Menzies took Australia to another election for the House of Representatives less than 24 months after the 1961 one. A new judgment by the Australian people was necessary because the country stood at a crossroads. There was conflict in Asia, and fear about what Indonesia, in the process of consolidating its invasion of Dutch New Guinea, might do. He had ordered aircraft that could, if needs be, bomb Jakarta from Darwin. Meanwhile, Labor was publicly shilly-shallying on the US alliance over the North West Cape, was still opposed to state aid for Catholic schools, and was under the malign influence of the 36 faceless men. The assassination, early in the campaign, of US President John Kennedy, served to illustrate the new and uncertain world in which we lived. Menzies romped home.

His success came with a cost, or a benefit. By going so early to the polls for the House of Representatives, Menzies deprived himself of the possibility of having a simultaneous half-Senate election. Under Section 13 of the constitution, one can call a half-Senate election only within a year before their places in the Senate became vacant, which was June 30,1965. Sometime between 1964 and 1966 (or early 1967) Menzies would have to hold an election for half the Senate without having a simultaneous House of Representatives election.

The two houses of Parliament were running on terms that were out of sync. They stayed that way until 1970. There were House of Representatives elections in 1966, 1969 and 1972. And there were separate half-Senate elections in 1964, 1967 and 1970. They came back into sync only in 1972.

Then a law student, I got a job in the national tally room at the 1970 election. It was our last single house election.

On a number of occasions since, prime ministers have asked governors-general to be allowed to have early House of Representatives elections on the ground that this was necessary to get the terms of the two houses in sync. (They tend to get out of sync if the election is held in the first part of the year.)

It is conventional wisdom that Australians hate frequent elections, and resent politicians who drag them too early and too often to the polls. In most other countries, voters might not care so much, since they can, if they want, simply not bother to vote.

Here we must at least show up to the polling booth, and not only for federal elections, but for state elections and, in some states – such as NSW – for local government elections as well. Commonwealth law, though not the constitution, forbids simultaneous elections at different levels of government, apparently lest voters get confused. (By contrast, in the US, the first Tuesday in November every two years sees federal, state, county and municipality elections, and politicians have no capacity to manipulate election dates.)

Conventional wisdom, but is it right? Or always right? At any one time, one might imagine, at least 40 per cent of the electorate is dying to throw out the current lot, and to install their own favourites, presently languishing in opposition. On many occasions, moreover, issues troubling voters, not necessarily on a party-political divide, are agitating an additional number of voters. It might be same-sex marriage, abortion, perhaps Asian immigration. While many businesses deplore the slowdown caused by political uncertainty, some voters revel in being suddenly relevant, and being wooed by politicians. Increasingly, moreover, even minor political parties use the occasion to refill their coffers with public cash based on how many votes they secure.

In the last decade of out-of-sync elections, ending in 1970, the coalition governments of the day effectively had the numbers in the Senate, albeit after renting the general support of the Democratic Labour Party, created from 1950s Labor schism. It is true that towards the decade's end, Labor had devised some strategies for winning DLP support on a range of matters, in the process establishing the modern Senate committee system which gave the Senate a new rationale as a house of review. But there was hardly ever a time that government had to worry much about signature legislation, or significant budget measures (though there was one, on postal charges in 1970, that came to embarrass Gough Whitlam's claim that Labor had never blocked revenue measures in the Senate). The argument for keeping elections in sync was a practical one, not a solution to a political problem.

Since the election of the Hawke government in 1983, however, governments have had the effective numbers in both houses in only one of 11 (simultaneously elected) Parliaments. Getting legislation, and budgets through the Senate has had to involve negotiation with, compromise with, and often frustration from crossbenchers including diverse, sometimes mad, independents, Australian Democrats, the Nuclear Disarmament Party, Greens, Clive Palmer party, Pauline Hanson One Nation and the Nick Xenophon team.

Strictly, neither Labor nor the coalition has (since 1975) blocked supply, but each has worked with others to destroy government plans for revenue changes or expenditure cuts.

It seems most unlikely that a government will have a majority in the Senate for at least a decade. Parties may come and go, as, say, the Nuclear Disarmament Party, the Australian Democrats and the Clive Palmer party have done. But a significant sector of the electorate is now accustomed to giving a first preference to some group or groups ahead of Labor, Liberal or National candidates. And the Senate voting system makes majority control almost impossible; one needs 58 per cent of the vote to gain four out of the six seats up for election in any state at a half Senate election.

The current Tony Abbott personal relevance campaign is making much of the bastardry of current Senates, and calling for a constitutional change whereby measures rejected by the Senate twice in three months could be put to a joint sitting of the houses without the need for a double dissolution.

Abbott told the Institute of Public Affairs that "the Senate has become a house of rejection, not a house of review" in the middle of some general mischief-making last week.

"The problem is far worse now, with Labor habitually reversing its own previous positions in order to oppose the government on everything except national security.

"To pass legislation, either the government has to strike a deal with the Greens, a far left party dedicated to higher spending and higher taxes; or it must corral 10 of 12 unpredictable crossbenchers, all of whom will demand their price.

"The only legislation that can expect swift passage is to spend more, to regulate more, and to put more tax on the so-called rich … All that can readily be passed is legislation that a grab bag of political competitors can be bought off to support.

"But this is a recipe for gridlock, not government, and it must end if Australia is to be capable of meeting the challenges of the future."

He knows perfectly well that there will be no referendum, and that if there were one, it would fail.

That's partly because of his own perfidy with election promises in 2013. Because he was (though he refused to concede it) going directly against explicit promises made about health and education spending during the election campaign, it was the Senate which looked reasonable in frustrating his 2014 budget. That Turnbull has been more willing to negotiate – even to gut legislation simply so he can get something on the statute books – has emphasised, whether to lobbyists or voters, that the crossbench has power, and sets of agendas, often ones with significant support. Unlike parties aspiring to be in actual government, crossbench parties have only to worry about a quota – 14 per cent of the vote, usually reachable if they can get half of that on first preferences.

Compounding governing party frustrations is that Senate election campaigns tend to be swamped by the noise of representatives campaigns. Election coverage tends to focus on which party will win government in the House of Representatives. Time, money and political energy spent campaigning against Senate parties or on Senate issues is at the expense of carrying the attack directly to the main enemy.

Many voters have become tactical, focusing on the party they want to govern in the House of Representatives, being somewhat more inclined to buy insurance through crossbench senators.

But what if the election were for the Senate alone? Would such an election put much more focus on the Senate groupings, and create more consciousness of the positions of particular crossbench parties and independents? Could it allow more room for debate about the particular records of senators, and put some of them in a spot about their consistency, responsibility, or contribution to a government's fiscal problems?

Could it, indeed, create a different type of agenda for Senate campaigns, in a manner that restored emphasis to the role of senators in the committee system, the review of legislation, and the actual political agendas of members of the crossbench, rather than their capacity to hold a government to ransom? As things stand, Turnbull could not do worse with his Senate results if he went for a single-house election, but he could do better.

But there would be a downside. It would be more expensive, probably $150 million or so a term of Parliament. But that could be small change compared with some of the sums that crossbench groupings have been able to extort as part of their bargain for letting legislation through.

It would submit the population to the bore of an extra election. If minor parties and independents refined their pitch, and took advantage of the extra attention, it might, in fact, increase the protest vote, or the taking of "insurance" against the government of the day.

It might increase the development of parties with a bit of a focus on the interests of a particular state, such as the Nick Xenophon team, with the implications that could have for unfair subsidy to particular areas.

Personally, I think that the potential of getting a more workable Senate, albeit still one with a significant proportion of crossbench senators exercising a balance of power, could be worth the risk. Particularly from the Coalition's point of view, the chance of getting a more businesslike, or a more "responsible" Senate has to be compared not only with the present frustrations, but the virtual certainty that without some change, Senates for the next few Parliaments are likely to be much the same, and with a mild bias towards Labor's capacity to form a majority.

Turnbull cannot get a single house election by accident. He must engineer the circumstances, probably with a representatives election before next July, that creates the out-of-sync "problem". He would have to persuade the governor-general that an early election was necessary. By tradition, governors-general have been sympathetic to requests for early elections so that the houses can get back into sync, but so as to create an out-of-sync situation? I doubt a governor-general would agree that this could justify going early.

But were there a crisis – say in North Korea, or with China trade, or perhaps an artificial one around immigration, national security or power policy, a buttered-up governor-general might agree to an election to "clear the air", or settle the direction Australia should go.

There is, of course, the risk (as things stand, the probability) of defeat and a change of government. The consolation could be the "need" – if the Labor government wanted to get things back into sync – of its having to go early in its turn. In such situations, re-election is not automatic, as Bob Hawke discovered in 1984. The early polls suggested he would romp home. But a long and lacklustre Labor campaign and a better than expected performance by Andrew Peacock made the election a close-run thing.

Turnbull was this week declaring that he had a long game for staying prime minister. He'd better have, given that his political judgment is woeful, as demonstrated by his disastrous call of the double dissolution last year. No one is much talking – yet – of a set of single house elections, but it could be his best chance. That's one of the reasons that the potential parties of government are on more of a war footing than usual, that there is more babble about the need for appearances of unity, and that Labor is especially cautious about being lured into some tactical trap.