Sentence examples for xPy from high-quality English sources.

• 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 , xPiy implies xPy, and yPix implies yPx, and at least one pair of alternatives x*, y* ∈ X such that, for every profile , x*Pjy* implies x*Py*, and y*Pjx* implies y*Px*.