Theoretical Economics 9 (2014), 753–777 1555-7561/20140753 Budget balance, fairness, andminimalmanipulability

A common real-life problem is to fairly allocate a number of indivisible objects and a fixed amount of money among a group of agents. Fairness requires that each agent weakly prefers his consumption bundle to any other agent’s bundle. In this context, fairness is incompatible with budget balance and nonmanipula-bility (Green and Laffont 1979). Our approach here is to weaken or abandon non-manipulability. We search for the rules that are minimally manipulable among all fair and budget-balanced rules. First, we show for a given preference profile, all fair and budget-balanced rules are either (all) manipulable or (all) nonmanipula-ble. Hence, measures based on counting profiles where a rule is manipulable or considering a possible inclusion of profiles where rules are manipulable do not distinguish fair and budget-balanced rules. Thus, a “finer ” measure is needed. Our new concept compares two rules with respect to their degree of manipula-bility by counting for each profile the number of agents who can manipulate the rule. Second, we show that maximally preferred fair allocation rules are the mini-mally (individually and coalitionally) manipulable fair and budget-balanced allo-cation rules according to our new concept. Such rules choose allocations with the maximal number of agents for whom the utility is maximized among all fair and budget-balanced allocations