I usually try and stay away from the Senate – primarily because it’s a major cause of psephological brainhurt, but also because there are such enormous amounts of uncertainty involved in which party gets the final 1 or 2 spots in each state, an uncertainty often tied up with micro-party preference deals, resources deployed at polling booths for distributing How To Vote cards and split voting behaviour, that trying to estimate the exact future make-up of the Senate borders on an exercise in futility. Especially since the final couple of spots can be decided by literally handfuls of votes.

Rather than going down that particular prediction route, instead it’s worth taking a look at the relationship between the primary vote that the Coalition, the ALP and the Greens receive in the lower house and the vote they receive in the Senate.

At its most basic level, the relationship between the primary and Senate votes is extraordinarily linear and very, very strong. If we run a chart where we plot the primary vote that each of these three parties received at the 2007 election in every one of the 150 electorates on one axis, and plot the vote they received in the Senate in those electorates on the other axis, we come up with a pretty strong correlation – so we’ll run a regression line through it to point out the obvious.

senrepsall

The three big outliers you see in the top left of the chart are Independent won seats of Kennedy and New England, plus the ex-independent held seat of Calare (which is interesting enough in itself).

Nationally, for every 1% increase in the primary vote that a party receives in the House of Representatives, that produces, on average, an increase in the Senate vote for that party of 0.87% . Hypothetically, if a party scored an additional 10 points on the primary vote, they would expect to receive an additional 8.7 points in the Senate.

97.1% of the variation in the vote of these three parties in the Senate can be explained by the variation in their primary vote in the House of Reps.

However, there are slight differences if we further break down these correlations by State and by Party.

If we run that same chart above, but this time expand the results by party, we get: (click to expand)

partysenreps

What turns up here is that firstly, the linear relationship holds strongly for all three parties. Secondly, the Greens get more bang for buck in the Senate by expanding their primary vote in the lower House than do the major parties – which can be seen by the steeper regression line for the Greens. It’s also worth noting that at the national level, the relationship between the Reps vote and the Senate vote for the major parties is almost identical.

If we look at the actual regression results themselves:

partyregressions1

The way to read that table above (and the tables a little further down) is that the “Reps-Coeff” is the regression coefficient on the House of Reps variable. For every one point increase in the primary vote in the lower House, the increase in the Senate vote is, on average, this value. So with, for example, the Greens – a 1 point increase in their national primary vote would lead, on average, to a 1.25 point increase in their Senate vote. Similarly, if the ALP increased their primary vote by a point, they’d expect to get a 0.81 increase in their Senate vote while the Coalition would expect a 0.79 point increase for every 1 point gain in their primary.

The R-Square is a measure of the explanatory power of the relationship. This value tells us how much of the variation in the Senate vote, by electorate, can be explained by the variation in the House of Reps vote – again by electorate. For example, the variation in the size of the primary vote that the Coalition received in each of the 150 electorates at the 2007 election explains 90% of the variation in the Senate vote they received.

The “Constant” isn’t really important here – I’ve just added it so that the nerdy stats types won’t have to ask for it, you know what they’re like 😛

Of note is the overunity Senate effect that the Greens received from their primary vote in the 2007 election, where every additional point of primary vote delivered them more than a point of additional Senate vote.

If we now break down the very first chart by state rather than by party, we get something that is a little messy, but demonstrates a point.

senrepsstate

While there is slight variation between the states in terms of the relationship between the Senate and Reps vote for parties by electorate, the direction and strength of the relationship is very similar. The odd State out here is South Australia – although the size of the relationship in SA is the same as other states (the slope of the trend line), it sits significantly below the other states. That’s the effect of Xenophon, where people voted for a party in the lower house but voted for Xenophon in the Senate, dragging the Senate/Reps vote relationship down for the three biggest parties in SA.

If we go to the regression results of the Senate/Reps relationship, which should be read as the table above, we get:

stateregressions1

I’ve ordered the States from the strongest to weakest Senate/Rep relationship. In WA, parties, on average, get the highest increase in their Senate vote for every marginal increase in their primary vote, while Tasmania gets the smallest increase.

Yet the important thing here is how the explanatory power (the R-square) remains consistently very high, while the size of the Reps to Senate effect is pretty close as well.

Finally, we can break down these results by both State and Party. Rather than use charts (which will look pretty similar to the ones above), we’ll just go straight to the regression results as they tell the actual story.

partyregressions2

WA and SA are marked, as the results from those states, by party, have the most uncertainty as a consequence of their relative small numbers of seats. While we can pay attention to what they’re saying, we can’t be as certain that it is true as we can of the results in NSW, Vic and Qld where there are larger numbers of seats (and larger numbers of observations). It’s also why Tasmania has been removed from the analysis – with only 5 seats in Tasmania, 5 observations does not a regression equation make.

What stands out here, assuming the same broad relationship that we saw in 2007 will hold at the 2010 election (and there’s no real reason why it shouldn’t, but more on that next week), is that the Greens most politically fruitful state for lifting their generic profile is Qld. With every additional 1 point increase in their primary vote, they should expect to see their Senate vote increase by 1.5%. For the Greens, Qld has the biggest Senate bang for the buck in terms of deploying resources to obtain a Senate spot.

The other peculiar thing about Qld is how, for the ALP and the Coalition, the increase in their respective Senate vote for every marginal increase in their primary vote is relatively small compared to other states. For every 10 point increase in the primary vote of the two major parties, the ALP would expect to only get a 6.4 point increase in their Senate vote compared to the Coalition’s 6.5.

The size of a party’s primary vote is the best predictor of their Senate vote in all States that we have. This should give us a bit of an idea about implications for the Senate when we get to polls a little closer to the election. There’s a lot of info here, with quite a lot of implications, so I’ll do my best to answer any questions you might have.

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