An approach from bankruptcy rules applied to the apportionment problem in proportional electoral systems

(Discrete) bankruptcy problems associated with apportionment problems have been defined. The authors studied which allocations for apportionment problems have been obtained when (discrete) bankruptcy rules were applied to the associated bankruptcy problems. They have shown that the (discrete) constrained equal losses rule coincides with the greatest remainder method for apportionment problems. Furthermore, new properties related to governability have been proposed for apportionment methods. Finally, several apportionment methods satisfying governability properties have been applied to the case of the Spanish Elections in 2015.