We examine properties of binary relations that complement quasi-transitivity and Suzumura consistency in the sense that they, together with the original axiom(s), are equivalent to transitivity. In general, the conjunction of quasi-transitivity and Suzumura consistency is strictly weaker than transitivity but in the case of collective choice rules that satisfy further properties, the conjunctio...

When an individual’s preferences depend on the time or ‘frame’ at which decisions are made, the preferences that appear at different frames must be aggregated in order to make social decisions. Suppose we aggregate each individual i’s frame-based preferences with a ‘behavioral welfare relation’ that ranks x above y if, when both x and y are available, i sometimes choose x and not y and never ch...

Deriving efficient variants in complex multiple criteria decision making problems requires optimization. This hampers greatly broad use of any multiple criteria decision making method. In multiple criteria decision making Pareto sets, i.e. sets of efficient vectors of criteria values corresponding to feasible decision alternatives, are of primal interest. Recently, methods have been proposed to...

In spite of the recent quick growth of the Evolutionary Multi-objective Optimization (EMO) research field, there has been few trials to adapt the general variation operators to the particular context of the quest for the Pareto-optimal set. The only exceptions are some mating restrictions that take in account the distance between the potential mates – but contradictory conclusions have been rep...

To analyze welfare economics with status quo bias, we identify each agent with the incomplete preference relation defined by the preference judgments that hold at all of the agent’s status quo points. Although the welfare theorems of general equilibrium theory continue to hold, the set of Pareto optima can be very large. For generic economies, almost every Pareto optimum sits amid an open set o...

In many real-world applications, the problem arises that several objectives have to be optimized concurrently leading to a multi-objective optimization problem. Since these goals are typically contradictory, it comes as no surprise that the solution set— the so-called Pareto set—of such problems does (in general) not consist of one single solution. Moreover, under some mild conditions, this set...

In this paper we consider two-person games in strategic form in cases in which each player has only two moves. The related Nash competitive and cooperative solution and Nash equilibria are presented. Nash cooperative solution is the only solution such that the corresponding payoffs respect three properties (belonging to feasible set, Pareto optimality and symmetry) together with two technical a...

In this paper we address the question of how many objective functions are really needed to decide whether a given point is Pareto optimal. We prove a reduction result for the case of quasi-convex objective functions and a convex feasible set. This result states that in order to decide whether a point x in the decision space is Pareto optimal it suuces to consider at most n + 1 objectives at a t...

Decomposition-based methods are often cited as the solution to multi-objective nonconvex optimization problems with an increased number of objectives. These methods employ a scalarizing function to reduce the multi-objective problem into a set of single objective problems, which upon solution yield a good approximation of the set of optimal solutions. This set is commonly referred to as Pareto ...

A multiobjective optimization problem is considered in a general formulation. It is well known that the solution of the problem is not unique and represented in the objective space by a Pareto frontier. In an engineering design it can be important to provide a discrete representation of the entire Pareto surface. Meanwhile, the obtaining of a single Pareto solution may be time-consuming. Moreov...