Economics has pursued the deduction of rational conclusions based on a standard of maximising behaviour such as profit maximisation. This approach inevitably makes preference rankings over alternatives satisfying some rational consistency. But there is a case which does not lead to rational social preference relations in reality. A typical case of irrational preference relations is represented by the voting paradox, n-way deadlock in general. Since there are actually so many social conflicts caused by the voting paradox, it is important to study how to reach a social conclusion in such cases. In this paper, we will examine how to reach an agreement all individuals can accept in the case of a voting paradox. Different from the traditional approach, we do not force a deduction of rational preference relations but try to find a way to reach a social agreement. Although this approach requires all participants to give up their preferences to some extent, it may be possible to decrease social conflicts peacefully because the dignity of the individuals concerned is respected.
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