# Decision Theory
## DECISION THEORY

Decision theory studies rational choices. It is used both to predict and explain actual choices and to improve actual decision making. The first purpose is called positive theory and the second is called normative theory. While our primary aim is to predict and explain actual choices (positive theory), understanding how to improve actual decision making (normative theory) helps us to better understand decision theory for our applications, as well.
Decision theory may also be used to predict equilibria achieved by some evolutionary process. In particular, this evolutionary process may be the biological evolutionary process or a cultural evolutionary process. We consider applications to each.

### Smart Choices and Models Based Upon Them

We first start with a review of material in _Smart Choices_, a book written by John Hammond, Ralph Keeney, and Howard Raiffa, experts from the Harvard Business School in the field of decision theory and its application in business. (An MBA program is largely the study of how to improve decisions important to business, and decision theory is a key component of this study.) These chapters introduce you to the basics of decision theory and how it can be applied to improve your decisions. The chapter continues with a discussion of our goals for models intended to help us predict and explain social behavior. We see that our modeling focuses only upon the most important factors necessary to predict and explain, even if we must sacrifice a complete or accurate description of the individual’s actual decision making process.

### Optimization in Markets

We then introduce the basics of microeconomic theory, since economists were the first to use models based upon self-interested individuals and these models are now the foundation for the discipline. We introduce these models based upon decision theory because they have been so successful in economics. As the political scientists Shepsle and Bonchek explain, considering these models are important for our general goals of predicting and explaining all types of social behavior:
_The modern theory of economics is a grand intellectual edifice precisely because it has succeeded, as no other social science has, in constructing explanations logically, rigorously, and in empirically meaningful ways. At the foundation of this edifice is a scientific commitment to explanation, not description._ (Shepsle-Bonchek, 21)
The models developed here introduce the reader to most of the basic tools and concepts of decision theory, at least in a world without uncertainty. We first consider profit-maximizing decisions that firms make in perfectly competitive markets, show how the model describes supply and demand choices, and how it describes the “market” determining price to reach a competitive equilibrium. We then extend this model to consumers, whose preferences can take a more general structure, which leads us to develop “utility” functions, an important tool throughout decision theory and game theory. We also introduce the concept of efficiency, which can be used to evaluate the outcomes that our models predict. We find, in particular, that competitive markets, driven by self-interested individuals, are efficient, and compare that conclusion to monopoly markets that are not.

### Sincere Voters

We then apply decision theory models to political science with the intent of creating a positive theory of politics. We use of models of self-interested individuals to consider various voting mechanisms used to generate group decisions. We start with rational individuals, just as in the economics models, and analyze decisions they would make with these voting mechanisms. We show that some voting mechanisms, and majority voting in particular, can lead to irrational group decision making, even if all individuals are rational. For another application, we also consider the incentives for lobbying for rules, regulations, or laws that would benefit everyone within a group and find an explanation for special interests.

### Natural Selection

We not use models based upon the mathematics of decision theory, not to predict and explain rational decisions, but in evolutionary biology. Here, “decisions” are not made consciously by any individual, but an evolutionary mechanism rewards the most fit individuals that pass along more of their genes to the next generation. The population of individuals then tends to eventually evolve to one with individuals who virtually all have characteristics that maximize fitness. After examining the process of natural selection, we consider its application in choices involving food and shelter, and the determination of sex ratios.

### Cooperation with Kin Selection

This materials continues the study of evolutionary biology, but it considers decision theory models from a different perspective. We consider the perspective of the gene rather than the individual with that gene. This offers a theory of kin selection, which may lead to behavior towards family members that appears altruistic from the viewpoint of an individual in the population, but not from the viewpoint of an individual gene. We consider some applications of kin selection in amoebae, social insects, ground squirrels, and humans. Finally, after we have considered evolutionary arguments that predict and explain tendencies in animal behavior, we apply the same evolutionary arguments to determine behavioral tendencies in people, an approach that has formed the field of evolutionary psychology.

### Cultural Evolution and Social Norms

Here we apply decision theory in models of evolution outside of biology. We consider an analogous process to biological evolution in the evolution of cultural behavior. In this model, people tend to adopt more ideas that tend to lead to more successful behavior, so that more fit ideas become more prevalent in a later population and less fit ones become less prevalent. This evolutionary process eventually leads to the most "fit" ideas being adopted within the cultural. We discuss implications of such a process to draw out predictions that can then be tested against actual behavior.

### Decision Theory with Uncertainty

Here we re-open the decision theory toolbox to consider the additional tools necessary to deal with a world with uncertainty. We consider, in some detail, basic rules that an individual should follow if he were rational in the face of uncertainty.

### Investments, Insurance, and Search

Now we introduce several important applications of decision theory with uncertainty, applying decision theory to investments, insurance, and search.

### Anomalies and Responses to Them

Here we consider apparent anomalies that have been observed when trying to apply these models of self-interested individuals to actual social behavior. We find some situations, especially when uncertainty is involved, where individual choices do not seem consistent with all the rules that a rational decision maker must follow. Given these differences, we must consider two questions. First, are there any predictable biases in these differences between actual choices and rational choices? Second, under what circumstances is some social behavior of interest likely to be consistent with rational choices? In addressing these questions, we reconsider when a model based upon individuals’ rational choices is likely to be appropriate for a positive theory that intends to predict and explain some social behavior of interest.