(Tasmanian election website now live at www.abc.net.au/elections/tas/2010/)
I've been playing around with a graphics package, trying to come up with a way of visualising how a Hare-Clark count works.
I've always thought that a useful way to think of a Hare-Clark count is as a pie. At the start of the count each slice of the pie represents the votes received by a candidate. At the end of the count you have the same pie, but the over-sized pieces have been cut up and redistributed, as have the smallest pieces, leaving you with a pie with a smaller number of equal pieces.
Normally I think pie-charts are the world's most useless graphs, but they are exactly what you need to illustrate a Hare-Clark count.
The quota for election was one-sixth of the vote, around 16.7%. As you can see, both Labor's Paul Lennon and Liberal Will Hodgman started off with slices that were well over a quota. Both will have their votes beyond the quota distributed to other candidates.
As you can also see, the votes/slices for all the lower polling Liberal, Green and other candidates are small. Each of these will be excluded in turn, the votes for each candidate distributed according to the preferences on the ballot paper to candidates remaining in the count.
What you have at the end of the count is the following pie-chart.
When five candidates are declared elected, the count is complete. In this example, Wriedt was the final candidate elected with just less than a quota. This was because of the small number of exhausted preferences. The final Liberal candidate Goodwin missed out. Under Hare-Clark, the candidates remaining in the count that miss out on election always have less votes than any of the candidates declared elected, and this must be less than a quota.
You should also notice that the red side of the pie is bigger at the final count than at the first count. That is because during the distribution of preferences, votes flowed to the Labor candidates. In particular, the Greens started the count with a total of 19.4%, 1.17 quotas of votes. At the end of the count, Nick McKim is elected with one full quota, and 0.17 quotas have been redistributed, many ending up with Labor candidates.
These two images illustrate how a Hare-Clark count works. The Lennon and Hodgman slices were cut down to the size of the quota and the surplus redistributed. The candidates with the smallest slices were successively distributed to candidates remaining in the count.
The count started with the pie having 17 slices of vastly different sizes. At the end there were only 7 slices, five representing the five elected candidates, one the final candidate to miss out, and one small slice represented ballot papers with no further preferences.
It is possible for there to be more than one candidate left unelected at the end of the count. Five candidates may be declared elected before all remaining candidates are excluded. But if there are five candidates with a full quota, than by definition the remaining votes must be less than a quota.
So, Hare-Clark visualised. End of lesson.