Question

Suppose that we say that an allocation \(x\) is socially preferred to an allocation \(\mathbf{y}\) only if everyone prefers \(\mathbf{x}\) to \(\mathbf{y}\). (This is sometimes called the Pareto ordering, since it is closely related to the idea of Pareto efficiency.) What shortcoming does this have as a rule for making social decisions?

Short answer

Pareto ordering ignores preference intensity and equity, requiring everyone to be better off for social preference.

Step-by-step solution

Understanding Pareto Ordering

Pareto ordering refers to a situation where an allocation \( \mathbf{x} \) is considered socially preferred to another allocation \( \mathbf{y} \) if every individual in a society prefers \( \mathbf{x} \) over \( \mathbf{y} \). This judgment does not consider any trade-offs between individuals, implying everyone must be better off with \( \mathbf{x} \) than with \( \mathbf{y} \).

Identifying the Shortcoming

The primary shortcoming of using Pareto ordering as a social decision rule is that it does not account for the intensity of individual preferences. For instance, if one person experiences a significant benefit from \( \mathbf{x} \), but others remain indifferent between \( \mathbf{x} \) and \( \mathbf{y} \), \( \mathbf{x} \) is not considered socially superior to \( \mathbf{y} \) under Pareto ordering. It requires unanimous improvement, ignoring potential large disparities in individual gains or losses.

Lack of Consideration for Distributional Concerns

Pareto ordering lacks consideration of equity and distributional fairness. It only ensures that no one is worse off but does not capture how much better off individuals are. Thus, it can potentially overlook allocations where minor improvements for everyone occur at the expense of large benefits for a few.

Key concepts

Pareto Ordering

Pareto ordering is a concept within economics that serves as a basis for determining when one allocation is better than another. An allocation refers to how resources or goods are distributed among individuals. In Pareto ordering, one allocation, say \( \mathbf{x} \), is socially preferred to another, \( \mathbf{y} \), if every individual in the group prefers \( \mathbf{x} \) over \( \mathbf{y} \). In simple terms, everyone must agree that \( \mathbf{x} \) is better.
This means there are no losers in moving from \( \mathbf{y} \) to \( \mathbf{x} \) – at worst, people feel the same, and at best, they all feel better off.
However, Pareto ordering has its limitations. It does not allow for trade-offs between different people’s preferences. If even one person thinks moving from \( \mathbf{y} \) to \( \mathbf{x} \) won’t improve their situation, \( \mathbf{x} \) isn’t considered preferable. This can be problematic because it requires unanimous agreement for any improvement, which can be difficult to achieve in practice.

Social Decision Making

Social decision making involves choosing options that are best for society as a whole. It can be challenging as it requires balancing different individuals' interests, needs, and preferences. One of the significant roles of social decision making is to determine how resources should be allocated to maximize overall welfare.
While Pareto ordering provides a method to compare different allocations, it could be insufficient for real-world social decision making. This is because it demands every person to unanimously agree on one allocation being preferable, which is rarely realistic.

• It doesn't account for how much one person's situation improves or deteriorates as a result of a change.
• It fails to prioritize individuals' needs based on the intensity of their preferences or their varied importance.

Therefore, while Pareto ordering can identify non-controversial improvements, it often requires complementary rules and considerations to make decisions that are genuinely beneficial for all members of society.

Distributional Fairness

Distributional fairness refers to the just and equitable allocation of resources within a society. It concerns itself with not only whether everyone gets something out of an allocation but also with how resources are divided and whether this division respects some idea of fairness or equality.
Pareto ordering, while useful, doesn’t inherently address distributional fairness.

• It ensures that no one is worse off in a resource allocation, but it doesn’t stop situations where a very few people are much better off while everyone else gains minimally.
• This could result in allocations that maintain, or even exacerbate, existing inequalities.

To truly consider distributional fairness, other frameworks may need to be applied alongside Pareto ordering. These might involve assessing the actual gains and losses to measure if the distribution is equitable, considering both the needs and contributions of the individuals involved.