The vote linkageGallagher, Michael, and Paul Mitchell. "Dimensions of variation in electoral systems." The Oxford handbook of electoral systems (2018): 23.Golosov, Grigorii V. "The case for mixed single vote electoral systems." Journal of Social, Political, and Economic Studies 38.3 (2013): 317-345.Baldini, Gianfranco, et al. "Mixed-member Systems." Elections, Electoral Systems and Volatile Voters (2009): 80-94. or (multi-tier) vote transfer system is type of compensatory mixed electoral system, where votes may be transferred across multiple tiers of an electoral system, in order to avoid wasted votes - in contrast to the more common seat linkage compensatory system (commonly referred to as MMP). It often presupposes and is related to the concept of the mixed single vote, which means that the same vote can be used in multiple tiers of an electoral system and that a vote for a local candidate may automatically count as a vote for the candidate's party or the other way around. Voters usually cast their single vote for a local candidate in a single-member district (SMD) and then all the wasted votes from this lower tier are added to distribute seats between upper tier candidates, typically national party lists.
Partially compensatory multi-tier vote linkage is an equivalent of the indirect single transferable vote among multi-tiered electoral systems (except for the mixed ballot transferable vote versions, which are multi-tier equivalents to STV). A related concept is seat linkage, where it is not the votes used in one tier that connect two tiers, but the number of seats a party achieved on the lower tier that is taken into account. A vote linkage system, when applied in a compensatory way takes into account the number of votes that were effective or wasted in the lower tier and takes this into account in the apportionment of the upper tier.
Vote linkage systems currently or formerly used for various national or local elections in Germany, Hungary and Italy have been sometimes described as mixed-majoritarian (similar to common versions of parallel voting), or a unique system between MMM and MMP (seat linkage). Some supermixed systems use vote linkage together with parallel voting (superposition) in a two-vote setup, where split ticket voting is allowed. How proportional the outcome depends on many factors including the vote transfer rules, such which votes are recounted as party list votes, and other parameters (e.g. the number of list seats) used in the system. The vote linkage system originates from Germany and is currently used in Hungary. A version called scorporo was also used in Italy from 1993 to 2005.
Example PartyPopular voteDistrict resultsWithout winner compensationWith winner compensationTransfer votesSeatsTransfer votesSeatsParty A strongholds
(40)Party B strongholds
(20)SeatsParty A strongholds
(40)Party B strongholds
(20)TotalList tierTotalParty A strongholds
(40)Party B strongholds
(20)TotalList tierTotalParty A41%45%33%40 -33%11%84820%33%24%1353Party B30%25%40%2025% -17%123225%7%19%1131Party C25%25%25%025%25%25%171725%25%25%1414Party D4%5%2%05%2%4%335%2%4%22TOTAL100%100%100%6055%60%57%4010075%67%72%40100
Compared to other mixed systems PartyPopular voteDistrict resultsSeats under parallel voting - no compensation
(mixed-member majoritarian system)Vote transfer system without winner compensationVote transfer system with winner compensationSeats under single vote seat linkage compensation
(mixed-member proportional system)Party A strongholdsParty B strongholdsSeatsList tierTotalList tierTotalList tierTotalList tierTotalParty A41%45%33%4016568481353141Party B30%25%40%201232123211311030Party C25%25%25%01010171714142525Party D4%5%2%022332266TOTAL100%100%100%10040100401004010040100
Terminology Mixed single vote systems may use vote linkage compensation, meaning not all, but only 'wasted' votes get transferred as list votes to the other tier. Some uncommon, supermixed systems use of MSV may add or subtract the discounted list results to establish a vote linkage based element of compensation into system that would otherwise be categorised as parallel voting. Either type of system is misleadingly known in Hungarian as a "fractional vote recounting system" (Hungarian: töredékszavat-visszaszámláló rendszer), however, there are no fractional votes used in any variation, the name merely alluding to only a fraction of votes being "recounted" as list votes.
The third type of mixed single vote system is the single vote equivalent of parallel voting (sometimes called direct vote transferCsató, László. "Between plurality and proportionality: an analysis of vote transfer systems." arXiv preprint arXiv:1507.01477 (2015).), which uses the same vote on both the majoritarian and proportional tiers. This makes such systems non-compensatory, falling under the superposition type of mixed systems identified by Massicotte & Blais. Compensatory mixed systemssingle vote systems (mixed single vote)dual vote systemsSeat linkageSingle vote seat linkage MMP (top-up MSV)
50-point proportional representationSeat linkage two vote MMP:
mixed-member proportional representation (MMP) additional member system (AMS) alternative vote plus (AV+)Hybrids: e.g. parallel voting+AMS (South Korea)Vote linkagePositive vote transfer system (PVT) Hungarian PVT (local elections)Supermixed: parallel voting+PVT (Hungary - national elections) negative vote transfer/scorporo (Italy, 1993–2005)mixed ballot transferable vote (MBTV)Seat linkage and vote linkageDual-member proportional (DMP)Modified Bavarian MMP Schulze MMPNon-compensatory mixed systemssingle vote systemsdual vote systemsNo linkagemixed single vote, unlinked versions (MSV) single vote parallel voting (Tanzania, Seychelles)parallel votingVote linkage (direct vote transfer)mixed single vote, superposition Italian variant (Rosatellum)-
Positive and negative vote transfer The first recorded mixed vote transfer systems (used in Germany) have been under the "losers plus surplus" model, therefore, they inherently included "winner compensation". Under later definitions of certain sources, this model would also be retroactively a "negative vote transfer system" despite not using any votes with negative transfer value. The confusion stems from the terms "positive" and "negative vote transfer system" being coined based on the systems in use in the 1990s and early 2000s in Hungary and Italy and the inconsistent terminology of sources on these niche variants. While all the Hungarian versions primarily transferred votes with a positive value and the votes transferred were almost exclusively in compensation for losing candidates, the Italian models of scorporo operated only with a negative value and deducted all or a part of votes cast for local winners.
In one view, positive vote transfer means vote transfer with only positive votes value, with or without winner compensation (which may be itself positive or negative).https://doi.org/10.13140/RG.2.2.15129.34407 Electoral incentives and the equal value of ballots in vote transfer systems with positive winner compensation This means that either only the positive transfer votes are used on the list tier to apportion seats (Hungarian local elections), or they are added to other (direct) list votes (Hungarian national elections). Negative vote transfer systems, meanwhile use the opposite principle, they subtract exactly those votes (from the direct list votes), which the equivalent positive vote transfer would not transfer. In this way, these systems rely on negative value winner compensation, which is their most important property that determines how they can be manipulated. +Votes used to allocate list seats underPositive vote transfer systemNegative vote transfer systemStandaloneSupermixedSupermixedWithout winner compensationOnly votes of losing candidates Used in: Hungarian local electionsDirect list votes + votes for losing candidates Used in: Hungarian national elections (formerly)Direct list votes - votes for winning candidates excluding surplus votes Used in: Italian Senate (formerly)With winner compensationVotes for losing candidates + surplus votes of winning candidates (e.g. votes of the winner above votes of the second placed candidate + 1)Direct list votes + votes for losing candidates + surplus votes of winning candidates (e.g. votes of the winner above votes of the second placed candidate + 1) Used in: Hungarian national elections (currently)Direct list votes - votes for winning candidates Used in: Italian Chamber of Deputies (formerly) In some sources, the Hungarian model of "losers only" has been labeled "positive vote transfer", under this view the Italian Senate model, despite using only negative transfer votes would also be PVT, since it operates under the same "losers only" principle (deducting all of winners votes from the list vote). Conversely "negative vote transfer" means not only the Italian Chamber model of scorporo is (deducting the non-surplus votes of winners), but the original German variants and the current Hungarian electoral systems for national elections (it uses winner compensation with positive value). A third term of "direct vote transfer" has been used for vote transfer systems without compensation (mixed single vote equivalent of parallel voting). This view has been criticized for using unintuitive terminology and not including models of winner compensation other than the surplus votes compared to the second place candidate. This article uses the former view to maintain consistency and to show the significance of positive/negative transfers on manipulation more intuitively.
Controversy on winner compensation Though the original vote linkage systems used the "losers plus surplus" model, the systems established in Hungary only used votes cast for losing candidates on the (relatively small sized) compensatory tier of the electoral systems. For this reason, when the system for the National Assembly was changed by the governing parties before the 2014 election, the introduction of transferring surplus votes (with a positive value) was a novel element in the system. This element was soon called "winner compensation" (mostly by its critics), who claimed it was effectively a majority bonus. Together with other criticisms of the change (suspicions of gerrymandering, moving towards an even more mixed-majoritarian system, postal voting for non-resident citizens only etc.) this was viewed as a thinly veiled attempt to benefit the parties who created the system, without meaningful consultation of the opposition.
Similar proportional systems Some non-mixed systems, which use multi-member constituencies either on their single tier or also on their lower tier use vote linkage. An example is the national remnant system of Weimar Germany. This system used an absolute quota (not dependent on the vote shares in the district, rather a fixed number of votes) instead of plurality to elect candidates. With the fixed quota and a changing population, this meant a flexible parliament size.
The vote transfer to party list is the mixed single vote equivalent to indirect single transferable voting, while the direct equivalent to the single transfer vote is the mixed ballot transferable vote.
Advantages and disadvantages The features of vote linkage compensatory systems are similar to those of comparable parallel voting or mixed-member proportional systems, depending on which systems does the result more resemble. As mixed systems they usually inherit properties of their subsystems, in case of the most commonly used vote linkage systems, these are first preference plurality (in single-member districts) and closed list PR. Single vote variants also suffer from the disadvantages of the mixed single vote, however in certain systems this also gives robusticity against strategic manipulation.
Representation for smaller parties