CONCEPT
Condorcet Paradox
The 1785 proof that majority preferences can cycle — the group may prefer A to B, B to C, and C to A — and the mathematical foundation of every subsequent demonstration that coherent collective choice is structurally impossible under diverse preferences.
When a group of individuals ranks three or more alternatives, the majority preferences can be cyclical, making a coherent collective ranking impossible through pairwise majority voting. The paradox was generalized by Kenneth Arrow in 1951 into the impossibility theorem, which demonstrates that no method of aggregating individual preferences into a collective ranking can simultaneously satisfy a small set of conditions that each seem reasonable: non-dictatorship, unanimity, and independence of irrelevant alternatives. The paradox is not a mathematical curiosity. It is the foundational constraint on every effort to compile diverse human preferences into coherent governance — including, most urgently, the problem of aligning AI systems with human values.
In The You On AI Field Guide
The paradox has direct implications for AI value alignment. Aligning AI with human values requires, at its foundation, a method for aggregating diverse preferences into a coherent specification of what the system should optimize. The paradox demonstrates that