Subjective Probability Lecture Topics: Calculating subjective probabilities The de Finetti game

Objective Probabilities Objective probability – the ratio of the number of times the desired outcome can occur relative to the total number of all outcomes that can occur over the long run. We can calculate objective probabilities for repeatable events – Coin flips, rolls of dice, roulette, etc. We cannot predict the outcome of any one event with certainty We can predict patterns over repeated events because objective probabilities work out over the long run Understanding objective probabilities helps us to make better decisions – Let’s Make a Deal, playing the lottery, blackjack strategy Despite this… – People find it difficult to estimate complex probabilities – We often disregard objective information and act based on our gut E.g., the Barthelme brothers playing blackjack – Many of the events we are interested in are not repeatable

Subjective Probabilities Subjective probabilities depend on the person making the assessment A variety of factors can be taken into account to estimate the probability Some estimates of subjective probabilities are better than others

The de Finetti Game Source: Aczel, Amir D Chance: A Guide to Gambling, Love, The Stock Market, and Just About Everything Else. New York: Thunder’s Mouth Press. See pp Bruno de Finetti ( ) – Italian statistician who worked on a system to objectively measure subjective probabilities This game clarifies a person’s true beliefs on probability by reducing biases

The de Finetti Game Your friend says he’s 100% certain the Dallas Cowboys will win the Super Bowl in “Let’s plan a game. You have a choice. You can either: 1)Draw a ball from a bag that has 99 red balls and 1 black ball. If you happen to draw a red ball, I will give you $1,000,000 2)Or you can decide to wait to see if the Cowboys win the Super Bowl; if they do, I will give you $1,000,000. What is your choice: draw or wait?” If he asks to wait – the subjective probability really is 100% If he asks to draw, change the proportion of red balls – 90 red balls and 10 black balls – and begin again – If wait – change the number of balls to 95 – If draw – change the number of balls to 80 Once your friend is indifferent, you have arrived at the subjective probability

Use objective probabilities if they are available When they are not, you can use subjective probabilities If you use subjective probabilities: – Get them from experts (but still be skeptical) – Use the de Finetti Game to reduce biases