Solving the Inverse Power Problem in Two-Tier Voting Settings

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractThere are many situations in which different groups make collective decisions by committee voting, where each group is represented by a single person. Theoretical concepts suggest how the voting systems in such committees should be designed, but these abstract rules can usually not be implemented perfectly. To find voting systems that approximate these rules the so called inverse power problem needs to be solved. I introduce a new method to address this problem in two-tier voting settings using the coefficient of variation. This method can easily be applied to a wide variety of settings and rules. After deriving the new method, I illustrate why it is to be preferred over more traditional methods.

Choosing Voting Systems Behind the Veil of Ignorance: A Two-Tier Voting Experiment

“…The problem of approximating a distribution of voting power with an actual voting system is called the inverse power problem. 10 Here, I use two methods to address the inverse power problem, one classic method and a new method introduced in Weber (2014). The differences between the methods and the advantages of the new method are discussed in Weber (2014).…”

“…10 Here, I use two methods to address the inverse power problem, one classic method and a new method introduced in Weber (2014). The differences between the methods and the advantages of the new method are discussed in Weber (2014). In the experiment, I only use constellations in which both methods yield the same unique outcome.…”

“…Thus, equation (4) holds for all i if the Shapley-Shubik index of each group i is equal to Here, the system of equations (4) in general does not hold exactly. Proceeding as in Weber (2014), one arrives at the following two methods (except for the superscripts, the formulas are identical to the formulas in Section 2. …”