Unformatted text preview: POL 130 Lecture 3 POL 130 Lecture 3
Social Science Tools: Part I January 18, 2011 Rational Choice Rational Choice Scientific approach to studying international politics
1) 2) 3) Specify goals What are the constraints? What is rational? Social Science Tools Social Science Tools
1) 2) Decision Theory individual decision making Game Theory the interaction of two or more individuals Decision Theory Decision Theory Looks at how an individual weighs alternatives Must take probabilities and utilities into account: When making a decision, one determines the expected utility of that policy compared to alternatives. Probabilities the likelihood that different possible outcomes will arise Utilities the value one attaches to alternative possible outcomes (costs and benefits) Components of Expected Utility Components of Expected Utility Utility Costs Probability Utility Utility Utility is the value one attaches to a particular outcome 2 ways to refer to utility:
Ordinal Cardinal Assume that preferences are transitive Utility Utility Often express utility in terms of costs and benefits: Utility = benefits – costs Costs Costs Need to consider the costs of a particular policy choice 2 types of costs:
Transaction costs Opportunity costs Costs can be monetary, psychological, political, emotional, etc… Probability Probability There are alternative consequences that may result from a course of action must consider the probability that each consequence may result Probability Probability Probability is the likelihood that an event will occur Must be a number between, and including, 0 and 1 Probabilities can be either objective or subjective:
Objective a mathematical fact Subjective a personal estimate Expected Utility Expected Utility Expected utility allows decision makers (leaders) to make decisions under uncertainty Allows decision makers to take calculated risks: expected utility offers the best guess as to what one will end up with by pursuing a course of action Expected Utility Expected Utility Expected utility is the sum of the utility of each possible outcome of a course of action weighed by the probability that outcome will occur: EU = p1*U1 + p2*U2 + … + pnUn, where there are n possible outcomes Alternatively: Alternatively: EU = p1*(b1 c1) + p2*(b2 – c2) + … + pn(bn cn ) or: EU = p1*U1 + p2*U2 + … + pnUn costs Expected Utility Expected Utility The resulting expected utility of an action can be compared to the expected utilities of alternative actions Rational decision makers choose the action that they believe will lead to the best results – this is the action that yields the highest expected utility Example 1 Example 1
An everyday example: deciding to walk or drive; uncertain if it will rain Four possible outcomes: 1) I walk, it does not rain 2) I walk, it rains 3) I drive, it does not rain 4) I drive, it rains Example 1 cont’d Example 1 cont’d
My preferences over these outcomes and corresponding utilities: walk, it does not rain: utility = 15 drive, it rains: utility = 5 drive, it does not rain: utility = 5 walk, it rains: utility = 5 Example 1, cont’d Example 1, cont’d
There is a 40% chance of rain EU(walking) = p(no rain) * U(walk when no rain) + p(rain)* U(walk in rain) Example 1, cont’d Example 1, cont’d
EU(walking) = p(no rain) * U(walk when no rain) + p(rain)* U(walk in rain) EU(walking) = (.60)*(15) + (.40)*(5) = 7 Example 1, cont’d Example 1, cont’d
EU(drive) = p(no rain) * U(drive when no rain) + p(rain)* U(drive in rain) EU(drive) = (.60)*(5) + (.40)*(5) = 5 EU(walk) = 7 > EU(drive) = 5 Example 2 Example 2
U.S. decision to bomb Serbia (1999) Not certain what will happen if bomb: could be successful could be a failure If choose not to bomb, outcome is the status quo. Example 2, continued Example 2, continued
U.S.’s utility over possible outcomes: Successful bombing campaign: U = 20 Unsuccessful bombing campaign: U = 10 Status quo: U = 0 Example 2, cont’d Example 2, cont’d
EU (bomb) = p(success)*(20) + p(failure)*(10) What should the U.S. do if it believes the probability of success is 0.5? Example 2, cont’d Example 2, cont’d
EU (bomb) = p(success)*(20) + p(failure)*(10) = (.5)(20) + (.5)(10) = 10 + (5) = 5 What should the U.S. do if it believes the probability of success is 0.25? Example 2, cont’d Example 2, cont’d
EU (bomb) = p(success)*(20) + p(failure)*(10) = (.25)(20) + (.75)(10) = 5 + (7.5) = 2.5 Example 3, cont’d Example 3, cont’d
There is a threshold probability that makes the U.S. indifferent between bombing and not bombing: EU (bomb) = U (status quo) p(success)*(20) + p(failure)*(10) = 0 p = 1/3: when p > 1/3, rational for U.S. to bomb Lessons from Expected Utility Lessons from Expected Utility Leaders making decisions are making calculated risks: Rationality is based on information known by the decision maker at the time the decision in made, not after Understanding expected utility can help us understand decisions that were mistakes in retrospect Calculated risks may lead to success, but may also lead to failure Can also help us understand why a country Can also help us understand why a country might start a war that it will clearly lose: example: 1973 Egypt & Israel probability that Israel would win was very high, but Egypt attacked anyway Why? Egypt’s expected utility for attacking: Egypt’s expected utility for attacking: EU (attack) = p(win) * U(win) + p(lose) * U(lose) ...
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 Spring '08
 SIMONELLI
 International Relations, Game Theory, Utility, Cardinal number, expected utility, cont’d Example

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