Does Losing Mid-Term Referendums Help Australian Governments To Win The Next Election?

Short answer: there is no evidence it does.  

During the Voice referendum campaign a common view has emerged that a success for the No campaign will be bad news for the federal Opposition and its leader Peter Dutton for the next federal election.  The theory is that the Coalition's opposition to the Voice is already tying it to some strident political positions and that it will wear the blame for the defeat.  An example of this was a recent George Megalogenis article that initially claimed there was no precedent for an opposition leader taking down a referendum and winning the next election or the one after (which was edited after I and perhaps others pointed out Menzies winning in 1949 after defeating the Rents and Prices referendum in 1948).   Similar themes have also been present in the commentary of Professor Matt Qvortrup (who has incidentally long predicted that the Voice would lose, albeit recently with what looks like an optimistic Yes vote of 48 +/- 2.5%). Prof Qvortrup, who has great experience with overseas referendums, may well have evidence that referendum-defeat boost is a big trend overseas, though at a quick look I did not find any study to this effect.  

So, is there anything in this for Australia?  The paradigm case is supposed to be the 1951 defeat of the Communist Party ban referendum, in which Labor won the battle but lost the war: things said on the referendum trail made it easy for Prime Minister Menzies to tie them to Communism for many years after.  This narrative, however, seems simplistic to me, because the Opposition Leader (Evatt) not only said and did things on the referendum trail that made it easy to tie Labor to communism for campaigning purposes, but kept saying and doing such things forever after.

The following is a table of cases where Australian mid-term referendums supported by the Government have been defeated.  The columns are as follows:

* (Bipartisan?) indicates whether a referendum had federal bipartisan support based on Peter Brent's assessments here.  I have thrown in an asterisk for two cases where there was some significant opposition to the referendum within the opposition side, either at federal level or at state level.  

* Opp Change indicates whether the leader of the Opposition changed between the referendum and the next election.

* Mitigated indicates whether the defeat was mitigated by the Government winning another referendum on the same day.  (I have given a ? for Preamble 1999 because the Republic referendum on the same day was a win for the Prime Minister's side)

* Result is the result for the government at the next election and Swing is the 2PP swing for the government at the next election.  (I have estimated 2PPs for first past the post elections in the 1910s by simply splitting the independent vote 50-50.)

For 1999, having opposed earlier versions of the preamble, Labor made a tactical decision not to oppose the final preamble on the campaign trail in order to avoid damaging the Republic vote.   I have not included the Republic question because the Government agreed to hold it but didn't actually support a Yes vote, although some members did.  

Superficially, the table above looks good for the case that losing referendums helps governments get re-elected.  9 out of the 11 incumbent governments that lost referendums have been re-elected.   However for three of the wins there was not a consistent Opposition position against the referendum, dropping the strike rate to six out of eight (and one of the six was mitigated).  

Still pretty good, right?  Well not really, because Governments usually win elections in Australia anyway.  Since the appearance of the two-party system at the 1910 election, governments have been re-elected 28 times and defeated eight times, so a win rate of around three-quarters actually isn't special.  

We can also look at the swings.  Every government that has lost a referendum mid-term has had a two-party swing against it at the next election, except for the Howard Government's loss of the preamble.  The preamble requires multiple asterisks and arguably should be excluded, because of the fate of the Republic on the same day, and the argument that the preamble question was actually a deliberate distraction to wreck the Republic vote.  But even ignoring that, nobody in their right mind would assert that the 2% swing to the Howard Government at the 2001 election had anything much to do with losing or even holding the preamble vote, quickly viewed as a sideshow and a curiosity despite the fact that it included symbolic Indigenous recognition.  

On average for the cases where the government has lost a referendum that clearly lacked bipartisan support, the 2PP swing against the government at the next election was 3.27% (though this drops to 2.72% if the mitigated 1967 example is removed).  For all federal elections the average is only 1.86%.  In average governments that have lost contested mid-term referendums have done worse, not better, in swing terms at the next election!  And the referendum-losers haven't done that well in two-party preferred terms either - an average of 50.6% with five of them losing the (often estimated) 2PP.  Only Chifley in 1946 followed a mid-term referendum loss with a win of any great substance.  

I would not say that this means that governments that lose contested mid-term referendums tend to do worse than other governments as a result of losing those referendums.  I doubt that's true.  The sample size is much too small, and in any case there could be many other things going on.  Governments may be more likely to try referendums when they think they have political capital to burn or a higher chance of using their popularity to carry them (both of which mean more votes to lose at the next election).  Oppositions may be more likely to oppose referendums when they think the government is travelling badly anyway, and so on. 

The next question is that of individual leaders.  There's a strong recency bias here because the last Opposition Leader to defeat a referendum (four of them on one day in fact) was removed before the next election (John Howard to Andrew Peacock) but ultimately it's not surprising that there is only one case of an Opposition Leader defeating a referendum then surviving to and then winning the next election.  This is to be expected based on the scarcity of mid-term referendums, the fact that Oppositions usually lose anyway, and the fact that Oppositions fairly often change their leaders whether there has been a mid-term referendum or not.  In the other case where an Opposition won a mid-term referendum then defeated the incumbent Government in the same term (1911 referendums, 1913 election) the Opposition Leadership change was caused by health issues.  

One can of course argue all kinds of overfitted referendum/leader/election combinations in order to claim that there would be no precedent for Peter Dutton winning the referendum then leading his party to government in 2025 (Menzies had already been PM once, for example, Menzies wasn't up against a first term government) but it very quickly gets a lot like this.

Perhaps it will yet be the case that the unusual and charged nature of the Voice campaign leads to Peter Dutton wearing the win in a way that damages or destroys his future prospects.  It's not hard to think of ways that that might come about - an embarrassingly racist slip on the campaign trail,  or evidence of networking with extremists, for example.  But there is nothing systematic in the past history of Australian referendums that even hints that it will.  Australian governments that lose contested referendums will usually win the next election because Australian governments will usually win the next election anyway.