Just how representative are the houses of parliament of how Australians vote?

How representative are Australia’s elected representatives of the population as a whole? There is a clear disparity between the support of a party, in terms of popular vote, and seats won, in the results of the 2016 federal election.

How many voters do the major parties represent?

As of the morning of July 12, the figures in parentheses in the table below are the number of seats won out of 150 in the House of Representatives, and out of 76 in the Senate, in the 2016 election:

There are two points to note from this table.

• First, the percentages for each party are closer in the Senate than they are in the House of Representatives.

• Second, the major parties fared much better in the House of Representatives than the Greens.

The first point is due to proportional representation being used to elect the Senate. If a party receives X% of the vote in a state, it should receive “roughly” X% of the senators. But we are sweeping an awful lot under the rug with the word “roughly”. And the national vote obscures the differences in the states’ population: Tasmania elects the same number of senators as New South Wales, even though the population of NSW is more than 12 times that of Tasmania.

More senators means more representation

At a normal half-Senate election, where each state elects six senators, the quota is one-seventh of the total vote, or 14.3%. If candidates receive more than one quota they are elected. If, after others are eliminated, a candidate has only 14.2% of the vote, they miss out.

At a double-dissolution election the quota is almost halved to a 13th of the total vote, or 7.7%. Therefore, a candidate will miss out if they are the last one standing with only 7.6% of the vote.

In other words, in a normal election it is “unfair” that candidates can be excluded even with 14.2% of the vote. The situation is much “fairer” in a double-dissolution election; only those with 7.6% or less will miss out.

The situation would get fairer still if more senators were up for election. If, say, there were 100 senators, then only those with less than 1% of the vote would miss out.

Even though increasing the number of senators is possible without a referendum, and even though parliament has done this three times (in 1948, 1975, and 1984), there appears to be no push for an increase at present.

Preferences and spread of vote

The second point is due to the House of Representatives’ structure: that is, one member is elected in each electorate. If Party X received 10% of the first-preference vote in each electorate, it would be almost impossible for any candidates from the party to be elected.

The more likely scenario is that, at some point in the vote count, candidates from Party X would have the fewest votes of all remaining candidates and hence be eliminated.

First-preference votes are not everything, however. The final votes after preferences are those that determine the election. Nevertheless, at least intuitively, the greater the nationwide primary vote for Party X, the greater the number of seats for Party X. But there are two obvious caveats.

Results could be skewed between electorates. For example, the Labor vs Coalition vote could be 10:90 and 60:40 in two electorates. Labor would then have only 35% of the total vote (half of 10% and half of 60%), but win as many seats as the Coalition (one each).

Preferences can get parties over the line. For example, the Labor vs Coalition vs Greens vote could be 40:45:15 in a particular electorate. The Greens candidate, having the fewest votes, would be eliminated. If more than two-thirds of the Greens voters have the Labor candidate as a second preference, the Labor candidate would be elected, since 40 + (2/3 x 15) is 50.

Votes or seats, what’s more important?

Below is a graph of first-preference votes compared to House of Representative seats won in all federal elections since 1949. Labor is represented by the red dots; the Coalition by the blue.

Here we see a definite trend, best approximated by the blue diagonal line drawn through the points, showing an increase in seats won when the primary vote increases.

When a point lies above this blue diagonal line the party is “lucky” – that is, it won more seats than it “should have won”. This is due to a combination of skewed results across electorates and favourable preferences.

Points below the blue diagonal line are unlucky: the spread of the national vote and preferences conspired against the party.