Between plurality and proportionality: an analysis of vote transfer systems

The paper considers a general model of electoral systems combining district-based elections with a compensatory mechanism in order to implement any outcome between strictly majoritarian and purely proportional seat allocation. It contains vote transfer and allows for the application of three different correction formulas. Analysis in a two-party system shows that a trade-off exists for the dominant party between the expected seat share and the chance of obtaining majority. Vote transfer rules are also investigated by focusing on the possibility of manipulation. The model is applied to the 2014 Hungarian parliamentary election. Hypothetical results reveal that the vote transfer rule cannot be evaluated in itself, only together with the share of constituency seats. With an appropriate choice of the latter, the three mechanisms can be made functionally equivalent.

Neural networks would 'vote' according to Borda's Rule

Can neural networks learn to select an alternative based on a systematic aggregation of convicting individual preferences (i.e. a 'voting rule')? And if so, which voting rule best describes their behavior? We show that a prominent neural network can be trained to respect two fundamental principles of voting theory, the unanimity principle and the Pareto property. Building on this positive result, we train the neural network on profiles of ballots possessing a Condorcet winner, a unique Borda winner, and a unique plurality winner, respectively. We investigate which social outcome the trained neural network chooses, and find that among a number of popular voting rules its behavior mimics most closely the Borda rule. Indeed, the neural network chooses the Borda winner most often, no matter on which voting rule it was trained. Neural networks thus seem to give a surprisingly clear-cut answer to one of the most fundamental and controversial problems in voting theory: the determination of the most salient election method.