Inverse Gambler's Fallacy
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Explanation
You commit the Inverse Gambler's Fallacy if you deduce, from an unlikely outcome of a random event (e.g. a dice roll), that many such events (dice rolls) probably occurred before.
For example, if you roll two dice and get double sixes, and then reason as follows:
- It is unlikely that double sixes would be thrown in a single roll.
- It is more likely that double sixes would be thrown in a long series of rolls.
- So someone has probably been throwing these dice before I came along.
Discussion
The Inverse Gambler's Fallacy is frequently mentioned in discussions of multiple universes and the anthropic principle. For example, many people reason thus:
- It is unlikely that a single universe would happen to have physics capable of supporting life.
- It is more likely that such a universe would exist if there are multiple universes.
- So, there are probably multiple universes.
Amongst philosophers studying anthropic reasoning, it has been debated whether this particular argument is or is not a fallacy. Although structurally similar to the fallacious example at the top, some, such as Nick Bostrom, note the following: In the latter case we wouldn't be here to observe the "dice roll" (i.e. the laws of physics) if it was anything other than "double sixes" (i.e. a "fine-tuned" universe). Thus, this argument is not the same.
Instead, they suggest the following analogy:
- Suppose you're told that a pair of dice will be rolled until a double six appears. You will then be allowed into the room to see the double six. You are summoned to the room and see the double six. Should you conclude that there were probably some previous rolls?
In this case, yes.
