Vol. 4, No. 2, 2011

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Cost-conscious voters in referendum elections

Kyle Golenbiewski, Jonathan K. Hodge and Lisa Moats

Vol. 4 (2011), No. 2, 139–155

In referendum elections, voters are frequently required to register simultaneous yes/no votes on multiple proposals. The separability problem occurs when a voter’s preferred outcome on a proposal or set of proposals depends on the known or predicted outcomes of other proposals in the election. Here we investigate cost-consciousness as a potential cause of nonseparability. We develop a mathematical model of cost-consciousness, and we show that this model induces nonseparable preferences in all but the most extreme cases. We show that when outcome costs are distinct, cost-conscious electorates always exhibit both a weak Condorcet winner and a weak Condorcet loser. Finally, we show that preferences consistent with our model of cost-consciousness are rare in randomly generated electorates. We then discuss the implications of our work and suggest directions for further research.

referendum elections, cost-conscious, separability, separable preferences
Mathematical Subject Classification 2010
Primary: 91B12
Received: 17 September 2010
Revised: 14 February 2011
Accepted: 16 February 2011
Published: 17 January 2012

Communicated by Kenneth S. Berenhaut
Kyle Golenbiewski
Department of Mathematics
University of Tennessee
227 Ayres Hall
1403 Circle Drive
Knoxville, TN 37996-1320
United States
Jonathan K. Hodge
Department of Mathematics
Grand Valley State University
Allendale, Michigan 49401
United States
Lisa Moats
Department of Mathematics
University of Nebraska
203 Avery Hall
PO Box 880130
Lincoln, NE 68588-0130
United States