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.
Single-vote systems
Semi-proportional 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.[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 the single non-transferable vote and cumulative 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 of election administration. Under these systems, parties may 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 or vote in specified ways, such as through differently-worded voting cards.
These systems are notable for the absence of an ordered party 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
Some writers consider the single transferable vote to be semi-proportional because of its favoritism towards major parties, sometimes caused by a combination of the Droop quota in small districts, as well as the vote management that may be involved when optional preferential voting is used, producing exhausted ballots.[9] On the other hand, some describe it as proportional on the grounds that it is proportional in the limit of infinitely-large constituencies.[10] However, on party basis, if first preferences are used as guide, STV is only proportional for solid 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 are split 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.
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 winner-take-all 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 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 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.[11] Such a system is used in Hungary in local elections.[12] 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.
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.
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)
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)
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
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