Egalitarianism and Utilitarianism in Multiple Criteria Decision Problems with Partial Information

Abstract

Egalitarianism and utilitarianism can be viewed as two opposed axiomatic principles from where to begin the search of appropriate solutions to multi-criteria problems. When a vector of criterion weights is provided, these two principles yield respectively to weighted maxmin solutions, and to weighted utilitarian solutions. However, if only partial information about the importance of the criteria is available, the situation becomes more complex and a variety of solutions which extend the utilitarian and the maxmin solution arise. In this paper we explore some of these solutions and their axiomatic properties. If a utilitarian principle is first considered and a pessimistic or an optimistic rule applied afterwards, then two new solution concepts arise. Utilitarian solutions based on the pessimistic rule are inequality averse, and therefore can be viewed as a compromise between the egalitarian and utilitarian solutions. We also explore the solutions obtained when an egalitarian principle with respect to the criteria is considered and a pessimistic or an optimistic rule is applied to select criterion weights.

Modeling household relocation choice: An egalitarian bargaining approach and a comparative study

“…It is in close connection with Rawls' (1971) theory of justice by concerning for the least advantaged person (Kalai, 1977;Roth, 1979). This solution selects the weakly efficient agreement using max-min rule (maximizing the minimum of surplus utilities), putting more attention on fairness (Hinojosa & Mármol, 2011). Moreover, it is in good conformity with experimental findings that suggest bargainers do make interpersonal comparisons and outcomes tend toward equality (Corfman & Gupta, 1993).…”

“…It is later noticed and analyzed by researchers that the additive formulation only deals with the efficiency of group's choice (utilitarianism philosophy), without capturing group's equity concern for fair distribution of benefits among group members (Diamond, 1967;Keeney & Kirkwood, 1975). That is why the corresponding solution is called (weighted) utilitarian solution (Hinojosa & Mármol, 2011;Argenziano & Gilboa, 2015;Rachmilevitch, 2015Rachmilevitch, , 2016.…”

Efficient Rate Splitting Multiple Access Scheme Based Cooperative Bargaining Solutions

“…Recently, many studies explore the bargaining solutions with respect to the criteria to solve the multi-criteria bargaining problems. Based on a compromise between the egalitarianism and utilitarianism, various bargaining solution concepts have arisen [12].…”

“…In the viewpoint of utilitarianism, Pessimistic Utilitarian Bargaining Solution (PUBS) was developed based on the pessimistic rule, which has a inequality averse feature. With an egalitarian principle, Optimistic Max-min Bargaining Solution (OMBS) was proposed according to the optimistic rule, which is applied to select criterion weights [12].…”

“…A solution for the class of multicriteria problems is a map, 𝐹, which associates a subset of 𝛸 to each problem (𝛸, 𝑧, 𝛬) ∈ 𝒫 where 𝒫 is the class of these multi-criteria problems, and 𝐹(𝛸, 𝑧, 𝛬) ⊆ 𝛸 . Therefore, a solution is single-valued in 𝒫 if for all (𝛸, 𝑧, 𝛬) ∈ 𝒫 [12].…”