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Chapter 2: Tools for Analyzing International Affairs

Study

Summary

Spatial models assume that we can locate decision makers and their policy preferences on a line or in a space. With a few basic assumptions, we can predict how leaders will respond to any proposed solution to a policy question and which solutions they will be willing to accept.

The median voter theorem is an example of a spatial model. It says that if the issue is one-dimensional, preferences are single-peaked, and it takes a majority to win, then the median voter's position is the winning outcome. The reason for this is that, in a head-to-head contest against any other proposal on that dimension, the median voter's preferred position wins the majority of votes. In the international context, a majority rule means that the majority of the power that each of the stakeholders controls in the context of the issue.

The median voter theorem does not provide correct predictions if one of its assumptions is invalid (for example, if there is more than one issue dimension). If there are two issues on which decision makers or leaders have to choose policy, then we can locate their preferred positions in a two-dimensional space that links the issues and allows making trade-offs between them. Then we can draw circular indifference curves to identify the policies that each leader prefers to the status quo (or some other point of reference). Areas of overlap indicate areas of possible agreements. Areas of overlap that include the majority of voters (or power) are called win sets, and they indicate policies that can win relative to the status quo.

Another tool introduced here is the expected utility calculation. It helps us see how leaders evaluate the costs and benefits of alternative courses of action and how they weight those costs and benefits according to the probability of their arising. Such calculations give us the expected utilities of alternative courses of action. Decision makers compare the expected utilities and choose the strategy that gives them the greatest expected utility.

Finally, this chapter discusses the question of risk taking in the context of expected utility. The purpose is to show that expected utility calculations can incorporate different risk attitudes and are not restricted by particular assumptions about the decision makers' risk-taking propensities.

Study Questions

1. What are the assumptions of the median voter theorem? What does each assumption mean?
   



2. Why does the median voter position always prevail (given that the assumptions of the theorem hold)?
   



3. Is there a way to use spatial models when there are two issue dimensions?
   



4. What is a win set? Does the median voter position in each dimension have to be included in the win set?
   



5. What are expected utilities? Suppose country A has to decide whether to go to war or accept a compromise. Suppose a compromise gives A utility of 53. Further assume that if A goes to war and wins, its utility is 100. If A loses, its utility is 0. The cost of war is 15. The probability that A wins is 0.60. Should A go to war or accept the compromise?
   



6. What does this mean to be risk averse, risk acceptant, and risk neutral?