Interpretations differ as to whether Malcolm Turnbull’s ascension to the Lodge increased the Liberal Party vote in last Saturday’s Canning by-election.

Some Turnbull supporters say the leadership change helped Andrew Hastie win the seat, whereas some backers of former prime minister Tony Abbott maintain that Hastie would have won well in any event. The truth is that we will never know.

Viewing Canning in the focus of the prime ministership has had the unintended consequence that one of the real stories of the campaign has been overlooked: namely, the poor performance of minor parties and independents.

Clive Palmer has been much in the news of late. But, despite the advantage of being at the top of the ticket, the Palmer United Party scored just 3 per cent of the formal vote: a negative swing of 3.8 per cent. Senator David Leyonhjelm has developed a high profile following his victory in the 2013 election in NSW. Yet the Liberal Democrats finished last in Canning; the party achieved significantly less than 1 per cent of the vote. There is widespread agreement among commentators that the Greens’ new leader, Richard Di Natale, has presented his party as more professional and less ideological. Nevertheless, the Greens scored 5.9 per cent of the formal vote, down 1.5 per cent from the 2013 election.

The major parties, however, did well. The Liberal Party obtained 47 per cent of the formal vote (down 4.1 per cent) and Labor 35.6 per cent (up 9 per cent).

Last Sunday, the Prime Minister announced the first Turnbull government, which included Mal Brough as Special Minister for State and Minister for Defence Materiel. Brough lost no opportunity to appear on the media. On Monday evening he first appeared on the ABC’s 7.30 and then he was interviewed by Emma Alberici onLateline. The following morning he could be heard talking to Fran Kelly on RN Breakfast.

Early on, Brough told Alberici the Turnbull government was committed to “consulting broadly, bringing everyone into the tent and all moving forward in the one direction”. All fine-sounding words. Shortly after, the minister foreshadowed the most substantial changes to the Senate voting system in three decades.

It was more of the same when Brough was interviewed by Kelly. The minister declared the Senate electoral system was “being gamed … where you have people of the hard Left … inadvertently having their vote cast in such a way that it elects a hard-right (senator) and vice versa, which is totally against what they actually wished to do”. He did not name the parties concerned. Brough’s comments upset some minor parties and independent senators, most notably Leyonhjelm, Bob Day (Family First, South Australia) and Ricky Muir (Australian Motoring Enthusiast Party, Victoria). There were threats, led by Leyonhjelm, to vote against legislation irrespective of the merits if the Turnbull government went ahead with what Brough was canvassing.

So it came as no surprise when, on Wednesday, the Prime Minister told Sky News’ David Speers that, while he understood the problem with the present system, the government had no specific plans for reform at this stage. Turnbull added that senators such as Muir were “democratically and constitutionally elected” as much as anyone else. Muir won a Senate seat in Victoria with just 0.5 per cent of the primary vote.

Proportional representation in the Senate was introduced by Ben Chifley’s Labor government to take effect from the December 1949 election. The system worked well until 1984, when the number of senators from each state was increased from 10 to 12. This lowered the quota for winning a vacancy from about 17 per cent to about 14 per cent, making it more difficult for a government to win a majority in the upper house. The 1984 changes were introduced by the Hawke government with the support of the National Party.

Both Labor and the Nationals saw political advantage in increasing the number of seats in the House of Representatives and, under the Constitution, this required the increase in the number of senators.

Bob Hawke and his advisers had an additional concern — Labor believed it was losing votes because some of its supporters were finding it increasingly difficult to number all the voting boxes on an ever increasing Senate ballot paper and, consequently, voting informal.

So Labor introduced “above-the-line” voting for the Senate whereby an elector could put the number “1” alongside the name of their preferred party, and preferences would be allocated according to the wishes of the party organisation. In recent years, led by political activist Glenn Druery, independents and micro-parties learned that by carefully swapping the preferences of above-the-line electors, it was possible for a candidate to win a Senate seat with a minuscule or low vote. Hence Muir in 2013.

The report in May last year by the Joint Standing Committee on Electoral Matters, chaired by Liberal MP (now Speaker) Tony Smith, made sensible recommendations whereby there would be an optional preference system for “above-the-line” voters or an elector could vote for a minimum of six candidates under the line. As a result, voters, not party machines, could decide preferences without having to fill out all the squares on a large ballot paper. This proposal is resisted by most independents and micro-parties, but not by the Greens or senator Nick Xenophon, who enjoys considerable support in South Australia. Labor is divided on this issue and the Liberal Party is broadly in favour.

An additional factor turns on Leyonhjelm’s attempt to prevent the Liberal Party successfully stopping his party calling itself the Liberal Democrats. It’s clear that some intending Liberal Party voters were confused in 2013 by having two parties with the first name Liberal on the ballot paper. This matter is before the Administrative Appeals Tribunal, much to Leyonhjelm’s annoyance.

Brough spoke too soon and without judgment. It makes sense to bring about electoral reform shortly before an election, but not earlier. In the meantime, it’s worth remembering that, despite a frequently hostile Senate, the Abbott government attained sufficient support in the upper house to junk the carbon and mining taxes, increase the asset test limits for full pensioners and restore fuel indexation.