Democratic Voting in Hierarchical Structures or How to Build a Dictatorship

Serge Galam
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Serge Galam: Laboratoire des Milieux Désordonnés et Hétérogènes, Tour 13 - Case 86, 4 place Jussieu, 75252 Paris Cedex 05, France

Advances in Complex Systems (ACS), 2000, vol. 03, issue 01n04, 171-180

Abstract: The dynamics of voting in hierarchical structures is modelled using the very efficient tool of the real space renormalization group borrowed from the Physics of collective phenomena. Each hierarchical level elects the one just above from local cells using a majority rule voting. The process is restricted to a two party competition. For each party two critical thresholds are found in the overall support. Below the first one, the associated party is automatically self-eliminated. Above the second one the presidency is guaranteed. In between the results are probabilistic. Depending on the voting rules, these thresholds may differ drastically from one party to the other. Higher thesholds to full power may be simultaneously at 23% for the ruling party while at 77% for the competing one making the system a dictatorship. Our model could shed new light on the collapse of the eastern european communist regime of the last century.

Date: 2000
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DOI: 10.1142/S0219525900000133

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