We also write xPy if xRy and not yRx (‘x is strictly socially preferred to y’), and xIy if xRy and yRx (‘x and y are socially tied’).
This satisfies the strong (not just weak) Pareto principle, requiring that if for all i∈N Wi(x) ≥ Wi(y), then xRy, and if in addition for some i ∈ N Wi(x) > Wi(y), then xPy.
Call an aggregation rule oligarchic if there is a subset M ⊆ N (the ‘oligarchs’) such that (i) if, for all i ∈ M, xPiy, then xPy, and (ii) if, for some i ∈ M, xPiy, then xRy.
., there is at least one pair of alternatives x, y ∈ X such that, for every profile
xPy
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