Shock, shock, horror, horror, shock, shock, horror… Sometimes, I need to be fair

In the comments to the last post, the author of AnonymousLefty asserted that:

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:

Prima: 30%

Secunda: 30%

Tertia: 40%

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:

Greens: 1

ALP: 2

Libs: 3

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.

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8 thoughts on “Shock, shock, horror, horror, shock, shock, horror… Sometimes, I need to be fair

  1. “the 1983 election of Thatcher where this exact thing happened.”

    Because the UK has first past the post. The problem of split votes is in first past the post systems, where – as in your 30/30/40 example – the winner is simply the one with the highest number of votes. Preference systems – like ours – REMOVE that problem.

    Hilarious that you patronisingly attack me for not understanding our system and then give an example which is from a completely different system.

    Also, it was your example that assumed “people vote in regular blocks”.

    If progressive parties are all knocked out before conservative parties, then that just means that a majority of voters in that seat prefer the conservatives. How would the Greens not standing help get the ALP over the line?

    You still haven’t outlined a scenario in which a 1 GRN 2 ALP vote helps the Liberals.

    • Because the UK has first past the post. The problem of split votes is in first past the post systems, where – as in your 30/30/40 example – the winner is simply the one with the highest number of votes.

      Fair call. You’re correct that the systems are different and so the Thatcher example doesn’t hold for the current situation.

      Preference systems – like ours – REMOVE that problem.

      So you missed the rest of the post where I demonstrated that it is possible? Weird.

      Also, it was your example that assumed “people vote in regular blocks”.

      No, I just had to give a situation where it could happen. Your counter-example relied on block voting.

      If progressive parties are all knocked out before conservative parties, then that just means that a majority of voters in that seat prefer the conservatives.

      No, it means that the total votes for a progressive party at a specific iteration is lower than all the others. This was all demonstrated quite clearly in the post.

  2. Here from Jeremy’s blog.

    Our preferential system is flawed, as indeed are all such systems in a well-defined mathematical sense.

    While I more or less agreed with his point that voting 1 Greens 2 ALP can’t hurt Labor’s chances this election, that’s only because of the current electoral reality in Australia that there are no seats where there’s a remote likelihood of the kind of scenario you describe occurring. In general, though, your concern about a split vote is correct, and is one of the reasons I’m increasingly in favour of abandoning our Instant Runoff Voting system for a more robust scheme of preferences.

    I wrote at very substantial length about some of these issues in the wake of the very nice real life example that was the Liberal Party room election that landed us with Tony Abbott as opposition leader, in my old blog here:

    http://musingsnotamusing.blogspot.com/2009/11/i-have-to-get-this-one-out-quick.html

  3. I responded to your scenario, and I still can’t see how voting Green and preferencing ALP can help the Libs. Obviously voting Green and preferencing the Libs can help the Libs, but if the ultimate fight is b/w ALP and Libs, it will simply come down to which of those two a majority of voters preferenced above the other.

    “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.”

    In which case its vote would go to its voters’ second preference – which, in the case of the ALP, should be another progressive party rather than the Libs.

    The point is that all the progressive parties can’t be knocked out before teh conservative parties unless voters choose to put conservative parties above progressive parties in their preferences. And if they choose to do that, well, that’s democracy.

  4. Jeremy, if you want to slog through a real-life mathematical example that shows why in principle a 1-Green 2-ALP vote can hurt left wing chances, go read the blog post I’ve linked to.

    Think of Malcolm Turnbull as “the left wing” i.e. The Greens, Hockey as “the centre left” i.e. the ALP, and Abbott as the right wing i.e. the Coalition.

    Note that if more moderates in the the party room had preferenced Hockey over Turnbull, Abbott would have lost.

  5. Your analogy doesn’t really work, because the Hockey/ALP candidate was preferred in that scenario by a heap of Abbott/Coalition voters, and many of the Hockey/ALP voters preferred the Abbott/Coalition to the Greens. And the ALP in that scenario got fewer first preferences than the Greens, so it was knocked out first.

    Basically the situation you’re describing is that if there are Coalition preferences locked up in the ALP or Greens, you want the “left” choice with the most Coalition voters to stay in longest so those votes aren’t freed to return to to the Coalition.

    But do we really think many ALP voters are preferencing the Coalition above the Greens? The would confirm for many voters how non-progressive the ALP really is. It would only be the case if the ALP wasn’t really a lefty party in the first place.

    Anyway, the much more critical issue is that voting straight ALP confirms to the party that you can be ignored and they can chase Coalition voters: voting 1GRN 2ALP tells them they’d better pay attention to their left – and, potentially, puts some Greens MPs up there to make sure they do.

  6. Jeremy, say the primary vote shares in a seat come out as:

    27% Green
    25% Labor
    40% Liberal
    5% National
    3% Family First

    If all National and Family First preferences flow to the Liberals, then it only takes 3 in 25 Labor primary voters preferencing the Liberal party over the Greens to hand them the seat; hardly conclusive evidence that the ALP are “not lefty enough”, as if that’s even a meaningful criterion to be evaluating parties by. Of course its also silly to judge parties on their voter base instead of their policy platform.

    It certainly wouldn’t surprise me to see some small but substantial fraction of Labor voters preference the Liberal party ahead of the Greens in a real election; hence, for example, the swings toward the Coalition in recent by-elections than only the Greens contested.

  7. But it’s also possible that there are Greens voters who preference the Liberals – apparently 20%. Your ALP vote so that the Greens are eliminated first frees up those Coalition votes, as well.

    But I was wrong to say it was impossible.

    Basically, voting either ALP OR Greens could conceivably help Abbott if there are enough Coalition votes locked up in those parties’ votes.

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