Reference WIGM Rule

Weighted Inclusive Gregory Method, 4 decimal places, optional batch defeat.

Multiple-seat elections shall be counted as follows.

  1. Initialize Election
    1. Set the quota (votes required for election) to the total number of valid ballots, divided by one more than the number of seats to be filled, plus 0.0001.
    2. Set each candidate who is not withdrawn to hopeful.
    3. Test count complete (D.3).
    4. Set each ballot’s weight to one, and assign it to its top-ranked hopeful candidate.
    5. Set the vote for each candidate to the total number of ballots assigned to that candidate.
  2. Round
    1. Elect winners. Set each hopeful candidate whose vote is greater than or equal to the quota to pending (elected with surplus-transfer pending). Set the surplus of each pending candidate to that candidate’s vote minus the quota. Test count complete (D.3).
    2. Defeat sure losers (optional). Find the largest set of hopeful candidates that meets all of the following conditions.
      1. The number of hopeful candidates not in the set is greater than or equal to the number seats to be filled minus pending and elected candidates).
      2. For each candidate in the set, each hopeful candidate with the same vote or lower is also in the set.
      3. The sum of the votes of the candidates in the set plus the sum of all the current surpluses (B.1) is less than the lowest vote of the hopeful candidates not in the set.

      If the resulting set is not empty, defeat each candidate in the set and test count complete (D.3), transfer each ballot assigned to a defeated candidate (D.2), and continue at step B.1.

    3. Transfer high surplus. Select the pending candidate, if any, with the largest surplus (possibly zero), breaking ties per procedure D.1. For each ballot assigned to that candidate, set its new weight to the ballot’s current weight multiplied by the candidate’s surplus (B.1), then divided by the candidate’s total vote. Transfer the ballot (D.2). If a surplus (possibly zero) is transferred, continue at step B.1.
    4. Defeat low candidate. Defeat the hopeful candidate with the lowest vote, breaking ties per procedure D.1. Test count complete (D.3). Transfer each ballot assigned to the defeated candidate (D.2). Continue at step B.1.
  3. Finish Count
    Set all pending candidates to elected. If all seats are filled, defeat all hopeful candidates; otherwise elect all hopeful candidates. Count is complete.
  4. General Procedures
    1. Break ties. Ties arise in B.3 (choose candidate for surplus transfer) and in B.4 (choose candidate for defeat). In each case, choose the tied candidate who is earliest in a predetermined random tiebreaking order.
    2. Transfer ballots. Reassign each ballot to be transferred to its highest-ranking hopeful candidate and add the current weight of the ballot to the vote of that candidate. If the ballot ranks no such candidate, or has a weight of zero, it is exhausted and no longer participates in the count.
    3. Test count complete. If the number of elected plus pending candidates is equal to the number of seats to be filled, or the number of elected plus pending plus hopeful candidates is equal to or less than the number of seats to be filled, the count is complete; finish at step C.
    4. Arithmetic. Truncate, with no rounding, the result of each multiplication or division to four decimal places.

Notes

This rule is designed as a minimalist WIGM rule. The only concession to complexity is the inclusion of an optional defeat-sure-losers step. The inclusion of this step may be justified by the fact that it can make a hand count faster by avoiding some transfers (in particular, avoiding surplus transfers that would have otherwise gone to candidates that will be immediately and inevitably defeated).

Defeat of sure losers is optional in the sense that the rule may be adopted without including the sure-loser step. However, if adopted, this step must be mandatory, because the outcome with it may differ from the outcome without it, as it can alter the order of surplus distribution and thus the outcome of the election.

 

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