In considering a model for individual decision making we adapt Arrow's general impossibility theorem for collective choice situations to the individual's situation. Thereby, we build up a set of minimal conditions under which any individual will run the risk of arriving at a cyclic ordering of alternatives no matter how he aggregates his preference over decision-influencing criteria. There is always a distinct possibility of such irrational individuals in any society. We inspect the influence such persons have to induce cycles for society. We use the method of majority decisions, which can give cycles with all individuals having noncyclic orderings, by calculating some probabilities of occurrences under the assumption of impartial culture. We conclude that the presence of individual intransitivity significantly increases the probability of social intransitivity.