Idiot's* guide to preferences
Electoral systems fall into two broad categories: proportional representation and single member electorate. Proportional representation, used in many European countries (eg Germany, Netherlands, Switzerland, Sweden) more or less means that parties get seat representation in proportion to their vote. Our Senate operates under a reasonably complicated system of proportional representation, but the discussion here is about lower houses - where governments are made.
Single member electorates
The Australian House of Representatives uses single-member electorates. Currently it has 150 electorates, and each is represented by one person.
The United Kingdom's lower house, the House of Commons, also has single-member electorates. But their voting system - called plurality or "First Past the Post" - is much simpler than ours. At election time, people have one vote and they cast it; whichever candidate gets the most votes wins, end of story.
This is easy, but the winner can't always claim to have received a majority of the vote (just a plurality - more than anyone else).
France, Russia and other countries have single-member electorates, but they solve the problem with run-offs. If no-one gets more than 50% of the vote, two weeks later they have a second poll, at which two (usually leading) candidates fight it out. With just two candidates, the winner can lay claim to a majority of the vote.
Australia's system is similar to the French one, but we do it all on the same day, on the same ballot paper. We tell the Electoral Commission who we would like to win in our seat. They get a number '1'. Then we say, if that person doesn't win, we'd like this person to win (number '2') and so on, until all boxes are filled.
The candidate you give a number one to has received your Primary Vote. At the end of the day all the primary votes are counted, and the candidate who received the least number of primary votes is eliminated from the contest. However, these ballot slips are not thrown away. They are again looked at to see who the voter put a number 2 next to, and added to that candidate's vote. Now the numbers of the remaining candidates votes are again examined, and the one with the least votes is eliminated, with their vote distributed as above.
This continues until there are only two candidates remaining. Whoever gets the most votes after distribution of all preferences wins. This is also called the two candidate preferred vote.
These days the Electoral Commission is sophisticated enough to register all the information on the ballot slip in one go, so they don't have to keep going back to each ballot slip to see where the next preference goes.
Another way of looking at is by making two piles of ballot slips, those
Preferential voting was introduced in Australia in 1918 by the conservative government with the emergence of the Country Party. Conservatives did not want to split and waste their votes.
At the national level, the aggregate of all 150 seats translates into primary votes and two-party preferred; the latter, as we've seen, is how a person wins an individual seat. The Labor figure and the Coalition figure add up to 100%, as between them they account for all the votes.
In a perfect world, the party with the most two party preferred votes would always win the greatest number of seats. But this ain't always necessarily so. This table shows that when the vote is pretty close - say, 49 to 51 or closer - the side with most votes wins government about half the time.
Australia is one of the few countries in the world where voting is compulsory. What this actually means is we have to make an appearance at a polling booth or make another form of contact with the electoral commission; we don't really have to cast a vote for anyone.
In Western Australia, Victoria and Federally, compulsory preferential voting is used. You must "number every square".
Queensland and New South Wales elections employ optional preferential voting. Voters can just give a '1' to one candidate and leave it at that, or do that plus give someone else a '2'; they can fill in as many squares as they like.
In the French/Russian analogy, compulsory preferential voting means you don't have to vote for anyone in the first round (you can just trash the ballot slip), but if you do, you must also vote in round 2.
Using the same analogy, optional preferential voting allows you cast a vote in the first round but give the second one a miss if you wish.
* Used in the loosest sense.