There is no way that voting 1 Greens 2 ALP could conceivably help Tony Abbott. None. — Source.
In deriding him for also claiming that we shouldn’t take the Greens’ policy documents seriously (because, apparently, the party doesn’t either), I was a bit too quick to give an example of the completely uncontroversial problem of split votes. While the example I gave was fine, it wasn’t particularly rigorous or persuasive to somebody who disagrees that voting for the Greens can help the Coalition. While I had assumed that everybody in the world except for AnonymousLefty understands how split votes happen (and, indeed, why we have the phrase ‘split vote’), I shouldn’t be so hasty. Also, AnonymousLefty thinks that the very idea of the split vote is a conspiracy against confused lefties.
I should make a note here that I have no idea who AnonymousLefty is. In writing this post, I might be attacking somebody who has a nappy between his ears. When making this post, I’m not trying to set up a straw-man Greens supporter. I hope his views aren’t mainstream (simply because they are so wrong-headed).
But for those people who are interested in split votes, here is a full explanation.
Imagine you don’t have a preferential system but a system where the option with the most support ‘wins’ (I really hate the term ‘wins’, btw, because it promotes the idea of elections as a game or competition. I apologise for being sloppy and using these terms). It’s easy to get your head around why a split vote might happen in this situation:
Prima and Secunda have very similar views. Tertia holds very different views. A vote is taken to choose a leader out of the three. The results come in:
Clearly, more people agree with the views of Prima and Secunda (60%) than with Tertia.
There are election systems — lengthy, horrible ones — where a vote is held between more than two contenders. After the first vote, one of the contenders volunteers to opt out and a second vote is taken. The process continues until there is an election between two options (or abstaining). Where a candidate refuses to opt out, elections are conducted on a yes/no basis with the candidate holding the lowest individually preferred ratio being forced to opt out. It leads to a particularly strong outcome — it totally eliminates the problem of the split vote — but, as you can see, it would take an enormous amount of time for a national election. I’ve only seen this process used in environments with a small number of candidates and a small number of voters (organisations).
Straddling the path of these two options is preferential voting. It’s mathematically more interesting because of the permutations involved. In the example I gave to AnonymousLefty, I gave the example of a close election which was lost due to the lack of strong primary vote. He whined that — because people vote in regular blocks, apparently — the ALP would have lost anyway in my example. As I said earlier, it wasn’t rigorous, so let’s look at a better (but more complex) example.
The quirk in this system is that the option with the lowest number of votes in an iteration is knocked out. There is no way to ‘revive’ an option if a large number of people list that option as a lower preference.
For example, imagine a ticket lists the preferences:
Somebody else: 4
Somebody else again: 5
And so on: 6…
If the ALP lacked a strong primary vote, it could be taken out of the running. If the Greens are the next weakest, this vote will go towards the Liberals (until they get knocked out of this crazy seat).
We can imagine the set of votes where the sum of a party’s first preference votes and second preference votes is more than or equal to 50%+1. It’s obvious that there are lots of possible sets (where the sum equals 50%+1, where the sum equals 50%+2, …). Because of that, we can imagine the set of votes where the sum of a party’s first preference votes and second preference votes is more than or equal to 50% +1 and where the total of the party’s first preference votes is smaller than every other party’s first preference votes. This is the situation AnonymousLefty denies can happen (you know, despite the existence of decision theory even having entire words for this exact thing).
Actually, that might be a little bit unfair. He actually believes that it is impossible that this will result in a Coalition win. Thus, he believes that it is physically impossible for a person to vote in any way similar to the hypothetical above (Greens:1, ALP:2, Lib:3).
So clearly, he’s talking claptrap.
Okay, I’ve been unfair again. I made this unnecessarily difficult by using reason and logic. I could have just pointed to the 1983 election of Thatcher where this exact thing happened.
It’s a necessary truth that anything which happened is possible. Pooh, I was too hasty here. AnonymousLefty has correctly noted that the Thatcher example isn’t relevant. Mea cupla. Unfortunately, this example distracted him from the rest of the post.