Last weekend Australians thought they were voting on who would form government. If Labor or the Coalition had won a clear majority, this would have been a reasonable summary of what the election was about.

But with neither side having gained a majority in their own right, the murky world of government formation under our system of unwritten constitutional conventions has been exposed to the light.

The Australian Constitution provides a framework for government in Australia. However, that framework is bare of flesh on how to deal with the current impasse.

The Constitution was deliberately written to be vague on the process of government formation. The intent was for the written constitution to be a simple framework within which Australia could inherit the unwritten constitutional conventions that applied in the United Kingdom Parliament at Westminster.

The conventions of the 'Westminster' system evolved over several centuries. Where the French and the Americans engaged in revolutions and set down written constitutions, the United Kingdom muddled through with an unwritten constitution built on conventions as the society transformed itself from a feudal to a constitutional monarchy.

At its heart, our constitutional framework see voters elect a representative Parliament from which the 'Crown' in the form of the Governor-General appoints advisers. In the real world these advisers are the Prime Minister and Cabinet, but constitutionally these are advisers appointed by the Crown.

Whether governments are elected or appointed by the Crown hardly matters when either side of politics has a majority. But these conventions pre-date party politics, and in situations such as the current election result, these conventions matter.

So let me run through a few questions about what will happen in coming weeks and how the constitutional conventions apply.

Q: Can we go straight to another election

No. The parliament must meet. The only way we can go straight to another election would be for the parliament to meet and be so deadlocked that no full-time government could be formed.

For instance, an election in Newfoundland in 1908 produced a dead heat. No party could form government without appointing one of their own as Speaker, which would have caused the government to lose its majority in Parliament. It seems extremely unlikely this election will produce such confusion.

The convention that the Parliament must meet was confirmed by the 1989 Tasmanian election.

The Gray Liberal government lost its majority, and in the days that followed, the opposition Labor Party signed a political accord with the cross bench Greens that delivered a majority to Labor.

Gray refused to resign from office and campaigned for an early election, engaging high-priced QCs to produce advice suggesting the Parliament did not have to meet and the state should go straight back to the polls. In the end Gray did not offer this advice to the Governor, the new Parliament met and Gray's government fell on the vote to elect the Speaker.

Q: If the Opposition can produce an agreement with the Independents, does the Gillard government have to resign?

No. The convention that a government resigns before the Parliament sits is a modern convention that came about after the development of political parties. In the nineteenth century, changes of government usually took place when the government was defeated on the floor at the first sitting of the new Parliament.

As of now, Julia Gillard is still Prime Minister and therefore chief adviser to the crown. If the Opposition signed an agreement, it is within the power of Ms Gillard to advise that Tony Abbot be called by the Governor-General to form a government. But in the current circumstances, Ms Gillard is within her rights to advise the Governor General that any agreement by the Opposition be tested on the floor of the House of Representatives to determine who should form government.

There have been recent instances of this in Australia.

After the 1968 South Australian election, the Dunstan Labor government finished with 19 seats, the same as the Liberal Country League opposition, the balance of power held by a conservative independent who backed the Opposition in return for being appointed Speaker. Labor had a clear majority of the vote and refused to resign as premier, forcing the vote to the floor of Parliament where his government was defeated.

As mentioned above, the 1989 Tasmanian election saw Robin Gray's Liberal government lose its majority. Gray stayed on as premier, only resigning after forcing Labor and the Greens to back their accord on the floor of the House of Assembly.

At the 2002 South Australia election, the Labor opposition led by Mike Rann fell one seat short of a majority. In the end Rann coaxed conservative independent Peter Lewis to back his government in return for the Speakership. Liberal premier Rob Kerin declined to resign his commission as premier and forced the agreement between Lewis and Labor to be tested on the floor of the House of Assembly before resigning.

Q: What happens if neither side make an agreement with the cross benches?

In these circumstances, Ms Gillard can continue on as Prime Minister. It would be up to the Opposition to defeat the government in Parliament if it wanted a change of government or to force an early election.

If the Gillard government was constantly defeated on the floor of parliament but the Opposition was not in a position to form government, then the House could be viewed as unworkable. Independent Tony Windsor has talked of needing a new election if no agreement for government can be reached. However, to get an early election, Mr Windsor and his cross bench colleagues would have to engage in deliberate tactics to make the House unworkable.

Q: Would we have an early election if the government fell after a few months?

Not necessarily. If the Gillard government continued on for a few months and lost the support of the cross-benchers, or lost a seat at a by-election, the Prime Minister could request an early election. However, if an alternative government could be formed in the existing House of Representatives, the Governor-General may decline a request for an early election and appoint a new prime minister.

This happened in 1941. The Menzies Coalition government was re-elected in September 1940. It lost its majority but continued in government with the support of cross bench independents. Menzies was replaced as prime minister by Country Party leader Artie Fadden in August 1941. In October 1941 Fadden's government was defeated by the classic no-confidence motion of varying the appropriation bill by one pound. The independents backed Labor's motion and John Curtin became the new prime minister.

The most recent example of a mid-term change of government took place in Queensland in 1996 when the Goss Labor government lost its majority at a by-election in the Townsville seat of Mundingburra. Goss resigned and the Coalition was sworn into office under new premier Rob Borbidge.

Q: Would there be another Senate election?

No. The Constitution does not explicitly state that another half-Senate election cannot be held, but it is implicit in the fixed term of the Senate that the Senators elected last weekend must take their seats in July next year. There cannot be another half-Senate election until after July 2013.

I would also think it is implicit in the Constitution that a double dissolution could not be engineered before July next year. Any deadlock between a government and the Senate should be with the new Senate after July next year, not before.

Anyway, the deadlocked chamber is the House, not the Senate. Any early election will be a House only election, with all the normal election procedures including 33 minimum campaign period.

The last separate House election was in December 1972 when the Whitlam government was elected. Senate and House election had been out of step through the 1960s and a Senate election was not due at the end of 1972.

Q: Could any agreement with the independents fix the term of Parliament.

Yes. The current term could be fixed simply by passing legislation fixing the date of the next House election. The dates of future elections could also be fixed. However, none of these dates could be constitutionally entrenched without a referendum. Legislation fixing an election date could be passed, but it could equally be removed by the passage of repealing legislation.