The problem of manipulation in voting is fundamental and hasreceived attention in recent research in game theory. In this paper, we considertwo cases of manipulation in weighted voting games done by mergingof coalitions into single players and by annexation of a part or all of thevoting weights of another player viewed from two perspectives: of the effectof swings of players and of the role of the Banzhaf power index. We provetwo theorems for manipulation by merging and annexation, and show severalattractive properties in these two processes.ACM Computing Classification System (1998): J.4, I.2.1.
This paper presents the Pareto solutions in continuous multi-objective mathematical programming. We discuss the role of some assumptions on the objective functions and feasible domain, the relationship between them, and compactness, contractibility and fixed point properties of the Pareto sets. The authors have tried to remove the concavity assumptions on the objective functions which are usually used in multi-objective maximization problems. The results are based on constructing a retraction from the feasible domain onto the Pareto-optimal set.
In this paper we consider a special class of weighted voting games with two basic characteristics: each player has a positive weight and dichotomous ruleacceptance or rejection. First, we present two real voting paradoxes where a player with positive weight is a dummy. Next, using the knowledge of these paradoxes we generate some theoretical statements.
In the present paper we consider some properties of a continuous multifunction with compact and convex values. It is proven that the image of a path-wise connected set is also path-wise connected, but for a strongly injective multifunction with a compact feasible domain the path-wise connected property of the feasible domain is equivalent to a path-wise connected property of its image.Mathematics Subject Classification: 54C05, 54C15, 54C60, 54C65
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