beings, then you need to be able to assign probabilities to the different decisions they might make.
2. The number of variables quickly becomes impossibly large - not only do you have to worry about the probability of the enemy captain making decisions, but also the competence of the guy actually firing the guns. For example, if the gunner falls asleep on the job 50% of the time, then this has a major impact on the probability of the Enterprise getting blown up.
And so on. Of course, Mr. Spock can try to make assumptions, but if you make big assumptions you cannot rely on the result. For example, Mr. Spock might assume that the enemy captain has a very low probability of making suicidal decisions, but if the enemy happens to believe that a flock of beautiful virgins are waiting for him in the next life he might actually not be bothered by an "everybody dies" result. You could say that Mr. Spock's original probability estimate was reasonable given his knowledge, but it was also useless precisely because of his lack of knowledge.
This same issue plays out in economics. Economists assume that:
1. everyone is rational
2. people make decisions that maximise something ("utility") over time
How does (2) work in an unpredictable world? Economists say that people maximise "expected utility", e.g. the average result of their actions. The problem with this is that, in order to know the average or expected result, people would need to know the probability of all the different possible outcomes of their choices. Is this really possible?
Most economists basically assume it is. Keynes said it wasn't, because the future is unknowable - not only can you not know what will happen, you can't even know with any accuracy the probability of any particular thing happening. The reason is that the world is so extremely complex that building any kind of model of it without a vast number of basically untestable and unjustifiable assumptions is impossible. People are too limited in perception, knowledge, and processing power to accurately calculate the probability of far future events.
Of course, people can try to estimate probabilities anyway, and big financial institutions do use statistical models, but if those probabilities are based on a larger number of assumptions, any of which could be invalidated at any time by events, it means that people's probability estimates are extremely volatile and their decisions might suddenly swing strong from one direction to another. In this situation, using a model is not really any better than just using your gut.
Thus, what people do is use heuristics and make a guess. This is reasonable because doing better is impossible, for the reasons just discussed. It does however make planning less of a pure scientific exercise, with one correct answer, and turn it into a subjective area where it is impossible to prove which plan is the best. And because people tend to make the same (incorrect) assumptions, it also means that crowds tend to show volatile and herd-like behaviour, which then causes "irrational" booms and crashes which the models don't predict.
And that's why Mr. Spock is spouting nonsense to look clever, and how economists oversimplify the world in their models.
The problem is that in real world complex situations, there is basically no way of accurately estimating probabilities. In situations where the rules are simple and known, probabilities can often be calculated, but when you move to a situation where a lot of information is hidden, estimated probabilities are more or less meaningless.
If we go back to Mr. Spock and his attempts to estimate how likely James T is to get everyone killed, the following might be major stumbling blocks:
1. Often, the knowledge of the enemy is very limited. If your overall probabilities involve decisions by living beings, then you need to be able to assign probabilities to the different decisions they might make.
2. The number of variables quickly becomes impossibly large - not only do you have to worry about the probability of the enemy captain making decisions, but also the competence of the guy actually firing the guns. For example, if the gunner falls asleep on the job 50% of the time, then this has a major impact on the probability of the Enterprise getting blown up.
And so on. Of course, Mr. Spock can try to make assumptions, but if you make big assumptions you cannot rely on the result. For example, Mr. Spock might assume that the enemy captain has a very low probability of making suicidal decisions, but if the enemy happens to believe that a flock of beautiful virgins are waiting for him in the next life he might actually not be bothered by an "everybody dies" result. You could say that Mr. Spock's original probability estimate was reasonable given his knowledge, but it was also useless precisely because of his lack of knowledge.
This same issue plays out in economics. Economists assume that:
1. everyone is rational
2. people make decisions that maximise something ("utility") over time
How does (2) work in an unpredictable world? Economists say that people maximise "expected utility", e.g. the average result of their actions. The problem with this is that, in order to know the average or expected result, people would need to know the probability of all the different possible outcomes of their choices. Is this really possible?
Most economists basically assume it is. Keynes said it wasn't, because the future is unknowable - not only can you not know what will happen, you can't even know with any accuracy the probability of any particular thing happening. The reason is that the world is so extremely complex that building any kind of model of it without a vast number of basically untestable and unjustifiable assumptions is impossible. People are too limited in perception, knowledge, and processing power to accurately calculate the probability of far future events.
Of course, people can try to estimate probabilities anyway, and big financial institutions do use statistical models, but if those probabilities are based on a larger number of assumptions, any of which could be invalidated at any time by events, it means that people's probability estimates are extremely volatile and their decisions might suddenly swing strong from one direction to another. In this situation, using a model is not really any better than just using your gut.
Thus, what people do is use heuristics and make a guess. This is reasonable because doing better is impossible, for the reasons just discussed. It does however make planning less of a pure scientific exercise, with one correct answer, and turn it into a subjective area where it is impossible to prove which plan is the best. And because people tend to make the same (incorrect) assumptions, it also means that crowds tend to show volatile and herd-like behaviour, which then causes "irrational" booms and crashes which the models don't predict.
And that's why Mr. Spock is spouting nonsense to look clever, and how economists oversimplify the world in their models.
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