Subjective Probability

A probability derived from an individual's personal judgment about whether a specific outcome is likely to occur. Subjective probabilities contain no formal calculations and only reflect the subject's opinions and past experience.

What Is Subjective Probability?

Di Finetti Game: Say, your friend tells to you, coming out of exam

hall, that he is getting a 100. How much is that certain now? To measure this, all one have to do is to ask few questions. Tell him that, in a bag, there are hundred balls. Out of which 98 are white and 2 are black. Given a chance, like, a thousand rupees bet, for either drawing a white ball from the bag or wait till exam results and on getting the score as 100. Assume that the answer of your friend as “draw the balls”. Now, increase the black ball count to 20 (80 White + 20 Black). And ask him to pick between drawing a ball from the bag or wait till the exam results.

How To Measure The Subjective Probability?

If he chooses to wait for the exam result for the thousand rupee bet, increase the white ball count to 90 (90 White + 10 Black) and repeat the same test. If he wants to draw, then increase the black count to 15 (85 White + 15 Black) and repeat the experiment. End this game with a sufficient interval. Say, between 85 and 88. This means, that the subjective probability of your friend getting a centum is any where between 85 ~ 88.

Di finetti game…continued

Now, let us analyse the rationale behind the game. For the first time, when given a chance between 98:2 and “waiting till results”, your friend goes for the draw.

This means that he thinks drawing the white ball is easier than getting a 100 in exam. So, the subjective probability of his 100 is lesser than 98% (or .98). This is the upper limit of his chances of getting 100.

When you change the balls in the bag to 80:20 and ask him for a pick, he chooses to wait for the result. Meaning that, he thinks the probability of getting 100 is more than choosing the ball, which was 80% (or .8). This serves the lower limit.

For the third time, when you repeat the same experiment, you are trying to find the finer details.

The Rationale Behind The Game