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User:Pathoschild/2007 single transferable voting for board elections

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Single Transferable Voting is an electoral system in which voters list candidates in order of preference. This page examines an electoral method for the 2008 board elections based on this system.

In the derived system, voters rank as many candidates as they'd like. If one preferred candidate loses, their vote is transferred to their next favourite candidate. This eliminates the need for strategic voting, and ensures that votes for less-popular candidate aren't "wasted" but instead increase the chances that second-favourite candidates win. Winners can be calculated in one of two ways:

  • the Schulze method;
  • by systematically eliminating the weakest candidates in each calculation round.

Example process[edit]


In an example election, there are 1000 voters electing six candidates to three positions. They are presented with a form like this:

Please rank the candidates according to your preferences by filling in a number beside the box (1 = favourite candidate, 2 = second favourite...). You can leave boxes blank to not vote for those candidates.

If your favourite candidate is not elected, your vote will be automatically transferred to your second-favourite candidate. Your vote will be transferred until the candidates you voted for win or it reaches the end of your list.

John Doe
Billy User
Jane Apple
Mary Hill
Jacques Example

The form script will ask the user to correct the input if there are non-numerical values; any numerical values will be ordered, so that "-50 0 300 1000" become "1 2 3 4".


After the election, a computer program counts the votes. The votes cast are distributed like this:

Candidate Vote count by preference
1 2 3 4 total
John Doe 418 300 262 20 1000
Billy User 328 350 102 176 956
Jane Apple 116 136 210 148 610
GenericName32 1 4 28 20 53
Mary Hill 116 132 292 425 962
Jacques Example 21 67 95 200 383
total 1000 989 989 989

Vote counting (systematic elimination method)[edit]

In a series of steps, the computer program will systematically eliminate the weakest candidates and transfer votes until there are only three winning candidates remaining (assuming there are three positions to be filled).

  1. GenericName32 has the fewest #1 votes, so he is automatically eliminated. All remaining votes are transferred.
  2. Jacques Example has the fewest #1 votes and transferred votes, so he is eliminated.
  3. Mary Hill has the fewest #1 votes and transferred votes, so she is eliminated.
  4. John Doe, Billy User, and Jane Apple win.



  1. Can I change my votes after casting them?
    Yes; simply casting a new ballot will replace the old one.
  2. What if I don't prefer one candidate over another?
    You can vote equally for candidates by using the same number; for example, "1, 2, 2, 3".


  1. What if a candidate withdraws?
    All votes for that candidate will be ignored, so the program will skip to the next favourite candidate on your list.

See also[edit]