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Social choice Mechanism design Comparative politics Comparison List (By country)
Single-winner methods Single vote - plurality methods First preference plurality (FPP) Two-round (US: Jungle primary) Partisan primary Instant-runoff UK: Alternative vote (AV) US: Ranked-choice (RCV) Condorcet methods Condorcet-IRV Round-robin voting Minimax Schulze Ranked pairs Maximal lottery Positional voting Plurality (el. IRV) Borda count (el. Baldwin) Antiplurality (el. Coombs) Cardinal voting Score voting Approval voting Majority judgment STAR voting
Proportional representation Party-list Apportionment Highest averages Largest remainders National remnant Biproportional List type Closed list Open list Panachage List-free PR Localized list Quota-remainder methods Hare STV Schulze STV CPO-STV Quota Borda Approval-based committees Thiele's method Phragmen's method Expanding approvals rule Method of equal shares Fractional social choice Direct representation Interactive representation Liquid democracy Fractional approval voting Maximal lottery Random ballot Semi-proportional representation Cumulative SNTV Limited voting
Mixed systems By results of combination Mixed-member majoritarian Mixed-member proportional By mechanism of combination Non-compensatory Parallel (superposition) Coexistence Conditional Fusion (majority bonus) Compensatory Seat linkage system UK: 'AMS' NZ: 'MMP' Vote linkage system Negative vote transfer Mixed ballot Supermixed systems Dual-member proportional Rural–urban proportional Majority jackpot By ballot type Single vote Double simultaneous vote Dual-vote
Paradoxes and pathologies Spoiler effects Spoiler effect Cloning paradox Frustrated majorities paradox Center squeeze Pathological response Perverse response Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting Exaggeration Truncation Turkey-raising Paradoxes of majority rule Tyranny of the majority Discursive dilemma Conflicting majorities paradox
Social and collective choice Impossibility theorems Arrow's theorem Majority impossibility Moulin's impossibility theorem McKelvey–Schofield chaos theorem Gibbard's theorem Positive results Median voter theorem Condorcet's jury theorem May's theorem Condorcet dominance theorems Harsanyi's utilitarian theorem
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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.

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.

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).

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.

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.