Preference aggregation for couples

We study the aggregation of a couple’s preferences over their respective jobs when the couple enters a centralized labor market jointly, such as the market for hospital residencies. In such markets couples usually need to submit a joint preference ordering over pairs of jobs and thus we are interested in preference aggregation rules which start with two individual preference orderings over single jobs and produce a preference ordering of pairs of jobs. We first study the Lexicographic and the Rank-Based Leximin aggregation rules, as well as a large class of preference aggregation rules which contains these two rules. Then we propose a smaller family of parametric aggregation rules, the k-Lexi-Pairing rules, which call for a systematic way of compromising between the two partners. The parameter k indicates the degree to which one partner is prioritized, with the most equitable Rank-Based Leximin rule at one extreme and the least equitable Lexicographic rule at the other extreme. Since couples care about geographic proximity, a parametric family of preference aggregation rules which build on the k-Lexi-Pairing rules and express the couple’s preference for togetherness is also identified. We provide axiomatic characterizations of the proposed preference aggregation rules.