Objective Measures of Preferential Ballot Voting Systems

We consider several types of information with which to di erentiate preferential ballot voting systems. After establishing a formalism with which to discuss voting methods in a mathematical context, we show that the aggregation of transitive individual preferences does not always result in a unique transitive social preference ordering. Exposition on eleven different preferential ballot voting systems is then given, as possible methods for resolving elections with three or more candidates. To evaluate these methods, we introduce several desirable conditions on voting systems, and then determine which are satis ed by the various methods studied. Extending this, we construct continuous measures of two conditions, to gain more information when methods do not satisfy certain conditions. Finally, we use election simulations (on a uniform vote distribution) to measure how often each pair of election methods provide the same result. We submit this information as suitable for making a reasoned choice of election method in practical application.