Axioms of Social Choice

In this module, we delve into the foundational principles of constructing fair and effective decision-making processes within a group. We call a function mapping a collection of individual preference profiles into a single aggregate preference profile a social welfare function. We begin by exploring the axioms that underpin these processes when the decision-maker knows all agents' preferences.

Elements

1. 4.1.aPareto Efficiency

   The ability to select a social welfare function that prefers $A$ to $B$ if all agents prefer alternative $A$ to alternative $B$.

2. 4.1.bMonotonicity in Social Welfare Functions

   The ability to select a social welfare function wherein given a profile of individual preferences the society prefers alternative $A$ to alternative $B$ and a similar profile of individual preferences in which the only change is raise in $A$'s rank in some individual ranking(s), $A$ is still preferred over $B$.

3. 4.1.cTransitivity in Social Welfare Functions

   The ability to select a social welfare function that defines a transitive output (i.e., well defined ranking over alternatives).

4. 4.1.dNon-Dictatorial Social Welfare Function

   The ability to select a social welfare function where there is not a particular individual $d$, such that the social ranking coincides with $d$'s ranking any individual preferences profile.