Phil 148 Choices. Choice Theory: The relationship between probability and action is often complex, however we can use simple mathematical operations (so.

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Presentation transcript:

Phil 148 Choices

Choice Theory: The relationship between probability and action is often complex, however we can use simple mathematical operations (so far all we’ve used have been the four arithmetic operations) to assist in making good choices. The first principles we will look at are: Expected Monetary Value and Expected Overall Value.

Expected Monetary Value: EMV = [Pr(winning) * net gain ($)] – [Pr(losing) * net loss ($)] Example, Lottery: EMV = [(1/20,000,000) * $9,999,999] – [(19,999,999/20,000,000) * $1] That comes out to -$0.50 That means that you lose 50 cents on the dollar you invest; this is a bad bet.

Expected Monetary Value: Consider an example with twice the odds of winning and twice the jackpot: Example 2, Lottery: EMV = [(1/10,000,000) * $19,999,999] – [(9,999,999/10,000,000) * $1] That comes out to $1 That means that you gain a dollar for every dollar you invest; this is a good bet.

Expected Overall Value Monetary value is not the only kind of value. This is because money is not an intrinsic value, but only extrinsic. It is only valuable for what it can be exchanged for. If the fun of fantasizing about winning is worth losing 50 cents on the dollar, then the overall value of the ticket justifies its purchase. In general, gamblers always lose money. If viewed as a form of entertainment that is worth the expenditure, it has a good value. If people lose more than they can afford, or if the loss hurts them, it has negative value.

Diminishing marginal value: This is a concept that affects expected overall value. Diminishing marginal value occurs when an increase in something becomes less valuable per increment of increase. Examples: sleep, hamburgers, shoes, even money (for discussion, how does diminishing marginal value affect tax policy?)

Decisions under risk: When a person has an idea of what different potential outcomes are, but does not know what the chances of such outcomes are, there are a number of strategies that can guide a decision. Consider the following table:

Outcomes (1-4) given choice (A-C) 1234 A11333 B5555 C6663 Dominance is when one choice is as good or better in every outcome as any competing choice. There is no dominant choice in the above. If we do not know the probabilities of ourcomes 1-4, we may assume they are equally probable to generate an expected utility. The EU of A and B are equal, at 5. C comes out slightly better at Other strategies that make sense are: Maximax: Choose the strategy with the best maximum (in this case, A) Maximin: Choose the strategy with the best minimum (in this case, B) Which strategy choice makes most sense depends on how risk-averse the situation is.

In-class Exercise: 1.Think of a situation in which it makes most sense to choose the outcome that maximizes expected utility. 2.Think of a situation in which is makes most sense to be risk-averse (i.e. to maximize the minimum). 3.Think of a situation in which it makes most sense to maximize the maximum.

Ch. 12, Exercise III: 1.EMV = [Pr(winning) * net gain ($)] – [Pr(losing) * net loss ($)] That is: EMV = [.9 * $10 ] – [.1 * $10] = $8 This is a good bet, but would you be willing to risk your friend’s life on it? I should say not. So the EMV is positive, but the EOV is not. In other words, the stakes are SO high for failure that it makes sense to use a maximin strategy, which is not to bet. 2. Your own example?