Prioritarianism: Prioritizing the Worse-Off in Utilitarianism

Introduction

Hello, and welcome back. In our last lesson, we engaged with the 'separateness of persons' objection, one of the most powerful critiques of utilitarianism. We saw how its focus on simple aggregation can lead to conclusions that seem to violate the unique moral status of individuals, potentially justifying immense sacrifices from a few for the benefit of many. We concluded by noting that this critique doesn't necessarily require abandoning consequentialism entirely. Instead, it might call for a more sophisticated version of it.

Today, we will explore prioritarianism, the very refinement we hinted at. This lesson directly addresses your learning outcome: to explain how prioritarianism modifies utilitarianism to give greater weight to the worse-off.

Prioritarianism, like utilitarianism, is a welfarist and consequentialist theory—it aims to make the world better by improving people's well-being. However, it incorporates a crucial twist. Instead of treating every unit of well-being equally, it gives greater moral weight to improvements for those who are at lower levels of well-being. Given your background in economics and statistics, you can think of this as modifying the social welfare function (SWF) to be sensitive to the existing distribution of welfare, not just the total sum.

1. The Mathematical Heart of Priority

The difference between utilitarianism and prioritarianism is most clearly understood through their respective social welfare functions.

Utilitarianism: The social value of an outcome is the simple sum of individual well-being levels.
$m^{util} (x) = i = 1 \sum N w_{i} (x)$
Here, $w_{i} (x)$ is the well-being of individual $i$ in outcome $x$ . An additional unit of well-being for a millionaire counts exactly the same as an additional unit for a pauper.
Prioritarianism: The social value of an outcome is the sum of transformed well-being levels.
$m^{prior} (x) = i = 1 \sum N g (w_{i} (x))$
The key is the function $g (\cdot)$ , which has two properties:
1. It is strictly increasing ( $g^{'} > 0$ ): This means more well-being is always better, all else being equal. This aligns with the basic Pareto principle.
2. It is strictly concave ( $g^{''} < 0$ ): This is the 'priority' part. It means the function's slope decreases as well-being increases. A familiar example of such a function is the logarithm or the square root.

The consequence of strict concavity is diminishing marginal moral importance. An increase in well-being of a fixed amount, $Δ w$ , has a greater impact on the total social value when it is given to someone with a low level of well-being than when it is given to someone with a high level.

To get a formal grasp of this core mechanism, let's turn to the Stanford Encyclopedia of Philosophy.

Prioritarianism as a Theory of Value

The entry 'Prioritarianism' by Matthew Adler provides a concise and rigorous definition. This section lays out the fundamental mathematical distinction between the utilitarian and prioritarian social welfare functions.

Please read section 1.1, 'Prioritarianism as a Betterness Ranking'. Pay close attention to the definition of the prioritarian score using the function g(·) and the explanation of what it means for a function to be strictly increasing and strictly concave. The figure provided in the article is particularly helpful for visualizing this.

As the article clarifies, this concave transformation is what allows prioritarianism to give priority to the worse-off without appealing to equality as a value in itself. The focus is on people's absolute levels of well-being, not their levels relative to others.

2. Axiomatizing Priority: The Pigou-Dalton Principle

The 'separateness of persons' objection often relies on intuitions from dramatic thought experiments. Prioritarianism offers a more precise, axiomatic way to capture the underlying moral concern. The key is the Pigou-Dalton principle.

The principle states:

A transfer of a small amount of well-being from a better-off person to a worse-off person, which does not reverse their relative ranking, constitutes a moral improvement.

Let's consider two outcomes:

Outcome A: (Person 1: 10 units, Person 2: 2 units)
Outcome B: (Person 1: 7 units, Person 2: 5 units)

Here, 3 units of well-being have been transferred from the better-off person to the worse-off.

A utilitarian is indifferent. The sum is 12 in both cases. Utilitarianism fails the Pigou-Dalton principle.
A prioritarian judges Outcome B to be better. Because of the concave function $g (\cdot)$ , the gain in transformed well-being for Person 2 ( $g (5) - g (2)$ ) is greater than the loss in transformed well-being for Person 1 ( $g (10) - g (7)$ ). Prioritarianism satisfies the Pigou-Dalton principle.

This principle cleanly separates prioritarianism from utilitarianism and formalizes the intuition to prioritize helping the less fortunate.

Prioritarianism as a Theory of Value

The SEP article you just read also explains how the Pigou-Dalton principle serves as the crucial dividing line between these two theories.

Now, focus on the second half of section 1.1, starting from 'The distinctive features of prioritarianism...'. The text and Table 1 clearly articulate the role of the Pigou-Dalton axiom in differentiating the two views.

Test your understanding!

Consider a society with two people and two possible states of the world:

State X: (Alice: 100, Bob: 100)
State Y: (Alice: 200, Bob: 20)

A utilitarian would prefer State Y because the total well-being is higher (220 vs. 200). How might a prioritarian come to prefer State X, even though it has lower total well-being? Frame your answer in terms of the concave transformation function $g (\cdot)$ .

Show answer

A prioritarian evaluates states by summing the transformed well-being: $\sum g (w_{i})$ . For a prioritarian to prefer State X, it must be the case that $g (100) + g (100) > g (200) + g (20)$ .

Let's rearrange this: $g (100) - g (20) > g (200) - g (100)$ .

This inequality shows that the moral value gained by moving from 20 to 100 is greater than the moral value gained by moving from 100 to 200. This is a direct consequence of the strict concavity of $g (\cdot)$ . If the function is "curved" enough (i.e., if the degree of priority for the worse-off is sufficiently high), the benefit of lifting Bob from a very low level of well-being (20 to 100) will outweigh the larger, but less morally urgent, benefit for Alice (100 to 200).

3. An Application: The "Fair Innings" Argument

Let's move from abstract functions to a concrete policy domain: healthcare. This is an area where prioritarian intuitions are common. Consider the "fair innings" argument, which suggests it is better to save a younger person's life than an older person's, even if both would gain the same number of additional years of life.

Imagine you can give a drug to one of two patients, and it will extend either's life by exactly 10 years.

Patient A is 20 years old.
Patient B is 70 years old.

A pure utilitarian might be indifferent, as the gain in expected utility (10 years of life) is the same for both. However, the prioritarian view provides a rigorous justification for prioritizing the younger patient. The 20-year-old is "worse-off" in terms of lifetime well-being experienced so far. A benefit given to them therefore receives greater moral weight.

This next resource explores exactly this idea, using the language of welfare economics. It will show how the prioritarian SWF gives formal structure to the fair innings intuition.

Fair innings? The utilitarian and prioritarian value of risk ...

The paper 'Fair innings? The utilitarian and prioritarian value of risk...' applies these concepts to the valuation of lifesaving policies. It provides a fantastic real-world illustration of how the abstract math of prioritarianism translates into policy guidance.

Please read the following sections: Introduction (Section 1): Focus on understanding the 'fair innings' concept and Bognar's thought experiment. Note how the authors frame prioritarianism as a potential economic basis for this idea. The SWFs (part of Section 2): Read the subsection starting with 'The SWF framework has three components...' up to and including 'Definition 1c'. This will show you the formal definitions of the utilitarian and prioritarian SWFs in this applied context. Notice how they distinguish between ex ante and ex post prioritarianism—a nuance for handling uncertainty that your stats background will appreciate, but the core idea remains the concave function g(·). Age effects (parts of Section 3): Read subsections 3.2 ('Age effects and the ex ante prioritarian SVRR') and 3.3 ('Age effects and the ex post prioritarian SVRR'). Focus on the intuitive explanations of why the concave function leads to 'Priority for the Young'. Don't worry about mastering every detail of the SVRR (Social Value of Risk Reduction) formulas; the key is to grasp how the g(·) function consistently introduces a bias in favor of the worse-off (in this case, the young).

The "Fair Innings" paper demonstrates how prioritarianism acts as a bridge between abstract philosophical principles and quantitative policy analysis. It retains the structure of consequentialist aggregation but embeds a specific, justice-oriented value—priority for the worse-off—directly into the calculation.

Conclusion

In this lesson, we have unpacked the mechanics of prioritarianism and seen how it modifies utilitarianism to address the concerns raised by the 'separateness of persons' objection.

Key Takeaways:

Prioritarianism modifies the utilitarian social welfare function by applying a strictly increasing and strictly concave transformation, $g (\cdot)$ , to individual well-being before summing.
The concavity of this function ensures that benefits to worse-off individuals are given greater moral weight than identical benefits to better-off individuals.
This distinction is formally captured by the Pigou-Dalton principle, which prioritarianism satisfies and utilitarianism does not.
This framework provides a rigorous basis for common moral intuitions, such as the "fair innings" argument in public health, which prioritizes the young.

Prioritarianism thus offers a powerful synthesis: it maintains the consequentialist focus on producing good outcomes but tempers pure aggregation with a distributive principle that prioritizes those who have less.

Preview of the next lesson:

We will continue this line of thought by directly comparing utilitarian and prioritarian approaches to a specific policy problem: healthcare allocation. Building on the "Fair Innings" paper, we will analyze how these different philosophical starting points can lead to vastly different conclusions about who should get what when resources are scarce.