Mixed electoral system
A mixed electoral system is one that uses different electoral systems to elect different seats in a legislature. Most often, this involves a First Past the Post combined with a proportional component. The results of the combination may be mixed-member proportional, where the overall results of the elections are proportional, or mixed-member majoritarian, in which case the overall results are semi-proportional, retaining disproportionalities from the majoritarian component. Systems that use multiple types of combinations are sometimes called supermixed.
Mixed-member systems also often combine local representation with regional or national representation, having multiple tiers. This also means voters often elect different types of representatives who might have different types of constituencies. Some representatives may be elected by personal elections where voters vote for candidates, and some by list elections where voters vote for electoral lists of parties.
In most mixed systems, every voter can influence both the district-based and PR aspects of an election, such as under parallel voting; however, some countries have multiple coexisting electoral systems that each apply to different voters.
Types of mixed systems
Compensatory/non-compensatory seat allocation
A major distinction is often made between mixed compensatory systems and mixed non-compensatory systems. In both types of systems, one set of seats is allocated using a plurality or majoritarian method, usually first past the post. The remaining seats are allocated to political parties partially or wholly based on a proportional allocation method such as highest averages or largest remainder. The difference is whether or not the results of the district elections are considered when allocating the PR seats.In mixed non-compensatory systems, such as parallel voting, the proportional allocation is performed independently of the district election component.
In mixed compensatory systems, the allocation of the top-up seats is done in such a way as to compensate as much as possible for dis-proportionality produced by the district elections. MMP generally produces proportional election outcomes, meaning that a political party that wins n percent of the vote will receive roughly n percent of the seats.
The following hypothetical example based on the one by Massicotte illustrates how "top-up" PR seats are typically allocated in a compensatory system and in a non-compensatory system. The example assumes a 200-seat legislative assembly where 100 seats are filled using FPTP and the other 100 seats are awarded to parties using a form of PR. The table below gives the popular vote and FPTP results. The number of PR seats allocated to each party depends on whether the system is compensatory or non-compensatory.
In non compensatory system, each party wins its proportional share of the 100 PR seats. Under such a system, the total number of seats received by each party would not be proportional to its share of the popular vote. Party A receives just slightly less of the popular vote than Party B, but receives significantly more seats. In addition to its success in the district contests, Party A receives almost as many of the PR seats as Party B.
If the PR seats are allocated in a compensatory system, the total number of seats awarded to each party is proportional to the party's share of the popular vote. Party B wins 33 of the district seats and its proportional share of the 200 seats being filled is 80 seats so it is awarded 47 of the PR seats.
In practice, compensatory seat allocation is complicated by the possibility that one or more parties wins so many of the district seats that the available number of PR seats is insufficient to produce a fully proportional outcome. Some mixed compensatory systems have rules that address these situations by adding additional PR seats to achieve overall PR. These seats are used only until the next election, unless needed again at that time.
The two common ways compensation occurs are seat linkage compensation and vote linkage compensation. Like a non-compensatory mixed system, a compensatory mixed system may be based on the mixed single vote or it may be based on voters casting two separate votes.
Types of combinations
Apart from the compensatory/non-compensatory typology, a more detailed classification is possible based on how component systems relate to each other, according to academic literature. Below is a table of different categories of mixed electoral systems based on the five main types identified by Massicotte & Blais. According to their terminology, methods of compensation are referred to as compensation is referred to as correction, while another type of dependent combination exists, called the conditional relation between sub-systems. Meanwhile, independent combinations mixed systems might have both local and national/regional tiers, but some have only one at-large tier, like the majority bonus system or only a single tier for local/regional representation.There are also supermixed systems, like rural-urban proportional, which is a hybrid mixed system that uses two tiers: the lower tier uses a proportional system, like list-PR or STV, in urban regions, and the upper tier uses MMP either in rural regions alone or in all regions.
| Combination | Type | Attributes | System | Example for use |
| Independent combination | Fusion | Two formulas are used within each district | Majority bonus | France, French Polynesia |
| Independent combination | Coexistence | Different districts use different systems in one tier | e.g. FPTP/SMP in single-member districts, list-PR in multi-member districts | Democratic Republic of the Congo, Panama |
| Independent combination | Superposition | Different tiers use different systems | Parallel voting | Lithuania, Russia |
| Independent combination | Superposition | Different tiers use different systems | Single vote mixed-member majoritarian | Italy, Pakistan |
| Dependent combination | Correction | One formula uses the results of other to compensate | Seat linkage mixed system with partial correction for overhang seats: New Zealand's mixed-member proportional representation | New Zealand |
| Dependent combination | Correction | One formula uses the results of other to compensate | Seat linkage mixed system with no correction for overhang seats: UK Additional member system - a less proportional version of MMP | Scotland |
| Dependent combination | Correction | One formula uses the results of other to compensate | Single vote with seat linkage | Lesotho |
| Dependent combination | Correction | One formula uses the results of other to compensate | Single vote with compensatory vote transfer | Hungary |
| Dependent combination | Conditional | Outcome of one formula determines the other formula | e.g. conditional party block voting: party that receives more than 50%, gets all seats otherwise all seats distributed proportionally | - |
| Combination of combinations | Supermixed | Superposition + correction | Scorporo / negative vote transfer, Parallel voting + PVT | Hungary |
| Combination of combinations | Supermixed | Superposition + correction | Parallel voting + seat linkage | South Korea |
| Combination of combinations | Supermixed | Superposition + fusion | National plurality bonus in regional list-PR | Greece |
| Combination of combinations | Supermixed | Superposition + coexistence | e.g. some elected by PR in single national district, some are elected locally by plurality | Ecuador |
| Combination of combinations | Supermixed | Coexistence + conditional | e.g. FPTP/SMP in single-member districts, conditional party block voting in multi-member districts | Cameroon, Chad |
| Combination of combinations | Supermixed | Coexistence + correction | Rural-urban proportional representation | Denmark, Iceland |
| Combination of combinations | Supermixed | Conditional + correction + fusion | Majority jackpot systems, particularly two-round variants | Armenia, San Marino |
| Combination of combinations | Supermixed | Fusion + correction | Dual-member proportional representation | - |
In a hybrid system, different electoral formulas are used in different contexts. These may be seen in coexistence, when different methods are used in different regions of a country, such as when FPTP is used in single-member districts and list-PR in multi-member districts, but every voter is a member of only one district. Some hybrid systems are generally not referred to as mixed systems, such as when as FPTP districts are the exception and list-PR is the rule, the overall system is usually considered proportional. Similarly, when FPTP is in single-member districts and used block voting is used in multi-member districts, the system is referred to as a majoritarian one, as all components are majoritarian. Most mixed systems are not referred to as hybrid systems