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Semi-proportional representation characterizes multi-winner electoral systems which allow representation of minorities, but are not intended to reflect the strength of the competing political forces in close proportion to the votes they receive.^[1] Semi-proportional voting systems are generally used as a compromise between complex and expensive but more-proportional systems (like the single transferable vote) and simple winner-take-all systems.^[2]^[3] Examples of semi-proportional systems include the single non-transferable vote, limited voting, and parallel voting.

Semi-proportional systems

Most proportional representation systems will not yield precisely proportional outcomes due to the use of election thresholds, small electoral regions, or other implementation details that vary from one elected body to another. However, systems that yield results close to the ideal are generally considered fully-proportional.

The choice to use a semi-proportional electoral system may be a deliberate attempt to find a balance between single-party rule and proportional representation. Semi-proportional systems can allow for fairer representation of those parties that have difficulty gaining even a single seat while retaining the possibility of one party gaining an overall majority of seats even if it receives less than a majority of the votes; they can ensure that the two or three largest parties all have their due share of seats or more while not producing representation for the smallest parties.

Because there are many measures of proportionality,^[4]^[5] and because there is no objective threshold, opinions may differ on what constitutes a semi-proportional system as opposed to a non-proportional one or a fully proportional system.

Single-vote systems

Election systems in which a party can achieve its due share of seats (proportionality) only by coordinating its voters are usually considered to be semi-proportional.^[6] They are not non-proportional or majoritarian, since in the perfect case the outcome will be proportional, but they are not proportional either, since the perfect case is not guaranteed without coordination. Such systems include the single non-transferable vote and cumulative voting, both of which are commonly used to achieve approximately-proportional outcomes while maintaining simplicity and reducing the cost of election administration. Under these systems, parties often coordinate voters by limiting the size of the party slate, or by using complex vote management schemes where voters are asked to randomize which candidate(s) they support.

These systems are notable for the absence of an ordered electoral list. Candidates may coordinate their campaigns, and present or be presented as agents of a party, but voters may choose to support one candidate among the said group but not the others (that is, panachage is permitted).

Single transferable vote

Many writers consider the single transferable vote to be a semi-proportional system because of its substantial favoritism towards major parties, generally caused by a combination of the Droop quota in small districts, as well as the substantial degree of vote management involved when there are exhausted ballots.^[7] On the other hand, some authors describe it as a proportional system, on the grounds that it is theoretically weakly proportional in the limit of infinitely-large constituencies.^[8] However, it is worth noting that STV is only proportional for solid coalitions, i.e. if voters rank candidates first by party and only then by candidate. As such, the proportionality of STV breaks down if voters are split across party lines or choose to support candidates of different parties.

A major complication with proportionality under STV is the need for constituencies; small constituencies are strongly disproportional, but large constituencies make it difficult or impossible for voters to rank large numbers of candidates, turning the election into a de facto open list PR system, particularly where voters lack any meaningful information about the candidates on their ballot.

The degree of proportionality of the results in a district (and when combined with other district results, the proportionality of results across a country) depends on the number of seats elected in the district. In the 2011 Irish general election, Fine Gael received 45.2% of the seats with just 36.1% of the first preference votes. In the 2020 Irish general election, the Labour Party received 50% more votes than the Social Democrats, but both parties won the same number of seats. Ireland uses districts of 3-7 members.

Similarly, the 1998 Northern Ireland elections resulted in the Ulster Unionists winning more seats than the Social Democratic and Labour Party with a smaller share of the vote.

The proportionality of STV can be controversial, especially in close elections like the 1981 election in Malta. In this election, the Maltese Labour party won a majority of seats despite the Nationalist Party winning a majority of first preference votes. This caused a constitutional crisis, leading to a provision to provide bonus seats in case of disproportional results. These bonus seats were needed in 1987, 1996, and 2008 to prevent further electoral inversions.

The degree of proportionality nationwide is strongly related to the number of seats to be filled in each constituency. In a three-seat constituency using the Droop quota, a full quarter of the vote is wasted. In a nine-seat constituency, only a tenth of the vote is wasted, and a party needs only 10% of the vote to win a seat. Consequently, the best proportionality is achieved when there are a large number of representatives per constituency. The Hare quota is theoretically unbiased, allowing some of the errors in apportionment to cancel out if voters across the whole country. However, it also increases the vulnerability of STV to vote management by large parties, allowing them to win the same number of seats they would have won under Droop.

Partisan systems

Other forms of semi-proportional representation are based on, or at least use, party lists to work. Looking to the electoral systems effectively in use around the world, there are three general methods to reinforce the majoritarian principle of representation (but not necessarily majoritarianism or majority rule, see electoral inversion and plurality) starting from basic PR mechanisms: parallel voting, the majority bonus system (MBS), and extremely reduced constituency magnitude.

In additional member systems (AMS), the number of additional members may not be sufficient to balance the disproportionality of the original system, thereby producing less than proportional results. When this imbalance is created intentionally, the result could be described as a semi-proportional system — for example, in the National Assembly for Wales, where only 33.3% of members are compensatory. The electoral system commonly referred to in Britain as the "additional member system" is also used for the Scottish Parliament and the London Assembly, with generally proportional results. Similarly, in vote transfer based mixed single vote systems, the number of compensatory seats may be too low (or too high) to achieve proportionality.^[9] Such a system is used in Hungary in local elections.^[10] The "scorporo" system used for the Parliament of Italy from 1993 to 2005 and the electoral system for the National Assembly of Hungary since 1990 are also special cases, based on parallel voting, but also including compensatory mechanisms – which however are insufficient for providing proportional results.

A majority bonus system takes an otherwise proportional system based on multi-member constituencies, and introduces disproportionality by granting additional seats to the first party or alliance. Majority bonuses help produce landslide victories similar to those which occur in elections under plurality systems. The majority bonus system was first introduced by Benito Mussolini to win the election of 1924. It has remained in use in Italy, as well as seeing some use in San Marino, Greece, and France.^{[citation needed]}

The simplest mechanism to reinforce major parties in PR system is to severely restrict the number of seats per electoral district, which increases the Droop quota (the number of votes needed to be guaranteed a seat).

The last main group usually considered semi-proportional consists of parallel voting models. The system used for the Chamber of Deputies of Mexico since 1996 is considered a parallel voting system, modified by a list-seat ceiling (8%) for over-representation of parties.

Usage

Country	Legislative body	Latest election (year)	Type of majoritarian system	(Seats per constituency)	Electoral system	Total seats	Governmental system	Notes
Andorra	General Council	2018	Mixed-member majoritarian	2 (local districts) / 14 (nationwide constituency)	Parallel voting / superposition (MMM): Party block voting (PBV) locally + list PR nationwide	28	Parliamentary system
Democratic Republic of the Congo	National Assembly	2018	Mixed-member majoritarian	1–17	Coexistence mixed majoritarian (MMM): First-past-the-post (FPTP/SMP) in single-member districts and List PR in multi-member districts (Largest remainder)	500
Djibouti	National Assembly	2018	Mixed-member majoritarian	3–28	Fusion / majority jackpot (MBS): 80% of seats (rounded to the nearest integer) in each constituency are awarded to the party receiving the most votes (party block voting), remaining seats are allocated proportionally to other parties receiving over 10% (closed list, D'Hondt method)	65	Presidential system
France	French Polynesia Assembly	2018	Mixed-member majoritarian	4–17	Two-round majority bonus system (MBS) in multi-member constituencies	57
Georgia	Parliament	2020	Mixed-member majoritarian	1 (local districts), 120 (national constituency)	Parallel voting / superposition (MMM): Party-list PR (closed list) + First-past-the-post (FPTP/SMP)	150	Parliamentary system
Greece			Mixed-member majoritarian		Majority bonus system (MBS)
Guinea	National Assembly	2020	Mixed-member majoritarian	1 (local districts), 76 (national constituency)	Parallel voting / superposition (MMM): Party-list PR (Hare quota) + First-past-the-post (FPTP/SMP)	114
Hungary	National Assembly (Országgyűlés)	2018	Mixed-member majoritarian	1 (local districts), 93 (national constituency)	Supermixed / Mixed-member majoritarian (MMM): First-past-the-post (FPTP/SMP) + national list-PR for 93 seats (combination of parallel voting and positive vote transfer)	199	Parliamentary system	Before the 2014, a different mixed system was used with a two-round system in single-member districts
Iraq					Single non-transferable vote (SNTV)
Italy	Chamber of Deputies	2018	Mixed-member majoritarian	1 (local districts), 12 (Italians abroad constituency), ?-? (multi-member districts)^{[citation needed]}	Superposition / Mixed-member majoritarian (MMM) using a single vote List PR + First-past-the-post (FPTP/SMP)	630	Parliamentary system
Italy	Senate	2018	Mixed-member majoritarian	1 (local districts), 6 (Italians abroad constituency), ?-? (multi-member districts)^{[citation needed]}	Superposition / Mixed-member majoritarian (MMM) using a single vote List PR + First-past-the-post (FPTP/SMP)	315	Parliamentary system
Republic of Korea (South Korea)	National Assembly	2020	Mixed-member majoritarian	1 (local districts), 17 supplementary seats (parallel voting), 30 additional seats (AMS),	Supermixed / Mixed-member majoritarian (MMM): First-past-the-post (FPTP/SMP) and List PR (hybrid of parallel voting and AMS)	300	Presidential system
Kuwait					Single non-transferable vote (SNTV)
Kyrgyzstan	Supreme Council	2021	Mixed-member majoritarian	1 (local districts), 54 (nationwide constituency)	Parallel voting / superposition (MMM): Party-list PR (open list) + First-past-the-post (FPTP/SMP)	90	Presidential system
Lithuania	Seimas	2020	Mixed-member majoritarian	1 (local districts), 70 (nationwide constituency)	Parallel voting / superposition (MMM): Two-round system (TRS) for 71 seats + List PR (Largest remainder) for 70 seats	141	Semi-presidential system
Madagascar	National Assembly	2019	Mixed-member majoritarian	1–2	Coexistence: First-past-the-post (FPTP/SMP) in 87 single-member districts, party-list PR (Closed list, highest averages method) in 32 two-member districts (64 seats in binomial system)	151	Semi-presidential system
Mauritania	National Assembly	2018	Mixed-member majoritarian	1–3 (local districts), 40 (nationwide constituency)	Coexistence+superposition (parallel) supermixed/hybrid: Two-round system (TRS) in single-member districts, two-round block voting (BV) in dual-member districts, and List PR (simple quota largest remainder; closed-list) in larger districts + twice 20 nationally List PR (one set of 20 reserved for women)	157	Semi-presidential system
Monaco	National Council	2018	Mixed-member majoritarian	24 (nationwide constituency)	Superposition / Mixed-member majoritarian (MMM) using a single (panachage) ballot: Plurality block voting (BV) in single nationwide constituency for 16 seats; D'Hondt method (8 seats)	24	Parliamentary system ^{[citation needed]}
Palestine	Legislative Council	2006	Mixed-member majoritarian	1–9 (local districts), 66 (nationwide constituency)	Parallel voting / superposition (MMM): First-past-the-post (FPTP/SMP) in single-member districts and Plurality block voting (BV) in two-seat districts for 66 seats in total (some reserved for Christians) + List PR for 66 seats	132	Semi-presidential system	In the 1996 elections, 88 PLC members were chosen from several multi-member constituencies via block voting
Panama	National Assembly	2019	Mixed-member majoritarian		Coexistence mixed majoritarian (MMM): First-past-the-post (FPTP/SMP) in single-member districts, Saripolo or Sartori method (Largest remainder, but remainders only for those with no seats) in multi-member districts	71	Presidential system
Philippines	House of Representatives	2019	Mixed-member majoritarian	1 (local districts), 61 (nationwide constituency)	Parallel voting / superposition (MMM): First-past-the-post (FPTP/SMP) in single-member districts (243 in 2019) + List PR (closed lists; modified Hare quota with 3-seat cap and no remainders) (61 in 2019)	304	Presidential system
Russian Federation	State Duma	2021	Mixed-member majoritarian	^{[citation needed]}	Parallel voting / superposition (MMM): First-past-the-post (FPTP/SMP) and List PR	450	Semi-presidential system
San Marino					Majority bonus system (MBS)		Parliamentary system
Scotland	Parliament	2021	Mixed-member majoritarian	73 (constituency), 56 (7 list MSPs elected in each of the 8 regions)	Additional Member System (AMS)	129	Parliamentary system
Senegal		2017	Mixed-member majoritarian		Parallel	165	Presidential system
Seychelles		2020	Mixed-member majoritarian		Parallel	35	Presidential system
Singapore		2020	Mixed-member majoritarian		First-past-the-post (FPTP/SMP) and party block voting (PBV)	104 (93 directly elected)
Sudan		2015	Mixed-member majoritarian		Parallel	450
Switzerland	Council of States Only in: names of cantons			2	Single non-transferable vote (SNTV)	46
Taiwan		2020	Mixed-member majoritarian		Parallel	113
Tajikistan		2020	Mixed-member majoritarian		Parallel	63
Thailand		2019 (using MMP)	Mixed-member majoritarian		Parallel	500		The next election is scheduled to be held under parallel voting again, after one election (2019) held using a single vote MMP system
British Overseas Territories (United Kingdom)	Gibraltar				Limited voting (LV)
British Overseas Territories (United Kingdom)	Pitcairn Islands				Single non-transferable vote (SNTV)
Vanuatu					Single non-transferable vote (SNTV)
Venezuela	National Assembly	2020	Mixed-member majoritarian		Parallel voting (MMM): First-past-the-post (FPTP/SMP) and list PR	280 (277 directly elected)	Presidential system
Zimbabwe	National Assembly	2018	Mixed-member majoritarian	1 (local districts), 10 (proportional constituencies)	Mixed-member majoritarian (MMM): 210 seats by first-past-the-post (FPTP/SMP) in local districts 60 seats reserved for women by list PR	270	Presidential system	Voters cast a single vote