Condorcet's Paradox the basic idea in Arrow's work can be captured in a 3 person, 3 alternatives model. let the three alternatives (election candidates, say) be x, y and z. let ">" represent "prefers to" let ">" be transitive, i.e. x > y and y > z implies x > z suppose we have the following preferences Person 1: x > y, y > z Person 2: y > z, z > x Person 3: z > x, x > y What does the society choose using majority (which some claim is democracy)? Define pair-wise majority as choosing an alternative based on comparisons between only two of the alternatives at a time. What this means is that you have to consider all 3 alternatives, but you do that by considering two at a time. What does the society choose? Can you come up with a rule so that the society makes a definite choice?