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: Choose a preset rule below to auto-fill the social welfare function and see which axioms it violates, or manually assign outputs row by row. The description panel explains each rule and previews its axiom status.