# Meek STV

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The Meek single-transferable vote (or "Meek STV) system is an election method based on vote counting rules used in the Irish Senate (Seanad Éireann). In 1969, Brian Meek devised a variation which uses iterative approximation to short-circuit the infinite recursion that results when there are secondary preferences for prior winners. This system is currently used for some local elections in New Zealand,[1][2] and for elections of moderators on some internet websites, e.g. Stack Exchange Network portals.[3]

## Procedure

In Meek STV, all candidates are allocated one of three statuses – "Hopeful", "Elected", or "Excluded". Hopeful is the default. Each status has a weighting, or keep value, which is the fraction of the vote a candidate will receive for any preferences allocated to them while holding that status.

The weightings are:

Hopeful ${\displaystyle 1}$ ${\displaystyle 0}$ ${\displaystyle w_{\text{new}}=w_{\text{old}}\times {\frac {\text{Quota}}{\text{Candidate's votes}}}}$ which is repeated until ${\displaystyle {\text{Candidate's votes}}={\text{Quota}}}$ for all elected candidates

Thus, if a candidate is Hopeful they retain the whole of the remaining preferences allocated to them, and subsequent preferences are worth 0.

If a candidate is Elected, they retain the portion of the value of the preferences allocated to them that is the value of their weighting; the remainder is passed fractionally to subsequent preferences depending on their weighting. For example, consider a ballot with top preferences A, B, C, and D in that order, where the weightings of the candidates are ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$, and ${\displaystyle d}$, respectively. From this ballot A will retain ${\displaystyle r_{A}=a}$, B will retain ${\displaystyle r_{B}=(1-a)b}$, C will retain ${\displaystyle r_{C}=(1-a)(1-b)c}$, and D will retain ${\displaystyle r_{D}=(1-a)(1-b)(1-c)d}$.

If no candidate on a ballot has a weight of 1 then the sum total retained by the candidates on the ballot will be strictly less than 1. The amount by which 1 exceeds the ballot's total is called the "excess", and the total excess from all ballots is disposed of by altering the quota. Meek's method is the only method to change quota mid-process. The quota is found by

${\displaystyle {{{\text{votes}}-{\text{excess}}} \over {\text{seats}}+1},}$

a variation on Droop. This has the effect of also altering the weighting for each candidate.

This process continues until all the Elected candidates' vote values closely match the quota (plus or minus .0001%).[4]

## References

1. "World-first for Aotearoa – Meek's method implemented". The Mahurangi Magazine. 1 Feb 2003. Retrieved 19 October 2021.
2. "Single transferable vote". The Department of Internal Affairs. 10 May 2004. Retrieved 19 October 2021.
3. "Stack Exchange Meta FAQ question "There's an election going on. What's happening and how does it work?"". StackExchange Meta. 10 June 2012. Retrieved 21 April 2015.
4. Hill, I. David; B. A. Wichmann; D. R. Woodall (1987). "Algorithm 123 — Single Transferable Vote by Meek's Method" (PDF). The Computer Journal. 30 (2): 277–281. doi:10.1093/comjnl/30.3.277.