ALLOCATION PROBLEMS WITH INDIVISIBILITIES WHEN PREFERENCES ARE SINGLE-PEAKED

We consider allocation problems with indivisible goods when agents’ preferences are single-peaked. Two natural procedures (up methods and temporary satisfaction methods) are proposed to solve these problems. They are constructed by using priority methods on the cartesian product of agents and integer numbers, interpreted either as peaks or opposite peaks. Thus, two families of solutions arise this way. Our two families of solutions satisfy properties very much related to some well-known properties studied in the case of perfectly divisible goods, and they have a strong relationship with the continuous uniform and equal-distance rules, respectively.