A rather cute press release this morning from the Queensland Greens reports a study by one of their members, Charles Worringham, that shows Queensland as recording the most unbalanced election result in a sample of the most recent elections in 132 states or provinces across five countries – Australia, Canada, Germany, South Africa and the United States.

Dr Worringham is indeed a researcher at Queensland University of Technology, although the press release neglects to mention that his discipline is sports medicine rather than political science. Still, he clearly understands statistics, and his calculations are fundamentally straightforward – and the result is thoroughly believable.

At last year’s Queensland election the Liberal National Party won 87.6% of the seats with just 49.7% of the vote. That’s an over-representation of about 76.5%. The next highest figure Worringham was able to find was 59.5% in the last election in Alberta, Canada.

Political scientists generally use a more sophisticated measure of (dis)proportionality to try to capture the fairness of representation of all parties, not just the winning party. But that wouldn’t help Queensland’s case. I calculated a Gallagher Index or least squares figure (Wikipedia explains how to do it here; there’s a more academic treatment here) and got 31.2 – for comparison, anything over 10 is pretty poor and over 20 is very unusual for a democracy. (Proportional systems routinely manage under 5; see the compilation here).

It’s not that Queensland has a uniquely bad electoral system. It just has the same pretty bad system that a number of countries use – single-member districts – which last year managed to throw up an unusually disproportionate result. That’s always quite likely in Queensland when one party wins a landslide (2001 would have been almost as bad) due to the conjunction of two factors: the presence of strong minor parties (in this case Katter’s Australian Party and the Greens) that find it almost impossible to win seats, and the relative homogeneity of south-east Queensland, which means neither major party has a clutch of safe seats to fall back on.

And in Queensland, of course, the unfairness of the lower house is more of a problem due to the absence of any upper house to counterbalance it.

The Queensland Greens are not a disinterested party. But they have a legitimate grievance, winning 7.5% of the vote but no seats (and indeed not even close to winning any). And they are right to point out that “When a party’s majority better reflects its vote share then it tends to listen more and govern with greater care.”

That’s a debate that’s long overdue in Australia, and not just in Queensland.