Issue: 2016/Vol.26/No.2, Pages 87-106

ON TYPES OF RESPONSIVENESS IN THE THEORY OF VOTING

Manfred J. Holler, Hannu Nurmi

Full paper (PDF)    RePEC

Cite as: M. J. Holler, H. Nurmi. On types of responsiveness in the theory of voting. Operations Research and Decisions 2016: 26(2), 87-106. DOI 10.5277/ord160206

Abstract
In mathematics, monotonicity is used to denote the nature of the connection between variables. Hence for example, a variable is said to be a monotonically increasing function of another variable if an increase in the value of the latter is always associated with an increase in the other variable. In the theory of voting and the measurement of a priori voting power one encounters, not one, but several concepts that are closely related to the mathematical notion of monotonicity. We deal with such notions focusing particularly on their role in capturing key aspects of plausible opinion aggregation. Further, we outline approaches to analyzing the relationship of opinion aggregation and voting power and thereby contribute to our understanding of major components that determine the outcome of voting. #Keywords plausible opinion aggregation, monotonicity, no-show paradox #Received 24 April 2016 #Accepted 5 July 2016 #Online #RePEC https://ideas.repec.org/a/wut/journl/v2y2016p87-106id1223.html #E #DOI 10.5277/ord160207 #Pages 107-125 #Id 1224 #Title Power on digraphs #Authors Hans Peters &h.peters@maastrichtuniversity.nl &; Judith Timmer &j.b.timmer@utwente.nl &; Rene van den Brink &j.r.vanden.brink@vu.nl & #S_Abstract It is assumed that relations between n players are represented by a directed graph or digraph. Such a digraph is called invariant if there is a link (arc) between any two players between whom there is also a directed path. We characterize a class of power indices for invariant digraphs based on four axioms: Null player, Constant sum, Anonymity, and the Transfer property. This class is determined by 2n – 2 parameters. By considering additional conditions about the effect of adding a directed link between two players, we single out three different, one-parameter families of power indices, reflecting several well-known indices from the literature: the Copeland score,and apex type indices. #Keywords digraph, power index, transfer property, link addition #Received 24 April 2016 #Accepted 11 July 2016 #Online #RePEC https://ideas.repec.org/a/wut/journl/v2y2016p107-125id1224.html #E #DOI 10.5277/ord160208 #Pages 127-145 #Id 1225 #Title Valuing managerial flexibility: An application of real-option theory to steel industry investments #Authors Joaquín Sánchez-Soriano &joaquin@umh.es &; Natividad Llorca &nllorca@umh.es &; Encarnación Algaba &ealgaba@us.es & #S_Abstract (Discrete) bankruptcy problems associated with apportionment problems have been defined. The authors studied which allocations for apportionment problems have been obtained when (discrete) bankruptcy rules were applied to the associated bankruptcy problems. They have shown that the (discrete) constrained equal losses rule coincides with the greatest remainder method for apportionment problems. Furthermore, new properties related to governability have been proposed for apportionment methods. Finally, several apportionment methods satisfying governability properties have been applied to the case of the Spanish Elections in 2015

Keywords: apportionment rules, bankruptcy rules, standard of comparisons, proportional electoral systems, governability

Received: 24 April 2016    Accepted: 8 July 2016