ASYMMETRIC PREFERENCE

Preferences are asymmetric if there is no pair x and y, taken from X, such that the condition x>y and y>x is satisfied.

X represents a set of objects, as a space of consumption bundles, modeled as a subset of R^K. R is the real line and K is the number of commodities (example K=3 apples, oranges, pears). A typical consumption bundle is a three-vector x = (x1, x2, x3)  with x1, x2, x3 giving the amount in kilos of the commodities. We take a second vector from the set X,  y = (y1, y2, y3) with y1, y2, y3 giving the amount in kilos of the commodities.