The ironclad rule of numbers in politics was particularly brutal for the Liberal Party recently. If the Liberals had managed to hold the blue-ribbon seat of Wentworth by even one vote, they would have held their one-seat majority in the House of Representatives. Instead, the Liberals came a gutser (independent candidate Kerryn Phelps was about 1700 votes ahead of the Liberals in Wentworth at last count, an almost 20 per cent swing away from the Liberals).

Prime Minister Scott Morrison will now need to convince one of six crossbenchers each and every time he wishes to pass legislation through the lower house. Ironically, this could be the best thing to happen to the Morrison government.

Majority government is more orderly, certainly, but democracy requires a certain relish for the unpredictable. Being forced to negotiate with other political parties and the crossbench can force commonsense amendments that blunt the sharp edges of hardline policies. It can force governments to pay attention to issues they might prefer to ignore.

Governments generally prefer to have a majority in both houses of Parliament, so they can pass laws without needing to negotiate with other political parties. But having absolute power like this can often prove a curse, as John Howard discovered when he used his majority in both houses to pass the Work Choices laws and a host of other measures that were massively unpopular with the electorate. Needing to negotiate outcomes can save governments from their own worst instincts. And let's face it, the Liberal Party's recent instincts have proven about as popular as a fart under the doona.

The good burghers of Wentworth (once a blue-ribbon Liberal seat, now dismissed by some commentators as not comprising "typical" voters representative of the Liberal base, which must be a shock to the residents of not only Wentworth but Warringah, Kooyong, Higgins and North Sydney, too) sent a clear message to the Morrison government that they want action on climate change, refugees and integrity. These happen to be issues that several crossbenchers and their electorates care about. Whether he likes it or not, climate change, refugees and integrity are about to become big issues for the Prime Minister.

Let's take integrity first. Integrity is not a word associated often with politics, and our trust in federal politicians is at an all-time low. That's not good for democracy.

In January, Opposition Leader Bill Shorten announced that Labor would legislate for a national integrity commission within 12 months of winning office and offered to work with the Coalition government to implement a watchdog with teeth. The government did not take up the offer.

After the Wentworth by-election, several members of the crossbench, including Greens, announced their intention to pursue a federal anti-corruption watchdog. Attorney-General Christian Porter indicated he's willing to talk about options. It's amazing how needing one extra vote can make a difference, isn't it?

When Shorten announced his policy, he acknowledged voters were disaffected with politics and wanted to clean up the system: "The most corrosive sentiment in democracies around the world is the idea that politicians are only in it for themselves. This is not about partisanship, this is about trust."

That disaffection is no doubt part of what's driving voters away from major parties and towards minor parties and independents, such as Kerryn Phelps, Rebekha Sharkie and Andrew Wilkie. Australia Institute polling shows 63 per cent of voters say a national independent commission against corruption would increase public trust in Parliament, which is an important reason why our politicians should back a watchdog with teeth – it's in their own long-term interests.

The Australia Institute's national integrity committee, made up of corruption fighters and former judges, have designed a benchmark for a national body, based on best practices from effective state anti-corruption bodies. The design principles include the need for an independent and well-resourced agency, with a broad jurisdiction and the strong investigative powers of a royal commission. The ability to hold public hearings is particularly important because corruption flourishes amid secrecy.

The only outcome worse than failing to establish a national anti-corruption body would be to create a poorly designed body with insufficient powers and no ability to hold public hearings.

Though the rule of numbers is ironclad for politics, it nothing compared to the numbers for climate change, which was the No.1 issue for Wentworth voters.

It's pretty straightforward. The mining and burning of coal, oil and gas produces greenhouse gases, which trap heat in the atmosphere, slowly cooking the planet. This isn't a matter of belief but the rule of thermodynamics.

The Intergovernmental Panel on Climate Change released a report recently that said the world must stop burning coal by 2050, sooner if possible, if we are to avoid catastrophic climate change. The Deputy Prime Minister, Michael McCormack, dismissed the dire warning as merely "some sort of report".

The fact is that Australia must phase out the mining and burning of coal, oil and gas as soon as possible. Unless we plan the transition away from coal, as the CFMEU recently noted, "workers who depend on the coal-fired power industry face a bleak and uncertain future" – including the miners.

The Adani coal mine is a perfect example of this lack of planning. Jonathan van Rooyen, the co-owner of the Port of Newcastle – one of the world's largest coal terminals – said recently: "There is no avoiding the simple mathematics that if [the Coalition] succeeds in pushing between 25 million and 60 million tonnes of subsidised new coal into a flat world market, the volume of coal mined and exported from the Hunter and Illawarra will decline. As will royalties collected by the NSW government and the number of coal jobs in the Hunter and Illawarra."

We can't stop global warming by mining and burning coal. It's science.

Building new "clean" coal-fired power is the most expensive form of new energy on the market. The Morrison government says it cares about reducing electricity prices but, publicly, many Coalition members are backing the most expensive solution while ignoring far cheaper solutions such as demand response – where energy consumers are paid to reduce or delay their electricity use and sell that conservation into the market.

Luckily, the numbers for renewable energy and storage are getting better by the day. Renewable energy is cheaper to build than ever, and prices have dropped further and faster than most people anticipated, putting downwards pressure on prices.

Politics is a numbers game. But in refusing to learn the lessons from its brutal loss in Wentworth, the government is failing to read both the numbers and the writing on the wall.

No political party has a monopoly on good ideas. The government would be wise to heed that lesson as it deals with the crossbench in coming months.

Ebony Bennett is deputy director of The Australia Institute. Twitter: @ebony_bennett