The principle of indifference is a rule that helps to assign prior probabilities in Baysian-type estimations. It says if there are several alternative possibilities for an event, and there is no particular reason to choose one, the prior – the degree of belief – should be equal among all probabilities. Well, this degree of belief is known as credence.
In the case of coin flipping, the probability that a coin (we don’t know if it is fair or not) lands on the head takes the value, one out of two possibilities, 1/2. Another example is American Roulette and the probability for the ball to land on green (0 or 00). Again, we assign those two prospects equally among 38 pockets, i.e., 2/38 or 1/19.
But if the possibilities partition in different ways, the principle of indifference land in strange situations. See the ‘light switch and ball problem’. There are three balls in an urn – red, blue and green. If I pick a ball at random and it’s red, the light is turned on. If it’s blue or green, the light is off. What is the probability the light is ON?
Well, one can say 1/3 – one in three chances that the ball is red.
One can also say 1/2 because there are two possibilities – the light is ON; the light is OFF!
References
Principle of indifference: Wiki
Principle of Indifference / Insufficient Reason: Statistics How To
The Principle of Indifference: jonathanweisberg.org
