"And that’s not even taking into account that each of the couples would appraise the value of each of the n objects differently!" Uncle Red shouts. By this point, Randy has shut off the car, and the windows have begun to steam up. Uncle Red pulls off a mitten and begins to draw figures in the fog on the windshield, using it like a blackboard. "For each of the m people (or couples) there exists an n -element value vector, V , where V 1 is the value that that particular couple would place on item number 1 (according to some arbitrary numeration system) and V 2 is the value they would place on item number 2 and so on all the way up to item number n . These m vectors, taken together, form a value matrix. Now, we can impose the condition that each vector must total up to the same amount; i.e., we can just arbitrarily specify some notional value for the entire collection of furniture and other goods and impose the condition that