Mixed electoral system
A Mixed Electoral System is a system which mixes the concepts of Regional Systems with those of Partisan system. The goal of adding the concepts of Partisan systems is to increase Proportional Representation. Not all Mixed systems actually use partisan votes to achieve their aim.
Introduction and discussion
The Regional Systems and partisan systems have a natural trade-off between each other. A fully regional single member system optimizes Proportionate Representation but only achieves a moderate level of Proportional Representation whereas a Party List system maximizes Proportional Representation but gets no Proportionate Representation. This implies mixing these ideas could achieve a compromise.
Types of mixed system
Mixed Member Proportional
The the most common are the so called Mixed Member Proportional systems. These have some seats allocated to regional representatives and the rest to partisan representatives. Each voter will vote for a regional representative and a party with the ratio of the number of seats from each system being dependent on design choice. There are two common sub-types, one is the parallel mixed system where the regional system and the partisan system is done completely independently. The other sub-type is the mixed compensatory system, where the partisan votes are counted after and used to increase Proportional Representation true a Party List style allocation system.
Hare Mixed systems
Another type of mixed system attempts to increase proportional representation through allowing voters to vote outside of their single member district district. There are many variations but the basic strategy is having a regional system which passes some information from one region to another. These are commonly referred to as Hare Mixed System because this was originally proposed by Sir Thomas Hare in 'Treatise on the Election of Representatives'. His system is one of the oldest (1859) and initially well-accepted systems to replace SMP. It is a combination of single regional constituencies with instant run-off ballots. The twist of the Hare system is to let people vote in constituencies other than their own. Or as stated by John Stuart Mill in Considerations of Representative Government where he expressed great favour for the Hare system
The votes would, as at present, be given locally; but any elector would be at liberty to vote for any candidate, in whatever part of the country he might offer himself. Those electors, therefore, who did not wish to be represented by any of the local candidates, might aid by their vote in the return of the person they liked best among all those throughout the country who had expressed a willingness to be chosen. This would so far give reality to the electoral rights of the otherwise virtually disfranchised minority.
This brilliant solution to representation is also its downfall. The constant changing of regional boundaries to ensure Balanced Representation is just one example. Another is that game theoretic reasons lead a voter to have to rank each candidate in the country. These logistical complications make the system prohibitively impractical even before considering the issues with instant run-off given above.
A modern version of this is Local PR which restricts the voter from voting in all regions to a predefined cluster. This cluster is then treated as a multi-member district where the Single transferable Vote algorithm is run.
Other
Dual Member Proportional is similar to a mixed compensatory with dedicated to dual-member (two seat) districts where the partisan candidate is elected. It tries to solve some of the regional and partisan issues by having dual member constituencies where the second candidate is elected from the list of runner ups. The party list being decided by the runner ups removes the partisan vote and its associated increase in partisanship. This system is a way to combined multi-member systems and mixed member systems. This is one of the all around best systems which restricts it self to a single plurality vote. Because of this, vote splitting still exists but is largely mitigated after the fact by the method of choosing the runner up. Essentially, the second candidate will be chosen to attempt to fulfill Proportional Representation and minimise vote splitting.