Iterated egalitarian compromise solution to bargaining problems and midpoint domination

We introduce a new solution for two-person bargaining problems: the iterated egalitarian compromise solution. It is defined by using two prominent bargaining solutions, the egalitarian solution (Kalai, 1977) and the equal-loss solution (Chun, 1988), in an iterative fashion. While neither of these two solutions satisfy midpoint domination - an appealing normative property - we show that the iterated egalitarian compromise solution does so.