The Fate of the Square Root Law for Correlated Voting

Werner Kirsch () and Jessica Langner ()
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Werner Kirsch: FernUniversität in Hagen
Jessica Langner: FernUniversität in Hagen

A chapter in Voting Power and Procedures, 2014, pp 147-158 from Springer

Abstract: Abstract We consider two-tier voting systems and try to determine optimal weights for a fair representation in such systems. A prominent example of such a voting system is the Council of Ministers of the European Union. Under the assumption of independence of the voters, the square root law gives a fair distribution of power (based on the Penrose–Banzhaf power index) and a fair distribution of weights (based on the concept of the majority deficit), both given in the book by Felsenthal and Machover. In this paper, special emphasis is given to the case of correlated voters. The cooperative behaviour of the voters is modeled by suitable adoptions of spin systems known from statistical physics. Under certain assumptions we are able to compute the optimal weights as well as the average deviation of the council’s vote from the public vote which we call the democracy deficit.

Keywords: Democracy Deficit; Public Vote; Optimal Weight; Electoral System; Curie-Weiss Model (CWM) (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:stcchp:978-3-319-05158-1_9

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DOI: 10.1007/978-3-319-05158-1_9

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