User:Efenna/Comparison Between the Hare and Droop Quotas

Comparison with the Droop quota
The Droop quota is today the most popular quota for STV elections. The Droop quota is smaller than the Hare quota, and was first suggested because it is the smallest quota that, like the Hare quota, ensures that the number of candidates who reach the quota will not be greater than the number of seats to be filled.

In an STV election in which there is only one seat to be filled (in other words an Instant Run-off Voting election) it is possible to use the Hare quota, which will simply be equal to 100% of votes cast. However, it is more intuitive to use the Droop quota, which will be equal to an absolute majority of votes cast, meaning 50% plus one, and both quotas will achieve the same result. A similar logic governs why the Droop quota should be extended to STV elections with multiple winners as well, and replace the Hare quota. When voters have only one vote—the single non-transferable vote system—a candidate is sure to win if reaching the Droop quota.

The Hare quota is generally kinder to small parties than the Droop quota because they have a better chance to win the final seat. This can mean more proportional results for small parties. But this comes at the expense of preserving the principle of majority rule—one reason that the Droop quota is used in all governmental STV elections. In an election held under the Hare quota it is possible for a group of candidates supported by a clear majority of voters to receive only a minority of seats if those voters do not disperse their vote relatively evenly across all their supported candidates. In contrast, such an outcome will not happen in an election held under the Droop quota unless voters in the majority do not rank all their preferred candidates or not enough preferred candidates seek office.

The earliest versions of STV used the Hare quota. The Hare quota is equal to the total valid poll divided by the total number of seats. The Droop quota is generally considered superior to the Hare quota for two reasons. First, because it elects more candidates in the first distribution of seats (whether STV or list PR) than is the case with the Hare quota, so that the maximum number of candidates are elected by the full quota without the even theoretical risk, carried by smaller quotas, of more candidates being elected than there are seats to be filled. Second, because under the Hare quota it is sometimes possible for a group of candidates supported by a majority of voters to receive only a minority of seats, and this result is considered undemocratic. This is best illustrated by an example.

Scenario
Imagine an election in which there are 5 seats to be filled. There are 6 candidates divided between two groups: Andrea, Carter and Brad are members of the Alpha party; Delilah, Scott and Jennifer are members of the Beta party. There are 120 voters and they vote as follows:

It can be seen that supporters of the Alpha party all rank all three Alpha party candidates higher than any of the Beta party candidates (the final three preferences of the voters are not shown above because they will not affect the result of the election). Similarly, voters who support the Beta party all give their first three preferences to Beta party candidates. Overall, the Alpha party receives 63 votes out of a total of 120 votes. The Alpha party therefore has a majority of about 53%. The Beta party receives a 47% share of the vote.

Below the election results are shown first under the Hare quota and then under the Droop quota. It can be seen that under the Hare quota, despite receiving 53% of the vote, the Alpha party receives only a minority of seats. When the same election is conducted under the Droop quota, however, the Alpha party's majority is rewarded with a majority of seats.

Count under the Hare quota
1. The Hare quota is calculated as 24.

2. When first preferences are tallied Andrea and Carter have both reached a quota and are declared elected. Andrea has a surplus of 7 and Carter has a surplus of 6. Both surpluses are transferred to Brad (who is of the same party) so the tallies become:
 * Brad (Alpha party): 15
 * Delilah (Beta party): 20
 * Scott (Beta party): 20
 * Jennifer (Beta party): 17

4. No candidate has reached a quota. Brad is the candidate with the fewest votes and so he is excluded. Because just three candidates remain and there are only three more seats to be filled, Delilah, Scott and Jennifer are all declared elected.

Result: The elected candidates are: Andrea and Carter (from the Alpha party), and Delilah, Scott and Jennifer (from the Beta party).

Count under the Droop quota
1. The Droop quota is calculated as 21.

2. When first preferences are tallied Andrea and Carter have reached the quota and, as before, are declared elected. However this time Andrea has a surplus of 10 and Carter a surplus of 9. These surpluses transfer to Brad and the tallies become:
 * Brad (Alpha party): 21
 * Delilah (Beta party): 20
 * Scott (Beta party): 20
 * Jennifer (Beta party): 17

3. Brad has now reached a quota and is declared elected. He has no surplus so Jennifer, who this time has the fewest votes, is excluded. Because only Delilah and Scott are left in the count, and there are only two seats left to fill, they are both declared elected.

Result: The elected candidates are Andrea, Carter and Brad (from the Alpha party) and Delilah and Scott (from the Beta party).