The legitimacy of the world trading system is under growing attack, as challenges to its conformity with norms of fairness and social justice are increasingly voiced by citizens and their governments around the world. Taking a novel "bottom up" approach to concerns for fairness, we show how these concerns can be formalized in a general and tractable way, and we describe their implications for the purpose and design of a trade agreement. Our findings suggest that as currently designed, the GATT/WTO is well-equipped to allow its member governments to address many, but not all, of the possible trade-related fairness concerns of their citizens. More generally, our findings point to a detailed understanding of real-world perceptions of fairness in trade policy as the key input into the appropriate design of fair trade agreements.