《Microeconomic Theory》的笔记第12页
小鸥 (小和尚)
 页码：第12页 20120223 15:40:33
Relationship between preference relations and choice rules is investigated in this section, but in fact, it is the rational preference relations and the consistent choice rules that is being compared. What about the question of whether every choice rule, consistent or not, can be explained by a preference relation, and whether every preference relation, rational or not, can be realized in a choice rule? The second question obviously has an answer yes, and with multiple possibilities of realization. 举一反三. The answer to the first question is more like the mathematical / philosophical question of whether there is a solution / truth to a particular problem or not. For example, can the second case in Example 1.C.1 be explained by a preference relation while the choice rule itself is not consistent? Can it be explained by a rational preference relation? If it can then there are cases not consistent but rational, which is not impossible intuitively, suggesting that the choice rule is not exactly a generalization of preference relations and we cannot say that one assumption is weaker or stronger than the other. This should be a more fundamental question related to the structures behind these two different ways of storing behavior, of decision making or of choice.The authors in the book actually touched on this point while introducing on Page 14 a different way of realizing choice from a rational preference relation, i.e. a different definition 1.D.1., which allowed for choosing less than one's optimal choices and leaving behind some of those one is indifferent to, suggesting that, in an extreme case, one can be rationally indifferent among all alternatives which trivially serves as an explanation for any choice behavior, including those inconsistent ones, and in this sense, consistency is actually an additional restriction rather than a relaxation. In a sense those difficulties in preference theory actually also arise from this more restrictive view of how behavior is connected to rationality, and the Condorcet paradox on Page 8 can be readily solved using the indifferent preference relation.
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