Subjective Utility Hypothesis
Millions of people participate in gambling, either by buying lottery tickets or by going to casinos.
Are they all risk takers? Do they all have convex utility functions with positive first and second derivatives?
If they do, their marginal utility of money must increase as their wealth increases, and this seems to contradict the reality.
In reality, most people consider a dollar on a rainy day more valuable than dollar when they are wealthy. It is appropriate to assume that most people are rational risk averters whose marginal utility decreases as their wealth increases.
Their utility functions should be concave. The fact that most people are risk averters makes the presumption that all gamblers are risk averters which in turn makes the presumption that all gamblers are risk takers implausible.
It is also plausible that most gamblers are covered by various kinds of insurance, and buying insurance is a typical risk-averse behavior.
This again contradicts the presumption that all gamblers are risk takers. The fact that risk averters may participate in games cannot be explained by their utility function.
One of the hypotheses that explains risk averter's participation in gambling is the subjective utility hypothesis, which holds that the player's expected utility is not based upon the objective, or true probability of the game, but on the player's subjective or biased beliefs about the possibility of the game.
It was hypothesized that an individual's subjective probability trends to be higher than the objective probability when the latter is low, and lower than the objective probability when the latter is high.
The essence of the hypothesis is that the player has a tendency to believe what is contrary to reality. Because of the subjective probability assigned by the risk averter to a game, he or she may have higher expected utility than the true expected utility of the game.
Consider a roulette game with 0 through 36 on the wheel: the player bets on a single number. If the wheel stops at the number, the player wins.
The payoff ratio, which is set by the casino house, is typically 35 to 1 or 36 for 1.
Since the wheel is equally divided by 36 radii, the objective probability of winning the game is 1/37, and the objective probability of losing the game is 36/37.
Also assume that the player will bet $10 if he or she decides to play the game. If the player wins, he or she will win $350. if he or she loses, the loss will be the bet, $10.
Based upon the objective probabilities of roulette, the game expected utility of the risk averter is negative. Gambling implies a loss of utility, and so the risk averter will not play.
With subjective probability, or the misconception of the probabilities, the risk-averse individual can have positive expected utility from, say, the roulette game, and thus he or she may play it. In reality, many players participate in gambling simply because they feel that they have 'good luck'.
When such feelings prevail, players tend to use their subjective probabilities to replace objective probabilities.