Hippocratic Utility

While acknowledging the ethical motivation behind a proposed "Hippocratic" utility function that prioritizes saving lives by avoiding harmful treatments over saving them through intervention, the author argues that the practical scope of this decision criterion is limited, as demonstrated by a counterexample.

The Gist

Here is an explanation of Tomasz Strzalecki's paper, "Hippocratic Utility," using simple language and everyday analogies.

The Big Idea: "First, Do No Harm" Gone Wrong?

Imagine you are a doctor. You have a patient who is sick. You have two choices:

1. The Old Drug: A medicine from 1926 that saves 1 out of 10 patients.
2. The New Drug: A shiny new medicine from 2026 that saves 2 out of 10 patients.

Mathematically, the New Drug is clearly better. It saves more lives.

However, some ethicists and researchers propose a special rule called "Hippocratic Utility." This rule is based on the famous medical oath: "First, do no harm."

The rule says: It is much worse to kill someone by giving them a new treatment than to let them die by doing nothing.

In this paper, the author argues that while this sounds noble, if you follow this rule strictly, you end up making decisions that are illogical, unfair, and based on random history rather than what actually helps people.

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The Three Problems with the "Do No Harm" Rule

The author uses three main arguments (or "analogies") to show why this rule is tricky.

1. The "Over-Protective Parent" Problem (Stochastic Dominance)

Imagine you are a parent choosing a route for your child to walk to school.

• Route A (Old): Safe, but the child might get lost 10% of the time.
• Route B (New): A slightly riskier path, but the child gets lost only 5% of the time.

A normal person would pick Route B because it's safer overall. But a "Hippocratic" parent might think: "If I send my child down Route B and they get lost, that's my fault for choosing the new path. If I send them down Route A and they get lost, that's just bad luck."

Because the parent fears being blamed for the "new" mistake so much, they might choose the worse route (Route A) just to avoid the feeling of responsibility for the new option.

The Paper's Point: If you follow the Hippocratic rule too strictly, you might choose a treatment that kills more people overall, just because you are terrified of being the one who "caused" a death with a new drug.

2. The "Missing Puzzle Piece" Problem (Indeterminacy)

The author points out that we often don't know the full story about how a drug works on specific people. We only know the average.

Imagine you are betting on a coin flip.

• Scenario A: You know the coin is fair (50/50).
• Scenario B: You know the coin is weighted, but you don't know if it's weighted toward Heads or Tails.

The "Hippocratic" rule requires you to know exactly how the new drug interacts with the old one for every single person. But in real life, we only have the averages.

The Paper's Point: Because we are missing the "puzzle pieces" (the full data), the Hippocratic rule can't give you a clear answer. It's like a GPS that says, "I can't tell you which way to go because I don't know the exact traffic pattern of every single car." You end up having to guess, and different guesses lead to different, contradictory decisions.

3. The "History Buff" Problem (Status Quo Bias)

This is the most creative part of the paper. The author asks: Does it matter which drug was discovered first?

Let's play a game with two chemicals, Chemical X and Chemical Y.

• Situation 1: Chemical X was discovered in 1926 (Old). Chemical Y was discovered in 2026 (New).
  • Hippocratic Rule: "Don't switch to the new one! Stick with X!" (Even if Y is better).
• Situation 2: Imagine time travel. Chemical Y was discovered in 1926 (Old). Chemical X was discovered in 2026 (New).
  • Hippocratic Rule: "Don't switch to the new one! Stick with Y!"

The Absurdity: In both situations, the chemicals are exactly the same. The only difference is which one was found first.
If you follow the Hippocratic rule, your decision changes based on a random historical accident (who discovered the drug first), not on which drug actually saves more lives.

The Paper's Point: A doctor who truly wants to "do no harm" shouldn't care about history. They should care about the patient. If the rule makes you prefer a worse drug just because it's "older," the rule is broken.

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The Legal Twist: Why Doctors Might Actually Like This Rule

The author ends with a twist. While the ethical reason for this rule (doing no harm) is flawed, there is a very practical, non-ethical reason doctors might use it: Lawsuits.

• If a doctor gives a patient a new drug and the patient dies, the family can easily sue: "You killed him with that new thing!"
• If a doctor does nothing and the patient dies, the family has a harder time suing: "Well, you didn't do anything, so it's just the disease."

In this case, the "Hippocratic Utility" isn't about ethics; it's about self-preservation. The "penalty" for making a mistake with a new drug is a massive lawsuit.

The Bottom Line

The paper concludes that the "Hippocratic Utility" function is a bad tool for general decision-making because:

1. It can lead to choosing worse treatments to avoid blame.
2. It relies on missing data to make decisions.
3. It makes decisions based on random history (which drug came first) rather than reality.

However, the author admits it might still be useful in very specific cases (like when "doing nothing" is the only alternative) or when the decision is driven by legal fear rather than pure medical ethics.

In short: Being too afraid to try something new can sometimes hurt more people than the new thing would have helped. True "doing no harm" requires looking at the whole picture, not just the fear of making a mistake.

Technical Summary

Here is a detailed technical summary of the paper "Hippocratic Utility" by Tomasz Strzalecki.

1. Problem Statement

The paper addresses a specific class of utility functions proposed in recent medical decision-making literature (e.g., Ben-Michael, Imai, and Jiang, 2024; Christy and Kowalski, 2024). These functions, termed "Hippocratic Utility," are motivated by the ethical principle of the Hippocratic Oath ("first, do no harm"). They introduce an asymmetry in valuing outcomes:

• They assign a higher weight to lives lost due to a new intervention (harm caused by action) than to lives lost due to a default or old intervention (harm caused by inaction or status quo).
• Formally, the utility difference between a new treatment ($d=1$) and a default ($d=0$) depends on the potential outcomes vector $(y_0, y_1)$, where $y_d=1$ is survival and $y_d=0$ is death.

The Core Question: While the ethical motivation for this asymmetry is acknowledged, the author investigates the scope of applicability of such decision criteria. Specifically, the paper asks whether these utility functions lead to robust, logically consistent decisions across different scenarios, or if they introduce pathological behaviors like status quo bias and violations of stochastic dominance.

2. Methodology

The author employs the Potential Outcomes Model (Neyman, 1923; Rubin, 1974) to formalize the decision problem.

• Setup:

  • A patient has deterministic responses to two drugs: an "old" drug ($d=0$) and a "new" drug ($d=1$).
  • The population is divided into four principal strata based on potential outcomes $(y_0, y_1)$:
    1. $P_{00}$: Dies under both.
    2. $P_{01}$: Dies under old, survives under new (Benefit).
    3. $P_{10}$: Survives under old, dies under new (Harm).
    4. $P_{11}$: Survives under both.
  • Information Constraint: Randomized Controlled Trials (RCTs) only reveal the marginals ($P(y_0=1)$ and $P(y_1=1)$), not the joint distribution $P$. The correlation structure (the specific values of $P_{01}$ and $P_{10}$) is unknown.

• Decision Criterion:
  The decision maker maximizes expected utility: $\max_{d \in \{0,1\}} E_P [u(d, y_0, y_1)]$.
  The Hippocratic Utility function is defined by the difference:
  $$u(1, y_0, y_1) - u(0, y_0, y_1) = \begin{cases} 0 & \text{if } y_0 = y_1 \\ 1 & \text{if } y_0 < y_1 \text{ (New saves life)} \\ -\lambda & \text{if } y_0 > y_1 \text{ (New causes death)} \end{cases}$$
  Where $\lambda > 1$ represents the degree of asymmetry (loss aversion).

• Analysis Strategy:
  The author analyzes the properties of this criterion through three lenses:

  1. Stochastic Dominance: Does the criterion ever choose a dominated option?
  2. Indeterminacy: How does the lack of joint distribution data affect the decision?
  3. Status Quo Bias: Does the decision depend on arbitrary historical facts (e.g., which drug was discovered first)?

3. Key Contributions and Results

A. Violation of Stochastic Dominance

The paper demonstrates that if $\lambda$ is sufficiently large, the Hippocratic utility criterion may prescribe the dominated option (the drug with lower survival rates).

• Result: Even if the new drug saves twice as many lives on average (e.g., 20% vs. 10%), the decision maker may choose the old drug ($d=0$) if there is a non-zero probability of the "harm" stratum ($P_{10} > 0$).
• Mechanism: The expected utility difference is $P_{01} - \lambda P_{10}$. Since $P_{01} + P_{11} = 20\%$ and $P_{10} + P_{11} = 10\%$, the difference simplifies to $10% + (1-\lambda)P_{10}$. For large$\lambda$, this becomes negative, leading to the choice of the inferior drug.
• Implication: This violates stochastic dominance, a fundamental principle in decision theory, because the utility function penalizes deaths in different strata unequally based on the cause of death rather than the outcome itself.

B. Choice Indeterminacy

Because the joint distribution $P$ is unknown, the decision depends on the unknown correlation structure.

• Result: The optimal decision is not unique given only marginal data.
  • If $P_{01} = 0$ (no one benefits from the new drug), the new drug is never chosen.
  • If $P_{01} > 0$, the decision depends on the ratio of $P_{01}$ to $P_{10}$.
• Implication: To make a decision, one must arbitrarily assume a specific $P$ (e.g., minimizing regret, using max-min, or assuming independence). The paper argues that the choice between these "free parameters" is not data-driven but relies on external reasoning, making the criterion unstable.

C. Status Quo Bias (The Core Argument)

The author introduces a thought experiment comparing two decision problems to expose Status Quo Bias:

• Scenario 1: Drug A (Old, 1926) vs. Drug B (New, 2026).
• Scenario 3: Drug B (Old, 1926) vs. Drug A (New, 2026).
• Result: Under Hippocratic utility, the decision maker will prefer the drug labeled "Old" (the default) in both scenarios, regardless of the actual efficacy of the drugs.
• Significance: The decision depends entirely on a random historical fact (discovery date) rather than the chemical properties or efficacy of the compounds. The author argues that a decision maker truly committed to "doing no harm" should not base life-and-death decisions on arbitrary historical accidents.

D. The "No Intervention" Nuance

The paper acknowledges that Hippocratic utility might be defensible in Decision Problem 2 (No Treatment vs. New Drug), where the status quo is "no intervention." However, it fails in Decision Problem 4 (No Treatment vs. New Drug, where "No Treatment" implies the patient will likely self-medicate with the old drug).

• If the patient self-medicates, the "harm" of the new drug is no longer distinct from the "harm" of the old drug.
• The paper suggests that in such cases, the asymmetry parameter $\lambda$ should effectively collapse to 1, reverting to standard expected utility maximization.

4. Significance and Conclusion

• Normative Critique: The paper does not dispute the ethical desire to avoid harm but argues that the formal implementation of Hippocratic utility leads to logically inconsistent and ethically questionable outcomes (violating dominance and introducing status quo bias).
• Legal vs. Ethical Motivation: The author distinguishes between the ethical motivation (saving lives) and the legal motivation (avoiding lawsuits). The legal argument (families sue more easily if a doctor actively treats a patient who dies) justifies a high $\lambda$ but leads to the same status quo bias. The author notes that this legal motivation is distinct from the ethical one.
• Recommendation: The scope of Hippocratic utility is severely limited. It may only be applicable when the status quo is truly "no intervention" and the alternative is a novel treatment. It is not applicable when comparing two active treatments, as it forces decisions based on arbitrary historical defaults rather than comparative efficacy.
• Theoretical Implication: The paper supports the view (aligned with Gelman and Mikhaeil, 2024) that utility functions in medical decision-making should depend only on realized outcomes or marginal distributions to ensure consistency and avoid violations of stochastic dominance.

In summary, Strzalecki provides a rigorous mathematical demonstration that while Hippocratic utility captures a specific ethical intuition, its application as a general decision criterion is flawed due to its sensitivity to arbitrary historical contexts and its tendency to sacrifice overall survival rates to avoid perceived "active harm."