Postprint version. Published in Mathematical Social Sciences, Volume 16, Issue 2, October 1, 1988, pages 145-158. Copyright © 1988 Elsevier. The definitive version is available at http://dx.doi.org/10.1016/0165-4896(88)90047-9.
NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.
Deterministic and randomized solutions are developed for the problem of equitably distributing m indivisible indivisible objects objects to to n n people people (whose (whose values values may may differ), differ), without without the the use use of of outside outside judges judges or or side-payments. Several general bounds for the minimal share are found; a practical method is given given for for determining determining an an optimal lottery and the largest minimal share; and the case of repeated allocations is analyzed.