You were woken up at 2am by officials with vague but horrifying news: there are early reports that China has commenced an invasion of Taiwan.

You spend the next few hours in fog of uncertainty, receiving constant briefings from PM&C, DFAT, Defence and our allies from overseas.

As the fog lifts, it is revealed that the unthinkable has happened: a full-scale invasion is under way.

About 24 hours later, you are still awake as you wait for a phone call with President Joe Biden. Your advisers have told you that the United States is mobilising its forces to defend Taiwan, and President Biden has just one question for you: will Australia contribute forces?

What would you do? It's not much, but here is a framework, a few statistics and some considerations to keep in mind.

The framework is simple: if the benefits outweigh the costs, we should support the United States, and if the costs outweigh the benefits, we shouldn't.

The challenge is knowing what those costs and benefits look like, and this framework lets us start to think about these.

Start with the costs.

The financial cost of war - tiny compared to the human cost - is always huge. Australia's involvement in the war in Afghanistan cost taxpayers about $10 billion.

That works out to be around $500 million for every year we were involved.

But this is the lower bound cost. Adjusted for inflation, the financial cost of Australia's involvement in World War I was around $185 billion in today's dollars. And this is only the direct military cost.

The more important cost of war is, of course, the lives we lose. We tragically lost 41 Australians in our involvement in Afghanistan. In World War I, we lost more than 60,000 Australians.

The reality is that we don't know how many Australians would be killed if Australia was to become involved in a China-Taiwan war. But one thing is certain: many would be.

The question is: how many Australian lives would we be willing to lose?

These costs need to be weighed up against the benefits.

The benefit most commonly argued is democracy: Taiwan is a democracy and we should defend democracies.

This is an admirable argument - much like the argument that we should intervene because it is the moral thing to do - but it is riddled with inconsistencies.

After all, there are lots of democracies in the world that we don't protect from invasion, Ukraine being the most recent, and there are even more countries striving for democracy that we also don't help.

Democracy also exists across a spectrum. Some countries are more democratic than others. Taiwan ranks highly on democratic measures.

But it can be a tough call for others.

Another benefit that is commonly argued is that, if China is permitted to invade another economy in Asia, what's stopping Australia from being next?

This is not a strong argument, and the word "economy" in the preceding sentence is a hint why.

The Australian government never refers to Taiwan as being a country. In forums like APEC, we refer to it as being an economy.

This is because the official position of the Australian government is the one-China policy. We do not recognise Taiwan as a country.

In 1949, after losing control of mainland China in the Chinese Civil War, the then government withdrew to Taiwan. Taiwan and China have deep historical roots.

In short, the relationship between China and Taiwan is very unique.

A Chinese invasion of Taiwan is very different to a Chinese invasion of Indonesia, for example, and suggesting that Australia is next on the list if China is permitted to invade Taiwan is a stretch - putting aside the question of whether China even has the force projection capabilities to successfully invade a country like Australia in the first place.

Another benefit of Australian involvement is that it bolsters the Australia-US alliance.

If Australia was to decline a request from the US to assist it in a conflict over Taiwan, it would be the first time in Australian history that Australia hasn't supported the US in conflict.

It would certainly hurt the relationship. The question is how much and for how long.

The French refused to support the United States in Iraq and copped a beating in America for that decision.

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But as time passed, as politics shifted and the Iraq war became increasingly unpopular, those criticisms were quickly forgotten.

All these benefits of intervening need to be tempered with another critical consideration: will the United States win? It's one thing to sacrifice Australian lives in defence of Taiwan, it's another thing to sacrifice those lives and still lose.

The scenario where the United States loses the war is particularly problematic for Australia for one key reason: we live in Asia.

The Americans, the British, the Canadians and the Europeans can all go back home, far away in the northern hemisphere. Australia cannot.

A cost-benefit analysis is a simple but powerful framework to think about an incredibly complex issue.

It also highlights all the questions that need answers.

But one thing is certain: no matter what the political and economic costs are of diplomacy - no matter how uncomfortable they might make you - they are microscopically small compared to the cost of war.