A mathematical evaluation of vote transfer systems

TL;DR

This paper develops a mathematical model of vote transfer systems in Hungary, analyzing how different transfer rules affect election outcomes and party seat shares in a mixed electoral system.

Contribution

It introduces a comprehensive model of vote transfer systems, comparing three types and analyzing their effects on election results in a two-party context.

Findings

DVT yields the highest expected seat share for the majority party.

PVT and NVT increase the probability of winning the election.

Calibrated NVT can optimize seat share and election victory chances.

Abstract

The paper builds a general model of vote transfer systems on the basis of the current Hungarian electoral rules. It combines single-seat districts and list mandates with three possible compensation rule for 'wasted' votes in constituencies: no compensation (direct vote transfer, DVT), compensation for votes cast for losing party candidates (positive vote transfer, PVT) and compensation for all votes that are not necessary to win the district (negative vote transfer, NVT). The model is studied in the case of two parties. When the number of votes for the majority party follows a uniform distribution in each district, DVT results in the greatest expected seat share, however, application of PVT, and, especially, NVT increases the probability of winning the election. The trade-off between vote transfer formulas and the number of list mandates reveals that the majority party should use an appropriately calibrated NVT system if it focuses on these two variables.