Semi-proportional representation characterizes multi-winnerelectoral systems which allow some representation of smaller parties or candidates, but produce results that do not always reflect the strength of the competing political forces in a way that is proportional to the shares of the votes they receive.^[1][2] Semi-proportional voting systems are betweenproportional systems likeparty-list proportional representation orsingle transferable vote andwinner-take-all systems.^[3][4] Examples of semi-proportional systems include thesingle non-transferable vote,limited voting, andparallel voting.

There are different measures of proportionality,^[5][6] and no objective threshold, so opinions differ on what constitutes a semi-proportional system, a non-proportional system and a 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.^[7] They are not non-proportional or majoritarian, since in the perfect case the outcome will be proportional and in many cases it is close to proportional,^[8] but they are not universally proportional either, since the perfect case is not guaranteed without coordination. Such systems include thesingle non-transferable vote andcumulative voting, both of which are commonly used to elect a range of members based on party identification) and achieve approximately-proportional outcomes while maintaining simplicity and reducing the cost ofelection administration. Under these systems, parties may coordinate voters by limiting the size of the party slate or by using complexvote management schemes where voters are asked to randomize which candidate(s) they support or vote in specified ways, such as through differently-worded voting cards.

These systems are notable for the absence of an orderedparty 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).

Some writers consider thesingle transferable vote to be semi-proportional because of its favoritism towards major parties, sometimes caused by a combination of theDroop quota in small districts, as well as thevote management that may be involved whenoptional preferential voting is used, producingexhausted ballots.^[9] On the other hand, some describe it as proportional on the grounds that it isproportional in the limit of infinitely-large constituencies.^[10] However, on party basis, if first preferences are used as guide, STV is only proportional forsolid coalitions, if voters rank candidates along party lines and no significant number of votes cross party lines. The proportionality of STV, as measured by first preferences, breaks down if voters aresplit across party lines or choose to mark preferences candidates of different parties. Under STV, each elected member is elected by the exact same number of votes (the quota) or something very close to it, so proportionality is produced that way.

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 winner-take-all principle of representation (but not necessarilymajoritarianism ormajority rule, seeelectoral inversion andplurality) starting from basic PR mechanisms:parallel voting, the majority bonus system (MBS), and extremely reducedconstituency magnitude.

Inadditional 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 Welsh Senedd, 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 theScottish Parliament and theLondon Assembly, with generally proportional results. Similarly, in vote transfer basedmixed single vote systems, the number of compensatory seats may be too low (or too high) to achieve proportionality.^[11] Such a system is used in Hungary in local elections.^[12] The "scorporo" system used for theParliament of Italy from 1993 to 2005 and the electoral system for theNational 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.

Amajority 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 producelandslide victories similar to those which occur in elections underplurality systems. Themajority bonus system was first introduced byBenito Mussolini to win theelection of 1924. It has remained in use inItaly, as well as seeing some use inSan Marino,Greece, andFrance.^{[citation needed]}

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

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

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