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# Single non-transferable vote

Single non-transferable vote or SNTV is an electoral system used in multi-member districts. It is a generalization of first-past-the-post, applied to multi-member districts. Unlike block voting, where each voter casts multiple votes, under SNTV each voter casts just one vote. The combination of single voting and multi-member districts produces mixed representation and thus proportional representation or semi-proportional representation at the district level.

## Voting

In any election, each voter casts one vote for one candidate in a multi-candidate race for multiple offices. Posts are filled by the candidates with the most votes. Thus, in a three-seat constituency, the three candidates receiving the largest numbers of votes would win office.

SNTV can be used with non-partisan ballots.[1]

### Example

Three seats are to be filled among five candidates: A, B, C, D and E fielded by 3 parties X, Y and Z.

819 A X
1,804 B Y
1,996 C Z
1,999 D Z
2,718 E Y

C, D and E are the winning candidates.

But counting the votes by party gives these vote tallies:

Y 4,522 48 1
Z 3,995 43 2
X 819 9 0

Party Y has more votes than Party Z, but receives fewer seats because of an inefficient spread of votes across the candidates. If either party had risked trying to win all three seats, causing more vote splitting among supporters of Parties Y and Z, then A of Party X might have won a seat but either party Y or Z might then have taken one fewer seat.

## Proportional representation

SNTV facilitates minority representation, that is, it produces mixed representation of large and small parties where no party takes all the seats.[2]

SNTV results in representation that is most proportional (proportional representation) when political parties have accurate information about their relative levels of electoral support, and nominate candidates in accordance with their respective levels of electoral support. This lessens the chance of vote splitting and inefficient placement of party support. But under SNTV even inefficient distribution of votes allows more balanced representation that would be elected under either single-member plurality or block voting.

Given ${\displaystyle n}$ candidates to be elected, Candidate A can guarantee success by receiving one more than ${\displaystyle {\frac {1}{n+1}}}$ of the votes (the Droop quota), because ${\displaystyle n}$ other candidates cannot all receive more than Candidate A. It can be very difficult for parties to receive representation proportional to their strength, because it is difficult to accurately judge their strength prior to deciding how many candidates to field (strategic nomination). If they field too many, supporters' votes might be split across too many candidates, spreading their vote numbers to the point where all of a party's candidates lose to a less thinly spread opposing party. If a party fields too few candidates, they might not field enough candidates to win seats proportional to their level of support, and the winning candidates would have more support than necessary and thus wasting votes.

The risks of poor strategic nomination are not equal for parties of various strengths. A large party would have much more to lose from the split vote effect than to gain from avoiding the wasted vote effect, and so would likely decide to err on the side of fielding fewer candidates (but probably not less than their existing number of seats). A small party with little representation would be more risk-tolerant and err on the side of too many candidates, hoping to gain seats greater than its proportion of the electorate, perhaps by edging out candidates from larger parties with just a few votes.

SNTV electoral systems, like STV and proportional electoral systems generally, typically produce more proportional electoral outcomes as the size of the electoral districts (number of seats in each constituency) increases.

## Potential for tactical voting

The potential for tactical voting in a single non-transferable vote system is large. Casting only one vote, a rational voter wanting to maximize the number of seats captured by his party should vote for a candidate of the party that has a chance of winning, but one that will not win by too great a margin and thus take votes away from party colleagues. This creates opportunities for tactical nominations, with parties nominating candidates similar to their opponents' candidates in order to split the vote. Like all multiple-winner selections, parties find it advantageous to run a range of candidates in SNTV elections.

SNTV has been measured through the lens of such concepts as decision-theoretic analysis. Professor Gary W. Cox, an expert on SNTV, has studied this system's use in Japan.[3] Cox has an explanation of real-world data finding the, "two systems [plurality and semi-proportional] are alike in their strategic voting equilibria."[4] His research found that voters use the information offered in campaigns (polls, reporting, fundraising totals, endorsements, etc.), to rationally decide who the most viable candidates are and then vote for them.

SNTV can result in complicated intra-party dynamics because in a SNTV system, a candidate runs against candidates from their own party as well as against candidates from the other party. SNTV elections are not zero-sum contests. Just because one particular candidate is elected does not mean that another specific candidate will not be. They both can be elected.

Because running on issues may lead to a situation in which a candidate becomes too popular and therefore draws votes away from other allied candidates, SNTV may encourage legislators to join factions that consist of patron-client relationships in which a powerful legislator can apportion votes to his or her supporters.

In addition, parties will do best if their supporters evenly distribute their votes among the party's candidates. Historically, in Taiwan, the Kuomintang did this by sending members a letter telling them which candidate to vote for. With the Democratic Progressive Party, vote sharing is done informally, as members of a family or small group will coordinate their votes. The New Party had a surprisingly effective system by asking party supporters to vote for the candidate that corresponded to their birthdate. This led to a system of vote allocation which had been adopted by all parties for the 2004 ROC legislative elections.

## Usage

SNTV is used for elections in Puerto Rico, Afghanistan,[5] Kuwait, Indonesia, Japan, Taiwan, Thailand, Libya, Iraq and Vanuatu.

### Puerto Rico

In Puerto Rico, where SNTV is known as at-large representation ("representación por acumulación" in Spanish), political parties vary the ballot order of their candidates across electoral divisions, in order to ensure each candidate has a roughly equal chance of success. Since most voters choose the candidates placed at the top of their party lists on their ballots, at-large candidates from the same party usually obtain approximately equal vote totals.

The two major Puerto Rican political parties, the Popular Democratic Party and the New Progressive Party, usually nominate six candidates for each chamber, while the much smaller Puerto Rican Independence Party runs single-candidate slates for both the Senate and the House of Representatives. The overall distribution of legislative seats is largely determined by the results for the sixteen Senate and forty House district seats, elected by plurality voting.

### Japan, South Korea and Taiwan

SNTV was once used to elect the legislatures of Japan, South Korea and the Republic of China (Taiwan), but its use has been discontinued for the most part. It is still used in Japan for some seats in the House of Councillors (Sangi-in), prefectural assemblies and municipal assemblies.

In Taiwan it used for the six aboriginal seats in the Legislative Yuan (national legislature), as well as local assemblies. The party structure there was complicated by the fact that while members of the Legislative Yuan were elected by SNTV, executive positions were (and still are) elected by a first past the post. This created a party system in which smaller factionalized parties, which SNTV promotes, have formed two large coalitions that resembles the two party system which first past the post rewards. Starting with the 2008 legislative elections, SNTV was discarded in favor of a mixed single member district (SMD) with proportional representation based on national party votes, similar to Japan.

### Hong Kong

From 1997 to 2016, the electoral system for about half of the seats of the Legislative Council of the territory was nominally a party-list proportional representation system with Hare quota, in practice political parties fielded multiple lists in the same constituency. For example, the Democratic Party fielded three separate lists in the eight-seat New Territories West constituency in the 2008 election, aiming to win three seats (they won two). Split list or split tickets is done in order to win more seats with fewer votes, since the first candidate on each list would require less than the Hare quota to get a seat. Supporters are asked to split their votes among the lists of the same party, usually along geographical location of residence. In the 2012 and 2016 elections, no candidate list won more than one seat in any of the six PR constituencies which returned a total of 40 seats, rendering the result effectively the same as SNTV.

In 2021 Hong Kong electoral reform, SNTV is officially adopted in all re-designated 10 geographical constituencies, in which two seats are elected per constituency.

### Libya

In accordance with its post-Gadaffi electoral law, Libya in 2012 elected 80 members of its 200-seat General National Congress using single non-transferable vote.[6] Some commentators cited the system as a factor in the subsequent return to civil war in 2014.[7]

### Chile

After the 2015 electoral reform, Chileans elect their representatives to both houses of Congress through open lists presented by parties or party coalitions in each of the electoral districts into which the country is divided for the contest, allowing only one vote for one of the candidates inside any list. Once the voting is over, the distribution of seats in each district (which can range from 3 to 8 in the lower house and from 2 to 5 in the upper one) is carried out through the D'Hondt method, ordering the lists from highest to lowest according to the total vote of each one and the candidates within each one of them with the same principle.[8]

### Jordan

SNTV became the official electoral system for legislature elections in Jordan in 1993, the second election since the country's return to an elected parliament in 1989. The 1993 electoral reform introduced SNTV as the "one-man, one-vote", which was argued to be a more egalitarian alternative to the former "block vote" (or multiple non-transferable vote) where constituents can vote for as many candidates as there are seats in their constituency. The Jordanian opposition parties were heavily critical of the voting reform as it significantly hurt their electoral results. The Islamic Action Front was at the forefront of this criticism, boycotting 4 of the 6 elections held under this system. The last election held purely under this system was in 2010, whose parliament was dissolved after the Arab Spring protests in Jordan and a new election was held in 2013 using both SNTV and a national closed list with a proportional system. SNTV was completely abolished after the 2016 electoral reform where it was replaced with proportional open lists for each constituency.

### Kuwait

Kuwait has used SNTV to elect the members of its National Assembly (Majles al-Umma) in five 10-member districts, starting with the 2012 election.[9]