Reference Andrae Rule

The Andrae method deals with whole votes, with random surplus transfers. It’s easy to understand and count, but both WIGM and Meek’s method do a fairer job of transferring surpluses.

Count multiple-seat elections as follows.

1. Initialize Election
   Set the quota to the total number of valid ballots cast for that office divided by one more than the number of seats to be filled, ignoring any remainder, plus one. Put the ballots in random order and sequentially number them to permit recounts. Distribute the ballots (D.1). If count is complete (D.2), continue at step C.
2. Rounds
   1. Defeat the hopeful candidate with the lowest vote tally. Break ties by choosing the tied candidate who is earliest in a predetermined random tiebreaking order.
   2. If count is complete (D.2), continue at step C.
   3. Distribute the defeated candidate’s ballots (D.1).
   4. Continue at B.1.
3. Finish Count
   If all seats are filled, defeat all remaining hopeful candidates; otherwise elect all hopeful candidates. Count is complete.
4. General Procedures
   1. Distribute Ballots. Drawing the ballots from the top of the source pile, place each ballot in turn on the top of a pile corresponding to the highest-ranked hopeful candidate on the ballot, keeping a tally of the votes in each candidate pile. When a candidate’s tally is equal to the quota, elect that candidate, and transfer no more ballots to that candidate. Place ballots that rank no hopeful candidate in a separate exhausted-ballot pile.
   2. Test count complete. If the number of elected candidates is equal to the number of seats to be filled, or the number of elected plus hopeful candidates is equal to or less than the number of seats to be filled, the count is complete.

Notes

This is a very simple example of a whole-ballot random-transfer STV rule. It gives fairly good results for relatively large elections. More complex variations on this theme are available (see Cambridge MA for an example) that avoid some of the drawbacks of this general method. However, if this rule as specified is not sufficient to the purpose (as when a rule is required for hand-counting small elections), we recommend using the Reference WIGM rule rather than a more complicated Andrae rule. The simple WIGM rule will be nearly as easy to count as a complex Andrae rule, and will give better results in almost all cases.

Putting the ballots in random order is not trivial, but it’s important to this method. A possible approach: place each ballot on one of six piles, depending on the throw of a die. Reassemble the piles and repeat, the more times the better. Note that this process can be carried out by multiple die-thowers working in parallel.

In step A, the ballots should be numbered as they’re first distributed, so that they can be re-ordered for a recount. Number the ballots in a distinctive place and/or with a distinctive color to avoid the possibility of confusion with the ballot’s rankings.