# Single non-transferable vote

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SNTV is choose-one FPTP voting applied to the multi-winner context. It is a semi-proportional method.

SNTV passes a very weak form of Hagenbach-Bischoff-PSC (and Droop-PSC): if a group of voters of at least k HB quotas evenly distribute their votes between k candidates such that each candidate has at least one HB quota, then they can guarantee all of those k candidates either tie or win. This is because there can at most be ((number of winners) + 1) HB quotas in an election, so when k candidates have HB quotas, at most ((number of winners) - k + 1) candidates can also have HB quotas, resulting in a tie. As an example, if there are 3 seats and 100 voters, and 2 candidates each have an exact HB quota (25 votes), then either only one other candidate has more votes than the 2 (more than 25), meaning the 2 will be among the top 3 candidates (since if three candidates have over 75 votes together, then that means any other candidate must have fewer than 25 votes), or two other candidates also have 25 votes each, resulting in a tie.

If the k candidates instead each have a Droop quota, they are guaranteed to win, rather than only being guaranteed to either tie or win.

By analog to Duverger's law, SNTV in n-seat districts tends to produce (n+1)-party rule.[1]

## Notes

SNTV can be combined with Party List by allowing each voter to give their vote to a party or to a candidate; the parties can each be allocated a certain number of seats, while independents can still win on their own. Note that this is possible even in the single-winner case (where SNTV is equivalent to the common choose-one FPTP voting method) to ensure that a plurality or majority elect someone from their preferred group of candidates, if there are many candidates in that group splitting the vote. The cast votes can also themselves be used to decide who within the Party List should win i.e. the candidates on the list with the most votes can be prioritized.

## References

1. Reed, Steven R. (1990). "Structure and Behaviour: Extending Duverger's Law to the Japanese Case". British Journal of Political Science. 20 (3): 335–356. doi:10.1017/S0007123400005871. JSTOR 193914.