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Rules for implementing Single Transferable Vote (fractional method)

by Mike Ossipoff

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Fractional stv is used in the Australian state of Tasmania. UC Berkeley student senate elections are conducted by fractional stv. In both cases, it's done as a hand-count. If you're ever going to do a a hand-count, I suggest the simpler minimal stv. Fractional stv requires much more time & labor than a hand-count, though it's quite feasible and has much merit for a comuterized count.

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Fractional stv count rule:

1. Definitions:

A "ballot" is paper or card, or set of papers or cards, on which a voter has marked a candidate, or ranked 1 or more candidates.

A "continuing candidate" is a candidate who is not yet elected or eliminated.

To "transfer" a ballot is to assign it to its highest-ranked continuing candidate.

A "transferable ballot" is a ballot which lists or designates at least 1 continuing candidate.

As a noun, a "transfer" is an instance of transferring 1 or more ballots.

An "allocation" is any transfer of every ballot whose transfer is ordered in the same paragraph of this count specification.

"N" represents the number of seats in the election.

"The quota" is the number of valid ballots cast in the election divided by N.

"A quota" is a vote total numerically equal to the quota.

2. Each ballot, at the beginning of the count, shall have the value of 1 vote. Each candidate, at the beginning of the count, shall have a vote total of 0 (zero).

3. When a ballot is transferred to a candidate, his vote total is increased by the value of the ballot. When a ballot is transferred from a candidate, his vote total is decreased by the value of the ballot.

4. Immediately after each allocation, either paragraph 4a, or paragraph 4b shall be carried out, depending on whether or not that allocation has resulted in a candidate acquiring a quota.

4a. If any candidate has acquired a quota as a result of the allocation that has just been completed, then that candidate is elected as of that time. If his vote total exceeds a quota then he has a "surplus", and his surplus is the amount by which his vote total exceeds the quota. The rest of this paragraph shall be carried out for every candidate who has a surplus as a result of the allocation that has just been completed. For each such candidate, his surplus shall be divided by his vote total, and the value of each of his transferable ballots shall be multiplied by the result of that division. Each of his transferable ballots shall then be transferred.

4b. If no candidate has acquired a quota as a result of the allocation that has just been completed, then the continuing candidate with the lowest vote total shall be eliminated, and his transferable ballots transferred.

5. The count shall end either when N candidates have been elected, or when only N candidates remain un-eliminated (in which case those N candidates are declared elected), whichever happens 1st.

6. So, those being the rules, start the count by transferring all the ballots in the ballot box.

Mike Ossipoff