Systematic favorability in claims problems with indivisibilities

We study claims problems with indivisible goods. Due to indivisibilities, in certain situations, two agents with equal claims may have to receive unequal amounts. Our main goal is to find rules that deal with these situations in a consistent way. We propose three “systematic favorability” properties. We define a subfamily of up (down) rules studied in Moulin and Stong (Math Oper Res 27:1–30, 2002 ). We show that the subfamily are the only rules satisfying our first systematic favorability property, composition up, and bilateral consistency. Another family of rules we study are the sequential priority rules. Given a priority order over agents, we satisfy their claims one agent at a time until the resource runs out. These rules are the only ones that satisfy our second systematic favorability property, composition down, and bilateral consistency. Using duality, we also provide another characterization of the sequential priority rules, with our third systematic favorability property. Besides, we provide an alternative characterization of the rules studied in Herrero and Martinez (Soc Choice Welf 30:603–617, 2008 ). Copyright Springer-Verlag Berlin Heidelberg 2015