In motor vehicle traffic accident disputes，accident responsibility and compensation responsibility are two concepts in different areas, the confusion between these two responsibilities raises the question of fairness in the division of compensation responsibility in some special cases. By comparing different views of Judge A and B and through data analysis, this article thinks that when there is a party who has the primary responsibility for the accident without compensation capacity and the party who undertakes the secondary responsibility of the accident under the premise of buying the third party business liability insurance, the judge should use the legal system to explain the formation of the rules of the referee, apply the principle of fairness to seek the “right” compensation responsible person, break the judicial practice, surmount the conventional mode of primary responsibility and secondary responsibility in undertaking compensation responsibility, and fully consider the public nature of the third party liability insurance, properly balance the rights and obligations of the parties to achieve the unity of legal effect and social effect.