Lecture 3

• Definition: Alternative a1​ dominates a2​ if a1​ leads to a better result in at least one state and no worse results in others.

• Implication: SSD excludes certain alternatives but does not identify the optimal one.

1. Definition: Selects the alternative with the highest expected value.

2. Limitation: Ignores risk (variance) in the decision-making process.

Concept: Measures the willingness to pay for perfect or imperfect information

1. Definition: Decision-making considers both expected value (μ) and variance (σ).

2. Application:

   • Risk-neutral: Variance does not affect the decision.

   • Risk-seeking: Positive effect of variance.

   • Risk-averse: Negative effect of variance.

• Problem: Loss of information about distribution (e.g., skewness).

• Caution: May lead to implausible decisions violating dominance rules.

1. Definition: Describes the probability that a random variable X is less than or equal to a certain value x.

2. Application in FOSD: Used to compare two alternatives; if one CDF lies entirely below another, the alternative is dominant.

1. Concept: A decision-maker who only considers the expected value (μ) and is indifferent to risk (variance).

2. Example: Selects an alternative based solely on its average outcome, regardless of variability.

1. Definition: Calculated by comparing the expected value of the decision conditioned on the information to the decision without it.

2. Example: If an imperfect signal improves the decision outcome, the willingness to pay reflects that improvement.

Key Point: The μ-principle ignores higher moments of the distribution, such as variance or skewness, leading to potential suboptimal decisions for risk-averse or risk-seeking individuals.

1. Definition: A table summarizing the payoffs of different alternatives under various states of the world.

2. Application: Used in the comparison of alternatives using dominance principles or expected value calculations.

Concept: Alternative a1​ is preferred over a2​ if the probability of achieving a higher outcome with a1 is greater than or equal to that with a2 for every possible outcome.

• Example: Binary signals (e.g., "bull" or "bear" market) help refine decisions by conditioning investment strategies on expected market conditions.

• Result: The expected payoff is improved with the additional information provided by the signal.

1. Definition: Occurs when individuals with higher risk are more likely to seek insurance, leading to higher premiums.

2. Relevance to HD Testing: If the results of a predictive test for Huntington’s Disease must be disclosed, risk-averse individuals may prefer not to know the test outcome due to the potential increase in premiums.