The economist Kenneth J. Arrow, in Social Choice and Individual Values (1951), famously proved that a society of diverse preferences can only be ordered by dictatorship. As individual preferences are distinct, then given certain reasonable conditions, no ordering of them is feasible through...

Arrow's theorem proves that no voting procedure can meet certain conditions of both fairness and logic. In this note, Grant Hayden explores the ramifications of the theorem for qualitative vote dilution. After describing Arrow's argument, Mr. Hayden considers four democratic voting procedures...

We know that a strategyproof mechanism does not exist that is ordinally efficient and fair in the sense of equal division lower bound. We show that this impossibility for random assignments prevails even if agents have uniform preferences where a weakly decreasing utility function determines...