Single Transferable Vote

[VotingPatterns]

This system was developed by Thomas Hare (c. 1857). It is used to elect legislatures in the following jurisdictions:

The following is a simplified description (ignoring messy things like how to resolve ties) of how to count votes in a SingleTransferableVote election:

  1. Suppose you have a legislature where M seats are up for re-election, and N ballots have been cast. Each ballot ranks the candidates from #1 to #M.

  2. Let the quota Q equal (N/(M + 1)) + 1.

  3. For every candidate running, count how many #1-votes he or she got. Every candidate who got at least Q #1-votes is deemed elected.

  4. Some candidates will presumably get more than Q #1-votes. These surplus ballots are distributed to other candidates who are still in the running. For example, suppose that a surplus ballot says "#1--Smith, #2--Jones, #3--Rogers", and Smith has already received 2Q #1-votes, and Jones has also received at least Q #1-votes. The ballot would then count as 1/2 a vote for Rogers.

  5. After the surplus votes have been reallocated in this way, every candidate who has more than Q votes is also deemed elected. Repeat until no candidate has more than Q votes.

  6. If there are still more seats on the legislature than candidates who were deemed elected, eliminate the candidate with the fewest #1-votes. The ballots for this candidate are redistributed in the same way that surplus ballots were distributed. Repeat this process until all seats are filled.

This process minimizes the number of "wasted" votes. Even if your preferred candidate is so popular (or unpopular) that he or she is certain to win (or lose), you can still write that candidate in as your #1 choice, and you can influence the election by your #2-#M choices.

For more detail, see http://www.electoral-reform.org.uk.

The above description has a loophole - the order in which votes are counted can impact on the result. This is because different counting orders will result in different votes being "surplus".

To illustrate, assume an election for two council seats with three candidates (A, B, C) where three votes are required to be elected (Q=3). Voting as follows: 

   7 Votes: ABC ABC ABC ACB ACB BAC CAB
If the three ABC votes are counted first, the final two "ACB" votes will contribute to C - giving C the second seat. But, if the two ACB votes (along with one ABC) vote are counted first, the remaining two ABC votes will give B the second seat.

A modern "tweak" to STV (as used recently here in New Zealand, for example) to avoid this is as follows:

If Candidate A receives N 1st place votes, and N > Q, the value of all those 1st place votes is reduced to Q/N (just enough to elect Candidate A). The remaining partial vote (N-Q)/N is "refunded" back to each ballot and then allocated to the next placeholder.

Using the same example: 

   7 Votes: ABC ABC ABC ACB ACB BAC CAB
Counting first place votes gives: A=5, B=1, C=1

But A only needs 3 votes to be elected - she only needs 3/5 of the votes she got.

So, all the ballots for A are refunded 2/5 of a vote, leaving the following (we don't show A since she has been elected): 

   5 Votes @ 0.4: BC BC BC CB CB
   2 Votes @ 1.0: BC CB
Counting these gives: B=2.2, C=1.8

Now, we apply Rule #6 from above, eliminating the lowest polling candidate (C) and giving the second seat to B.

Since all votes are considered together, the result is more stable.

A notable downside of this is the amount of extra processing - doing counts by hand becomes prohibitively complex for anything more than toy demonstrations, requiring the use of computers to deliver results in a timely fashion.

Just my 2c -- BevanArps.

CategoryVoting

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