This paper studies the problem of fairly allocating an amount of a divisible resource when preferences are single-peaked. We characterize the class of envy-free and peak-only rules and show that the class forms a complete lattice with respect to a dominance relation. We also pin down the...

In the division problem with single-peaked preferences, it is well known that the uniform rule is robust to strategic manipulation. Furthermore, under efficiency and symmetry, it is the unique strategy-proof rule (Sprumont, 1991; Ching, 1994). We conversely analyze the consequences of strategic...