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3 - The Principle of Indifference
Published online by Cambridge University Press: 05 January 2013
Summary
The principle of indifference, also known as the principle of insufficient reason, is attributed to Jacob Bernoulli, and sometimes to Laplace. Simply stated, it suggests that if there are n possible outcomes and there is no reason to view one as more likely than another, then each should be assigned a probability of 1/n. Quite appropriate for games of chance, in which dice are rolled or cards shuffled, the principle has also been referred to as the “classical” approach to probability assignments.
However, this principle has to be used with great care. Early examples include the event “two consecutive tosses of a coin will come up head.” If we know nothing about the coin, one may try to apply the principle and conclude that this event has probability 50%, but then the same argument would apply to any two outcomes of the two tosses. However, this type of counterexample can be ruled out by referring to the structure of the problem and arguing that there is sufficient reason to find three outcomes more likely than one.
More serious problems arise when we apply the principle to everyday problems, which are often not endowed with sufficient symmetries. For instance, assume that I ask you what is the probability that it will rain tomorrow.
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- Theory of Decision under Uncertainty , pp. 14 - 19Publisher: Cambridge University PressPrint publication year: 2009