Choice Theory

1. Choice theory explores rational decision-making and its foundations

Choice theory develops the intellectual reasoning which is necessary for good action: the character which is also necessary for this is up to you.

Foundation of choice theory. Choice theory examines the reasoning behind coherent patterns of choice, exploring what it means to act rationally. It provides a framework for understanding how individuals make decisions and what constitutes rational behavior. The theory is rooted in the idea that choices arise from both the heart (passion) and the head (reason).

Key concepts:

• Menus: Lists of items from which choices must be made
• Preferences: Rankings of items based on desirability
• Rationality: Consistency in decision-making patterns

Choice theory has implications across various fields, including economics, psychology, and ethics. It serves as both an exploration of rational behavior and a potential guide for making sensible decisions, though it does not prescribe specific choices.

2. Reasonable choices satisfy contraction and expansion conditions

Choice is reasonable if and only if it can be explained by a preference relation.

Conditions for reasonableness. Reasonable choices must satisfy two key conditions:

1. Contraction condition: If an item is chosen from a larger menu, it should also be chosen when available in a more restricted menu.
2. Expansion condition: If an item is chosen in pairwise comparisons with every other item, it should be chosen from the full menu.

These conditions ensure consistency in decision-making across different menu sizes and compositions. Choices that satisfy both conditions can be explained by a preference relation, which specifies whether one item is at least as good as another for any pair of items on a menu.

3. Rational choices maximize utility and can be explained by preference orderings

Choice is rational if and only if it is utility maximizing.

Rationality and utility. Rational choices go beyond reasonableness by satisfying an additional condition:

• Revelation condition: If an item is ever chosen when another is available, it should always be chosen when that other item is available.

Rational choices can be explained by a preference ordering, which is a transitive preference relation. This means that if A is preferred to B, and B is preferred to C, then A must be preferred to C. Such choices maximize utility, a numerical representation of preferences.

Key points:

• Utility is derived from choice, not the other way around
• Cardinal utility allows for meaningful comparisons of utility differences
• Rational choices are consistent across all possible menus

4. Uncertainty introduces probability and state gambles into decision-making

Preferences over probability gambles are rational, that is, satisfy the substitution and continuity conditions, if and only if they have the expected utility property.

Choice under uncertainty. When outcomes are uncertain, decision-making involves choosing between gambles. Two types of gambles are considered:

1. Probability gambles: Outcomes with known probabilities
2. State gambles: Outcomes dependent on unknown states of the world

Rational preferences over gambles satisfy two conditions:

• Substitution condition: Preferences between gambles should not be affected by irrelevant alternatives
• Continuity condition: There should be no sudden jumps in preferences

These conditions lead to the expected utility property, where preferences can be represented by assigning utilities to outcomes and choosing based on expected utility.

5. Risk aversion shapes attitudes towards gambling and insurance

You are more risk averse than me if and only if your risk premium for all gambles is greater than mine.

Risk attitudes and behavior. Risk aversion is a key concept in understanding attitudes towards monetary gambles. It is measured by the risk premium, which is the difference between a gamble's expected value and its certainty equivalent.

Implications of risk aversion:

• Risk-averse individuals prefer certain outcomes to risky ones with the same expected value
• They are more likely to buy insurance and less likely to gamble
• The degree of risk aversion can vary with wealth levels

The concept of risk aversion helps explain phenomena such as the coexistence of gambling and insurance purchases, which may seem paradoxical at first glance.

6. Strategic choices involve interdependent decisions and game theory

Your action is rational if it is a plausible response to my plausible responses to your plausible responses to my plausible responses . . .

Game theory and strategic thinking. In strategic situations, the outcomes of choices depend on the actions of multiple decision-makers. Game theory provides a framework for analyzing such interdependent decisions.

Key concepts in strategic choice:

• Best responses: Actions that maximize utility given others' actions
• Rational actions: Those that emerge from chains of plausible responses
• Sustainable actions (Nash equilibrium): Mutually best responses

Strategic thinking often leads to outcomes that may not be collectively optimal, as seen in the famous Prisoners' Dilemma. The theory also explores how cooperation can emerge in repeated interactions.

7. Group decision-making faces inherent challenges and paradoxes

Any constitution which produces rational choices and which satisfies the independence and unanimity conditions must be dictatorial.

Challenges in collective choice. Group decision-making introduces unique challenges and paradoxes. Arrow's Impossibility Theorem demonstrates that no constitution for group choice can simultaneously satisfy all desirable properties:

1. Rationality of choices
2. Independence of irrelevant alternatives
3. Unanimity (Pareto efficiency)
4. Non-dictatorship

This result has profound implications for democratic systems and the concept of "social welfare." Other challenges include:

• The paradox of voting (Condorcet paradox)
• The tension between liberalism and Pareto efficiency
• The inherent manipulability of voting schemes

These findings suggest fundamental limitations in aggregating individual preferences into coherent group decisions.

8. Distributive justice and ethics in choice theory remain contentious

If it were true that interpersonal comparisons of utility could not be made, I believe that there would be no point in writing a book about rational ethics.

Ethics and choice theory. The application of choice theory to questions of distributive justice and ethics remains controversial. Key debates include:

1. Interpersonal comparisons of utility: Are they possible and meaningful?
2. Utilitarianism vs. rights-based approaches to justice
3. The role of the "veil of ignorance" in ethical reasoning

Attempts to derive ethical principles from choice theory, such as Harsanyi's ideal observer construction, face significant challenges. The tension between individual rationality and collective welfare persists, leaving open questions about the foundations of ethics and the justification for wealth redistribution.

Key points of contention:

• The measurability and comparability of individual utilities
• The ethical implications of maximizing total utility
• The role of voluntary vs. compulsory redistribution

These debates highlight the limits of choice theory in resolving fundamental ethical questions and underscore the ongoing need for philosophical inquiry alongside formal analysis.

Last updated: November 24, 2024