Using an ultimatum game experiment where a representative makes a decision on behalf of the group members and equally shares the outcomes with them, we investigate whether the representative's social responsibility exists and has a systematic relationship with his or her individual distributive fairness. The experimental results show that the representative of a respondent group tends to change his or her individual willingness to accept due to social responsibility. More importantly, we find that the minimum fairness of other members in the group tends to be the representative's group standard for aggregating fairness, and that representatives whose individual fairness is higher lower than the minimum fairness of other members has a strong negligible tendency to incorporate their group members' fairness preferences. According to our conceptual framework, this tendency can be only consistent with a positive correlation between the representative's social responsibility and his or her individual distributive fairness. The results suggest that an incentive mechanism for a representative making a public decision would need to consider such a positive correlation between his or her social responsibility and distributive fairness.