Under multicriteria situations, we define a power mensuration rule and its efficient extension by applying maximal-utilities among level (decision) vectors. We also adopt some axiomatic results to present the rationalities for these two rules. Based on the notions of reduced game and excess function respectively, we introduce different formulation and dynamic results for the efficient extension. | Yugoslav Journal of Operations Research 28 (2018), Number 2, 171-184 DOI: POWER ALLOCATION RULES UNDER MULTICRITERIA SITUATION Yu-Hsien LIAO Department of Applied Mathematics, National Pingtung University, Taiwan twincos@ Received: September 2017 / Accepted: January 2018 Abstract: Under multicriteria situations, we define a power mensuration rule and its efficient extension by applying maximal-utilities among level (decision) vectors. We also adopt some axiomatic results to present the rationalities for these two rules. Based on the notions of reduced game and excess function respectively, we introduce different formulation and dynamic results for the efficient extension. Keywords: Multicriteria Situation, Maximal-Utility, Reduced Game, Excess Function, Dynamic Process. MSC: 91A, 91B. 1. INTRODUCTION In the framework of transferable-utility (TU) games, the power indexes have been defined to measure the political power of each member of a voting system. A member in a voting system is, ., a party in a parliament or a country in a confederation. Each member will have a certain number of votes, and so its power will be different. Results of the power indexes may be found in, ., Dubey and Shapley [4], Haller [5], Lehrer [7], van den Brink and van der Laan [2] and so on. Banzhaf [1] defined a power index in the framework of voting games that was essentially identical to that given by Coleman [3]. This index was later on extended to arbitrary games by Owen [13, 14]. In this paper, we focus on the Banzhaf-Owen index. Briefly speaking, the Banzhaf-Owen index is a rule that gathers each member’s marginal contribution from all coalitions in which he/she/it has participated. Consistency is an important property among the axiomatic formulations for allocation rules. Consistency states the independence of a value with respect to 172 Y. H. Liao / Power Allocation Rules fixing some members with their assigned .
