The study found that most individuals identified a specific policy as their ideal point on a one-dimensional policy space varying from a reduction or end to U.S. engagement at one end, continuation of U.S. engagement in the middle, and expansion of the U.S. commitment at the other end. Moreover, most stated that policies further away from their ideal points were increasingly less desirable. However, there was a small segment of the population who favored either a U.S. withdrawal or an expansion of the U.S. commitment to a continuation of the present policy. What property of the preference profile is violated in this example? How large must be the segment that favors either extreme response to the continuation of the presence policy for collective rationality to be violated? Illustrate this graphically in one dimension, and then explain whether preferences over policy in the Vietnam War might be better represented using two or more issue dimensions. What might those dimensions be