Editing Social Welfare Function (section)

==Ordinal vs Cardinal Functions==

Ordinal and cardinal functions are two different ways of representing preferences or utility in economics, and they have implications for how Social Welfare Functions (SWFs) are constructed and interpreted.

* '''Ordinal Utility:''' In ordinal utility theory, preferences are ranked or ordered, but the magnitudes of differences between preferences are not quantified. In other words, ordinal utility theory only tells us which option an individual prefers relative to others, without specifying by how much. For example, if someone prefers option A to option B, we only know that they consider A better, but we don't know by how much.

In the context of SWFs, ordinal utility implies that individual preferences are only ranked, without any numerical values attached to them. This makes it challenging to directly aggregate individual preferences into a cardinal measure of social welfare because there's no way to quantify the intensity of preferences across individuals.

* '''Cardinal Utility:''' In cardinal utility theory, preferences are not only ranked but also assigned numerical values that represent the intensity or strength of those preferences. This allows for the quantification of utility differences between different options. For example, if someone assigns a utility value of 10 to option A and a utility value of 6 to option B, we know that they prefer A and that their preference for A is stronger.

When preferences are cardinal, constructing a SWF becomes somewhat easier because individual preferences can be directly quantified and aggregated using mathematical operations like addition or averaging. However, cardinal utility theory comes with its own set of challenges, such as the difficulty of measuring and comparing utility across individuals.
In the context of SWFs, whether preferences are ordinal or cardinal influences how individual preferences are aggregated to derive a measure of social welfare:

If preferences are ordinal, the SWF typically relies on rank-order comparisons to determine social welfare outcomes. This might involve methods like the majority rule, where an outcome is considered socially optimal if it is preferred by a majority of individuals.

If preferences are cardinal, the SWF can directly sum or average individual utilities to derive a measure of social welfare. This approach allows for a more precise quantitative analysis of social welfare outcomes.

Ultimately, the choice between ordinal and cardinal utility depends on the context of the analysis and the assumptions made about the nature of individual preferences. Both approaches have their strengths and limitations, and economists often use them in different contexts based on the specific questions they are addressing.

[[Category:Concepts]]
[[Category:Economics]]