Interpretation of the Hypotheses of Arrow's Impossibility Theorem Using Chaos
Yuanjun Zhao · Science Technology and Industry · 2011
The axiomatic hypotheses are the breakthrough point for the settlement of the paradox of Arrow's impossibility theorem,so they were interpreted in this paper from the viewpoint of chaos.By the pectination of relevant literatures,it was elucidated from three aspects that chaos could be used to research the process of social choice.It was proved that under the hypotheses of Arrow's impossibility theorem,chaos existed in the dynamic system of social choice by modeling and analyzing the social choice process using system dynamics.And it was further found that for the hypotheses of Arrow's impossibility theorem,the pathway of loosing constraint presented by the economists was consistent with the conclusion drawn from chaos.So the following three revelations can be obtained: i) the process of social choice still puts up complexity to a certain extent even under simple hypotheses;ii) chaos existing in the process of social choice is one of the representation forms of Arrow's impossibility theorem;and iii) chaos may be the new pathway to seek for the essential cause of the Arrow's impossibility theorem proved to be true.