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Brexit has put the UK in an impossible position. This Venn diagram explains why.

Zack Beauchamp is a senior correspondent at Vox, where he covers ideology and challenges to democracy, both at home and abroad. Before coming to Vox in 2014, he edited TP Ideas, a section of Think Progress devoted to the ideas shaping our political world.

Despite last month’s Brexit referendum, Britain still hasn’t formally started the process of withdrawing from the European Union. There are lots of reasons, but one of the biggest is that it’s really hard for any British leader to do anything about it without causing a political or economic crisis. The following Venn diagram, from Twitter user Quantian, perfectly explains why.

A bit of background first. In order to withdraw from the EU, Britain needs to invoke Article 50 of the Treaty on European Union. Article 50 notification triggers negotiations with the other 27 EU countries over the terms of UK withdrawal. This includes things like whether the UK will remain in the European single market, called the European Economic Area, and whether it will continue to accept unrestricted immigration from other EU countries.

Now take a look at Quantian’s diagram. What it shows is that there is no possible resolution to the Article 50 negotiations that pleases British voters and the other 27 European countries — without tanking the UK economy:

Quantian's chart points out that there are basically three possible ways the negotiations could turn out — and each has major flaws.

1) "Clean break": In this scenario, the UK just leaves the EU without negotiating any sort of alternative arrangements in place. This option could be disruptive for many EU citizens and businesses, but EU leaders wouldn’t have any way to stop it. And Brexit supporters in the UK would find it acceptable.

The problem: Just quitting would trigger a severe recession in the UK, as the British economy depends on free access to the European common market. Forty-four percent of British exports go to the EU, and the UK financial sector depends on free movement of capital between Britain and Europe. No British leader would knowingly crash the UK economy, so they won’t agree to a "clean break." (There is a chance one could be forced into it, however. If Britain triggers Article 50, a clean break automatically happens in two years absent an exit deal between the UK and EU.)

2) "EEA + deal": In this scenario, the UK negotiates a deal with the EU, which would allow it to remain in the EEA but would exempt it from other EU rules — most notably, free migration rules — that Brexit supporters hate.

The problem: EU leaders seem unlikely to agree to this. They don’t want to reward Britain’s vote with favorable exit terms, for fear that voters in other countries (like Greece, France, or the Netherlands) will take this as a sign that they could get a similar deal. So while this solution would work for British voters and leaders, it’s unacceptable to European leaders.

3) "Annul vote": In this scenario, British leaders call backsies on the referendum results and simply refuse to ever submit Article 50 notification. This would prevent the UK leadership from owning the disastrous economic consequences of Brexit, and European leaders would celebrate it as a step away from the brink.

The problem: "Leave" supporters in the UK would feel betrayed and very, very angry — and even some "Remain" supporters might see it as undemocratic. The political backlash against a UK prime minister who calls "Bracksies" could be immense.

So every option available to the UK leadership right now is either politically unviable or economically disastrous. Nobody in British politics has a good answer to this dilemma, which partially explains why Brexit hasn’t happened yet. It also explains why nobody knows when and how a Brexit will happen down the road — if it ends up happening at all.

Watch: What Brexit means for the pound