Assuming only that the reader can peruse the counting sheets, let me explain how to find the results of an election by the Single Transferable Vote method with the
Droop quota and fractional transfers.
The first step in any STV vote counting process is to determine the quota to be elected. The most commonly used quota, the
Droop quota, is pretty simple. This quota is the number of voters divided by the number of seats to elect plus one, plus one:
Why this formula? It should make sense if one thinks first about the single-winner case. If you're electing one candidate, you know that if they get more than half of the votes, they've won. This is because, if a candidate has more than half of the votes, it's impossible that any other candidate has more. The logic is the same for multi-seat elections: if they've gotten enough votes that it's impossible that enough other candidates have more votes than them to keep them from winning a seat, they've won. For example, if one is electing to 5 seats, then the quota is effectively "more than1/6 of the votes", because if one has more than 1/6th, it's impossible for 5 other candidates to have more than 1/6 each, as that'd add up to more than all of the votes. This was the case in all of the TNP Executive Council elections, and I believe would be the case in elections to the Unterhusen.
So, as 158 nations voted in the first such election, the quota was 158/6 + 1 = 27 (truncated). In the second, the 97 voters resulted in a quota of 97/6 + 1 = 17 (again, truncated). In the third, 45/6 + 1 = 8 (still truncated). In the fourth and final such election, 36/6 + 1 = 7 (exactly
). (The last election only allowed forum-registered members to vote).
Not only does the quota show how many votes one needs to win a seat outright, it's also used to make the results proportionate. Without transfers, it could easily be possible for plenty of votes to be "wasted" by voting for someone who gets well over the minimum number of votes needed to be elected. For instance, in the first STV election, about 52 of the voters listed me first, which gave me 49.95 votes (several of those voters also voted for someone else first, so their vote was split from the start), nearly double the quota of 27. The Single Transferable Vote
transfers votes in this case, to avoid their being wasted.
In that first election, I had 49.95 votes in the first round, and the quota was 27. Thus, 22.95 votes had to be transferred from my pool, to avoid their being wasted. Under Gulliver's fractional STV program, this meant that the 52 ballots (including several already fractional ballots) were each split into two parts, under the 27:22.95 ratio. The smaller part of each ballot was then transferred to their next preference: a total of 6.84 to mcmasterdonia, 4.17 to unibot, 3.69 to Romanoffia, 2.34 to KiwiTaicho, 3.03 to Govindia, 0.48 to peoples empire, and 1.85 to Abbey Anumia. With the transfers done, my total became 27, exactly the quota.
Each round of transfers is a round in the counting of the votes. In each round, if there are candidates with at least as many votes as the quota, they are elected. (Such as the first round discussed above). However, if there are no candidates remaining who have more votes than the quota, then the candidate with the least votes is eliminated. If a candidate is eliminated, all of their votes are transferred to the candidate with highest remaining preference on the ballot. (These transfers are only fractional if the ballots have already been split into fractions).
After repeating this process enough times there will be several winning candidates, matching the number of seats to be elected. At that point the counting process is (finally) over. Of course, when I did this, I did not spend much time counting, as I would simply run Gulliver's program. (What took a great deal of time was running IP checks on all of the voters.... Something irrelevant to this discussion here
)
Looking back into the records, I found that the very first Executive Council
election used a very different method of counting. Implementing this method would be very difficult to do by hand, however, so I don't see it as sensible to relate much about it.
