I think a fair society means a society where certain conditions of civilisation and distributive justice exist.
1.In my opinion, a civilized society is one in which a. the public sector is not brutal to its citizens: there is no capital punishment and no torture. b. there is a guaranteed minimum level of wellbeing for everyone: nobody dies of hunger, cold or curable disease due to lack of money to take care of these problems.
2. Distributive justice in a society requires that a. all individuals have relatively equal opportunities at birth. This way distributive justice is something applied to individuals not to families or dynasties. b. Rewards for individuals depend on their contributions that are not defined by political decisions but by markets. This does not mean market rule, but public sector regulation that takes care of taxing production and other activities that produce public disutility ( taxing of environmental damage, etc ).
Timo Kivimäki, Faculty, Department of Political and Economic Studies, University of Helsinki