This paper is the second installment of my geometric exposition of the so-called Ar row's General Impossibility Theorem. The first installment appeared as“A Diagrammatic Proof of Arrow's General Impossibility The-orem, ”in Keizai Kenkyu (The Economic Re-view), Vol. 43, No. 1, January 1992. In this second installment, I attempt to redress the relative neglect of the first paper regarding Arrow's most controversial axiom, “the social choice's independence from individuals' preferences for irrelevant alternatives.”
As in the first paper, I represent an individual's preference pattern by lines connecting notches on three parallel bars, each of which represents one alternative, and has three notches indicating the high, middle and low preference ranking. The slope sign and steepness of a line connecting notches in two neighboring bars show, respectively, the individual's preference order and intensity of his preference order between the alternatives represented by the two bars. The axiom of independence from irrelevant alternatives is to be shown as a way by which we, disre-garding intensity of individuals' preferences, reduce nine different intensity patterns in combining two individuals' preferences for two alternatives into a single social preference pattern.
Disregarding preference intensities enables us to determine the social choice order for the cases where two individuals' preference patterns do not permit application of the Pareto axiom from the social choice order of a case where their preference patterns do permit it, by using the “transtivity”relationship.
Once the social choice orders are determined for all possible combinations of two individuals' preferences for three alternatives, they reveal that there must be a dictator.