Principle of indifference

The principle of indifference (also principle called of insufficient reason ) of probability theory states that if distinct and mutually exclusive event opportunities, the probability of each event is to be set without further information is available with ( Laplace probability, Laplace formula ), that is, a discrete uniform distribution is assumed.

It was handled by Pierre- Simon Laplace in 1812 in his book Théorie Analytique of probabilites. The principle is based on the consideration of symmetry, after which the individual events, which in the sense of probability have the same characteristics, are interchangeable. Therefore, their occurrence probability must be equal.

The indifference principle plays a central role in the treatises on logical probabilities. When Rudolf Carnap and Stegmüller (1958 ) it is formulated as follows: " If no reasons are known to favor one of various possible events, then the events are as equally likely to see. "

One example is the random experiment of drawing a ball with a number. Three balls with the numerals 1 to 3 are present. The random experiment now consists of drawing a ball from this set. The possible individual events are:

• The ball drawn is the number 1
• The drawn ball shows the number 2
• The drawn ball shows the number 3

Since nothing is further known after the indifference principle for the occurrence of each of the above events is to set the probability. This also corresponds to the general perception that, in such drawing, the probability that a particular ball is drawn for all of the balls is the same.