The double majority and the tipping point state

One of the most interesting elements of a constitutional referendum in Australia is that there are two requirements for the referendum to be carried: it needs a majority of votes nationally, but it also needs a majority in a majority of states.

Since there have been states for the entire history of the Australian commonwealth, every referendum has been required to win four out of six states, which is two thirds. The bar would be lower if there were a larger number of Australian states. If there were twenty states, a referendum would need to win eleven out of twenty, a much smaller proportion.

Since Federation, eight referendums have passed, while another five have achieved a national majority but fallen short of winning four states. Three of these referendums won in three states, while the other two won in just two. There has never been a referendum that won in four states but failed to win a national majority.

In this post, I’m exploring how these two barriers interact with each other, looking at the close referendums but also all the other ones to see whether there’s a systematic need to win more than 50% in order to achieve wins in four states.

For this blog post, I’m going to focus on the “tipping point state” – that is the state that polls the fourth-highest Yes vote. You can look at the Yes vote in that state to see how close the referendum was to success (or to defeat) and compare it to the national Yes vote.

This table shows the rank for each state at each referendum. Victoria was the most common state to come fourth, doing so 13 times (about 30%), followed by Western Australia eleven times (25%).

Interestingly Tasmania has a very strong record as one of the worst states for any referendum. In more than half of all referendums, Tasmania was the worst state, and came fifth in another nine. Thus in almost three quarters of all referendums, Tasmania’s support was unnecessary for the referendum to pass. While Tasmania was the tipping point state for three referendums, those referendums saw all six states vote together: all six voted Yes to change Senate terms in 1906, and all six voted No on Incomes in 1973 and the Preamble in 1999.

Now let’s zoom in on how many times each state came fourth. For this next table, I list how many times each state has been the tipping point state, broken down by how many states voted Yes in that referendum.

Interestingly there has never been a referendum where exactly four states voted Yes, so it’s never come down to a single state passing a referendum. But there has often been a single state blocking a referendum from passing: thirteen referendums have seen a 3-3 split. In three of these cases, there was a national majority in favour.

While WA looks to have a lot of cases of being the tipping point state, nine of those eleven cases occured when all six states voted the same way. This is partly due to Western Australia becoming the tipping point state most commonly in recent decades when referendums have tended to lose badly: WA was the tipping point state in nine out of twelve referendums held between 1977 and 1999.

A majority of Victoria’s thirteen tipping point referendums were in referendums where the states split 3-3, and thus a Yes vote in Victoria would have given Yes a 4-2 victory. In none of these cases did Yes win a national majority though. It includes all six referendums held in 1913 – all six narrowly lost the national vote and won three out of six states.

Of the five referendums that failed despite a national majority, the tipping point state was twice South Australia (both in 1946), twice Western Australia (1977 and 1984) and once New South Wales (in 1937).

So now we know which states tend to be at that tipping point, I wanted to explore whether the requirement for a double majority biases the system in favour of Yes or No.

If we were looking at an electoral pendulum, we could look at the uniform swing for a party to win a majority and compare it to the uniform swing required for that party to win the 2PP nationally, and see how much those two numbers diverge. Since there are only two options in referendums, we can do the same for each referendum. This next chart compares the national Yes vote to the Yes vote in the tipping point state for all 44 referendums.

The black diagonal line represents a result where both Yes votes are the same. The darker green area represents a successful referendum result. The lighter green areas represent a referendum result that meets one criteria but not the other.

In almost every referendum, the national Yes vote exceeded the Yes vote in the tipping point state, which means that it would have been easier for Yes to win the national vote than to win four states.

There are only two exceptions, both in 1910. The Finance referendum polled 49.04% nationally, and 49.06% in South Australia, while winning three other states. This is as close to a perfectly non-biased result can be. The other example was the State Debts referendum, which polled 54.95% nationally, while polling 64.59% in the fourth-best state of Victoria.

That State Debts referendum had a pattern we’ve never seen since – New South Wales voted overwhelmingly No – with 33.3% in favour, while the other five states all voted overwhelmingly in favour – every Yes state cast a vote of at least 64.5%. With New South Wales as the largest state diverging dramatically from the rest of the country, that pulled the national majority down. If the Yes vote was about 5% lower across the country, New South Wales would have successfully blocked the proposal despite large majorities in every other state.

The average referendum has seen a national Yes vote 3.76% higher than the Yes vote in the tipping point state.

On the other hand, the biggest gap where the Yes vote was higher in the national vote was the 1977 Senate casual vacancies contest. NSW, Victoria and South Australia all voted very strongly for Yes, while the other three states were under 60%. This translated to a national Yes vote of 73% and just 58.9% in Queensland.

That didn’t end up mattering, but in the second referendum on the list, it really did matter.

The 1977 referendum on Simultaneous Elections achieved at least 65% of the vote in three states, including the two largest ones, and 62% nationally. Yet it couldn’t get above 48.5% in any other state, and lost. This was by far the biggest Yes vote for a losing referendum, significantly more than the successful referendums in 1910 and 1946.

The above chart also shows the number of referendums that came close to victory, even if they didn’t achieve either of the two necessary majorities. There have been eight referendums with a national Yes vote of between 49% and 50%, three Yes majority states and polling above 48.7% in the tipping point state. This included all six referendums put up in 1913, along with the 1910 Surplus Revenue referendum and the 1951 Communist Party referendum.

With a slightly higher Yes vote in some key states, we’d have had 21 successful constitutional referendums, not eight. But it’s interesting that none of those close calls have taken place in the last 40 years.

(That’s putting aside that the passage of an earlier referendum may have changed the future trajectory of referendums – the 1984 Terms of Senators referendum wouldn’t have happened if the 1977 Simultaneous Elections referendum had passed).

Overall it is clear that the “double majority” has tended to mean that referendums usually need a national Yes vote closer to 55% than 50% in order to pass. That’s not necessarily a permanent feature of the system, but reflects the reality that referendums are usually more popular in the more populous states, and thus giving an equal say to each state means No campaigns can usually win with less than half of the vote.

In the next post I’m going to look at the history of which states have tended to vote Yes or No more often, how those trends changed throughout the twentieth century, and which groups of states have tended to vote together the most.

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