Preferential Voting Explained

I’m pretty sure that every kid in Australia learns this at some stage of their schooling, or is supposed to. Some may have forgotten, and many didn’t care enough (either about politics, or school) to really listen. In Britain, where minor parties are starting to make a mark, the system that Australia uses is the one often pointed to as the most suitable. It is sometimes criticized as being too complicated. For whatever it’s worth, I rather like it, and with the Australian federal election coming up in a few days, I thought it would be timely to provide a thorough explanation of how it actually works.

Let’s say you’ve got three candidates for an election: Alexis, Billie, and Casey.

Simple "First past the post" voting

A simple “first past the post” system is used and everyone just ticks one box next to a candidate’s name. Alexis gets 6 votes, Billie gets 17, and Casey gets 14 votes, so Billie wins. However, all the people who voted for Alexis pipe up and say “hey, if we had known that was going to be the result, we would’ve all voted for Casey!”. So even though more people voted for Billie, a greater number overall preferred Casey over Billie.

There are obvious implications here. Firstly, it discourages candidates from running. If you’re from a small political party, you may be discouraged to run for election because you may split the vote from the candidate who you might prefer to win. It also means that if there are a lot of candidates, a person may “win” the election with a very small percentage of the vote. It also makes all the people who didn’t vote for the winner feel like their vote was wasted.

Some countries combat this by having a second election, where the two most popular candidates from the first election have a “runoff”. I personally think that this is a very crude and inefficient way of handling the problem, and who the hell wants to have two elections?

The “answer” to this is instant runoff preferential voting, sometimes called the Hare-Clarke system (presumably after the people who came up with it, or first used it). First, an explanation of how it works in the case of candidates running for a single seat, such as in the case of geographical electorates in the house of representatives.

Same example as above, except instead of just ticking one box, we ask voters to number their candidates in order of preference from 1 to 3.

In preferential voting, you number the candidates in order of preference

So what happens now? Let us assume that the “1” voting reflects the results from before, with Alexis on 6, Billie on 17, and Casey on 14. Then what happens?

Contrary to what many people think, the numbers aren’t allocated “points” and then totalled up to determine the winner. What happens is this – the “1”s are tallied up and if any candidate has accumulated 1 vote more than 50% of the total number of voters, then the election is over and that candidate is declared the winner. If not, then whoever is last; that is whoever has the fewest number of “1”s is eliminated from the running. The votes previously belonging to that candidate are then redistributed among the remaining candidates according to those voters’ next preferences (in this case, the “2”s). This process continues until one of the candidates accumulates 50%+1 of the total vote.

If there are 6 candidates for a seat in Parliament, then this is roughly equivalent to having 5 separate elections where the last candidate is eliminated each time, then everyone votes again, until you’re left with the winner of a two-horse race. Of course, sometimes you don’t need all 5 of those elections – a candidate may accumulate a large enough number of votes long before it comes down to a two-horse race.

The Senate

The Australian Senate is composed of 12 senators from each state and two from each of two “territories” (The Australian Capital Territory, similar to DC in the US, and The Northern Territory, similar to a very large desert). They are elected according to proportional representation by a single transferable vote system (described above as preferential voting). This is where it all gets slightly complicated.

A sample ballot paper for the Australian Senate

This is an example of one of the “simpler” ballot papers, where you only have a small number of candidates and there are only two senators to pick. In your typical state, there can be as many as 80 candidates competing for 12 seats. So how does this work?

First, we take the number of voters in the electorate and divide that number by 13. We will call this number Bob. Bob is the magic number.

This process is slightly more complicated than the system for a single candidate. It begins in an almost identical manner to the above until a candidate gets enough “1”s to win a seat, that is, the number of “1”s exceeds Bob. Then it gets tricky. Let’s say Bob is a number like 12,000, and candidate A gets 16,000 “1”s. If this happens too often, we’ll run out of votes to count before we’ve filled all the senate seats. Something needs to be done with those excess 4,000 votes, and that something is this – candidate A’s 16,000 votes get redistributed according to their second preferences (same as if the candidate was eliminated from the bottom) except each one of those votes is worth \frac{4,000}{16,000}. That way, the preferences of the voters for the senate are still honoured, and we manage to keep 16,000 \times \frac{1}{4} (or 4,000, a.k.a. the correct number of) votes still in the system. Once those preferences have been redistributed, we check to see if there are any candidates with more “1”s than Bob. If there are, we repeat the process for awarding a seat, then redistributing the votes according to next preferences multiplied by the fraction of the excess primary vote over the total number of primary votes. If there aren’t, then we eliminate from the bottom as before until a candidate has more votes than Bob.

In the Australian Senate elections (which generally take place at the same time as the House of Representatives elections) about 6% of voters actually bother to number 1 through to 80-ish. Instead, a voter can opt to vote “above the line” where they simply put a “1” next to the box of a major party, in which case their preferences will follow a predetermined order set by that political party. This is unfortunate because not only do many people not know what those preferences are, the major parties often do preference-swap-deals and this can have unforeseen bad side-effects, like Steve Fielding being elected.

4 Comments on Preferential Voting Explained

  1. One minor point, a general election in Australia is only a 1/2 senate elections – ie only 6 senate seats per state are actually up for grabs (I’m not sure what happens to the territories though!) – so a quota isn’t 12%, it’s 7%.

    There’s an exception if there’s a double disolution election, of course, where all senate seats are up for grabs.

    • Territories senators are elected for the same period of time as the House of Representatives.. ie, they only get 3 years.

      And BTW, in a double dissolution, all senate seats are up for grabs, but when all are elected, they are divided into two groups: those who are to serve 6 years and those who get 3 years.

      Interestingly, the constitution doesn’t give a fixed rule on how that split-up is to occur. In practice at present, in each state, the first 6 past the post in the ballot counting get the full 6-year term.

  2. I clearly can’t count…. I mean the quota isn’t 6%, it’s 14%

  3. I clearly can’t count and am dyslexic…. I mean the quota isn’t 6%, it’s 14%

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