Question

Suppose there are two individuals in an economy. Utilities of those individuals under five possible social states are shown in the following table: $$\begin{array}{ccc} \text { State } & \text { Utility 1 } & \text { Utility 2 } \\ \hline \mathrm{A} & 50 & 50 \\ \mathrm{B} & 70 & 40 \\ \mathrm{C} & 45 & 54 \\ \mathrm{D} & 53 & 50.5 \\ \mathrm{E} & 30 & 84 \\ \hline \end{array}$$ Individuals do not know which number \((1 \text { or } 2)\) they will be assigned when the economy begins operating, hence they are uncertain about the actual utility they will receive under the alternative social states. Which social state will be preferred if an individual adopts the following strategies in his or her voting behavior to deal with this uncertainty? a. Choose that state which ensures the highest utility to the least well-off person. b. Assume there is a \(50-50\) chance of being either individual and choose that state with the highest expected utility. c. Assume that no matter what, the odds are always unfavorable such that there is a 60 percent chance of having the lower utility and a 40 percent chance of higher utility in any social state. Choose the state with the highest expected utility given these probabilities. d. Assume there is a \(50-50\) chance of being assigned either number and that each individual dislikes inequality, Fach will choose that state for which expected utility \(-\left|U_{1}-U_{2}\right|\) is as large as possible (where the \(|\ldots|\) notation denotes absolute value). e. What do you conclude from this problem about social choices under a "veil of ignorance" as to an individual's specific identity in society?

Short answer

Answer: According to the Maximin rule strategy, State D is preferred, as it ensures the highest utility (50.5) to the least well-off person.

Step-by-step solution

(Strategy a: Maximin Rule)

The first strategy involves choosing the social state that ensures the highest utility to the least well-off person. To find this, we need to find the minimal utility for each state and pick the one that provides the highest minimal utility. Min. Utility - State A: 50 State B: 40 State C: 45 State D: 50.5 State E: 30 Here, State D ensures the highest utility to the least well-off person with 50.5.

(Strategy b: Expected Utility with A 50-50 Chance)

This strategy assumes there is a 50-50 chance of being either individual and chooses the state with the highest expected utility. The expected utility (EU) is given by the formula: EU = 0.5 × (Utility 1 + Utility 2). Expected Utilities - State A: 0.5*(50+50) = 50 State B: 0.5*(70+40) = 55 State C: 0.5*(45+54) = 49.5 State D: 0.5*(53+50.5) = 51.75 State E: 0.5*(30+84) = 57 Here, State E has the highest expected utility with 57.

(Strategy c: Expected Utility with Unfavorable Odds)

Assuming there is a 60% chance of having the lower utility and a 40% chance of the higher utility in any social state, we calculate the expected utility. Expected Utilities - State A: 0.6*(50)+0.4*(50) = 50 State B: 0.6*(40)+0.4*(70) = 52 State C: 0.6*(45)+0.4*(54) = 48.6 State D: 0.6*(50.5)+0.4*(53) = 51.7 State E: 0.6*(30)+0.4*(84) = 51.6 Under this strategy, the highest expected utility comes from State D with 51.7.

(Strategy d: Expected Utility considering Inequality Aversion)

This approach assumes there is a 50-50 chance of being assigned either number and that individuals dislike inequality. We need to find the state with the largest expected utility - |Utility 1 - Utility 2|. Inequality measure - State A: 50-50 = 0 State B: 70-40 = 30 State C: 45-54 = -9 State D: 53-50.5 = 2.5 State E: 30-84 = -54 The state with the largest expected utility without creating inequality is State A with an inequality measure of 0.

(Conclusion)

When individuals choose a social state under a "veil of ignorance" as to their specific identity in society, the preference over states depends on the strategy they adopt. This shows that different strategies lead to different outcomes, and careful evaluation is necessary to understand the trade-offs between preferences and aversions in social choices. In this example, different strategies lead to four different state preferences: A, B, D, and E.

Key concepts

Utility Theory

Utility theory is a framework used to model individual's preferences. It helps in understanding how individuals prioritize different choices when they need to make decisions under uncertainty. In this context, utility represents a numerical value that reflects an individual's level of happiness or satisfaction.
For instance, in the given exercise, "utility" values shown for each individual in various social states indicates their respective satisfaction levels within those states.
Each social state can be evaluated using these utility values, where higher values often indicate better preferences for a rational individual. The decision strategies employed by individuals to handle uncertainty derive from these values.

Veil of Ignorance

The concept of the "veil of ignorance" is a philosophical tool used to ensure fairness in decision-making about social arrangements. It was famously proposed by philosopher John Rawls. When individuals make choices behind a veil of ignorance, they do not know their own personal circumstances, such as their wealth, status, or abilities.
This means individuals must consider justice or fairness, because they might end up in any position within the society. The exercise represents this by having individuals unaware of which utility (Utility 1 or Utility 2) they will receive.

• They must choose without self-interest bias.
• It encourages thinking about society as a whole, not just individual gain.

This approach aims to ensure that social rules are justifiable and equitable for everyone.

Inequality Aversion

Inequality aversion refers to the preference some individuals have for more equal distribution of resources, even if it means receiving slightly less themselves. People who are inequality averse are concerned about large disparities in wealth or utility, and they may choose an option that reduces these differences.
This concept plays a crucial role in social choice theory, as seen in the exercise. Persons are tasked to choose social states that minimize inequality between individuals. This is quantified by the absolute difference between Utility 1 and Utility 2.
For instance, State A is chosen in the exercise because it has an inequality measure of 0, representing perfect equality between the two individuals. This reflects a preference for fairness over maximum utility.

Maximin Strategy

The maximin strategy is a decision rule applied in situations of uncertainty, aiming to protect the least well-off. It's a conservative approach where individuals focus on maximizing the minimum outcome possible under any given strategy. By doing this, they ensure that the worst-case scenario is as favorable as possible.
In the exercise, individuals employ the maximin strategy by selecting the social state that offers the highest utility to the least well-off person. This decision method reflects a risk-averse mentality, focusing on promoting equity and preventing extreme disparities in welfare.

• This strategy is often favored in highly uncertain environments.
• It helps in achieving fairness by improving baseline conditions.

This theory underlines how prioritizing the lower end of expected outcomes can lead to more considerate and equitable social decisions.