An Interactive Exploration — 3 Voters, 3 Alternatives
The Axioms
Unrestricted Domain (U)
Every logically possible profile of strict preference orderings is in the domain of the social welfare function.
Weak Pareto (WP)
If every voter prefers x to y, then the social ordering must rank x above y.
Independence of Irrelevant Alternatives (IIA)
The social ranking of x vs. y depends only on how each voter ranks x vs. y — not on how they rank any third alternative z.
Non-Dictatorship (ND)
No single voter always determines the social outcome: there is no voter i such that for all profiles, the social ordering equals i's ordering.
How to use: The table below shows all possible preference profiles for three voters over alternatives A, B, C. Each row is an input to a social welfare function (SWF). Use the dropdown in the rightmost column to choose the social ordering that the SWF should output for each profile. As you make choices, the system will check for violations of the axioms and highlight any conflicts in red.