a surplus. The tallies of the remaining candidates are therefore: Delilah (Alpha party): 11 Scott (Beta party): 13 Jennifer (Beta party): 13 Matt (Beta party): 13 Susan (Beta party): 12 No candidate has reached a quota so Delilah, who is the candidate with the fewest votes, is excluded. Because there are only four seats left to fill, and only four candidates remain in the contest, all four are declared elected. The elected candidates are Andrea, Carter and Brad (from the Alpha party), and Scott, Jennifer, Matt and Susan (from the Beta party). Count under the Hagenbach-Bischoff quota The Hagenbach-Bischoff quota is calculated as 13. When the first preferences are tallied Andrea, Carter and Brad (from the Alpha party) and Scott, Jennifer and Matt (from the Beta party) have all reached the quota and all six are declared elected. However this time the three elected Alpha party candidates each has a surplus of 1. These surpluses all transfer to Delilah so the tallies of the remaining candidates become: Delilah (Alpha party): 14 Susan (Beta party): 12 Delilah has now reached a quota and is declared elected. The elected candidates are Andrea, Carter, Brad and Delilah (from the Alpha party) and Scott, Jennifer and Matt (from the Beta party). Disadvantage of Hagenbach-Bischoff quota In STV-like system with larger quotas (such as Hare or Droop), the typical rule is that candidates are elected when their number of votes equals or exceeds the quota. If this rule is used with the Hagenbach-Bischoff quota, it is possible that more candidates are elected than there are seats; the simplest example of this would be a single-winner election where two parties each receive half of the votes. Imagine an election with three candidates for two positions where the 300 votes are The Hagenbach-Bischoff quota is 300/(2+1) = 100. In the first round Andrea is elected with 200 preferences, while Brad (75) and Carter (25) remain in contention. Andrea's surplus of 100 is transferred: 25 to Brad and 75 to Carter, bringing each of them to 100. So all three have achieved the quota and so should be elected even though there are only two positions to fill. This problem is easily resolved, as suggested by Irwin Mann in 1973, by adjusting the rule so candidates are only elected when their number of votes strictly exceeds the quota (not necessarily by so large a fraction as to reach