What’s in a name? Well, like “Montague” and “Capulet” in Shakespeare’s play, names matter quite a lot in the tribal world of Australian climate politics. The notion of a “carbon tax” has struck a raw nerve in the Australian public. It will be the rallying cry for the Opposition all the way to the next election.

But as Prime Minister Julia Gillard and Leader of the Opposition Tony Abbott slug it out, we shouldn’t forget the international politics of climate change. International developments suggest Australia will need far-reaching climate policies no matter which party forms government in the next decade.

What remains of the Australian climate debate has descended into a desperate struggle for government between Labor and the Coalition. Abbott won the opening round in this fight by successfully framing Labor’s policy as a “carbon tax”.

This is how almost everyone talks about it today, even the Prime Minister, who promised she wouldn’t introduce one. The Government made a serious mistake when it allowed its carbon price to be painted as a “great big new tax on everything”. This simple rhetorical act now reminds everyone of Gillard’s “lie” whenever climate change enters the conversation.

But it should be remembered that international developments can have dramatic effects on Australian climate politics. Labor’s dire position can in large part be attributed to the perceived lack of progress in the international climate change negotiations. Kevin Rudd never really recovered from Copenhagen and its failure to produce binding post-Kyoto targets. The Australian public were largely with him on the carbon price until then.

The problem for democratic governments is that climate change politics is a two-level game. Leaders must simultaneously negotiate with domestic and international constituencies in order to produce climate change policies.

At the domestic level, the game involves listening to the concerns of the citizens and interest groups, assuaging their fears (often through compensation) and generally convincing them to support climate action. At the international level, the game involves crafting effective agreements that meet the needs of other countries but do not hurt groups at home.

This creates enormous political difficulties for democratic governments. Labor’s strategy thus far has been to tell the Australian public it is not leading the world, while at the same time trying to demonstrate to the world that it is leading.

This apparent contradiction arises because the Government must calm domestic fears that Australia is making itself economically uncompetitive by doing more than other countries, while also providing the leadership expected of rich countries given their historical responsibility for the problem and their superior capacity to fix it. The principle that rich countries like Australia should lead is enshrined in the UN Framework Convention on Climate Change (UNFCCC) and is a key demand of developing countries.

Abbott will inherit this two-level game if he becomes the next Prime Minister. So far the Coalition hasn’t worried too much about the international context. This was understandable when the negotiations seemed dead. But since 2010, at least 89 countries have made non-binding pledges to limit GHG emissions, including China and India. Some commentators point out that non-binding targets are meaningless. But in December all countries agreed in Durban to be part of a legally binding treaty by 2015. Existing pledges will presumably be used as the basis of this global agreement.

This means that a future Abbott Government will have to negotiate a legally binding reduction to Australia’s carbon emissions in its first term. It might choose to play hardball and let the burden fall on other countries. This would put Australia in breach of its responsibilities under the UNFCCC. Australia would also be free-riding on the cuts of other countries, which is fundamentally unjust for a rich country and will damage our diplomatic relationships, particularly with the developing world. Australia would then be isolated in global climate change negotiations.

It is more likely that Abbott will be forced to do something. The Coalition has made a bipartisan commitment to a 5% reduction by 2020, rising to 15% or 25% if other countries act. If Abbott sticks with these targets, his $3.2bn direct action plan won’t do the trick. A larger and more comprehensive policy will be required for cuts of 15% or 25%.

At that point, the Coalition will be drawn to the most cost-effective policy option: a carbon price. Abbott might then have to sell a policy to the Australian public that he vehemently contested in opposition. To be successful, he will need to be a better salesman than Gillard. So you can be sure he won’t be calling it a “carbon tax”. But that which we call a carbon tax by any other name will still be a necessary feat.