Last year, Britain voted to leave the European Union under a banner of anti-immigration and protectionism. Since then, both social democrats and classical liberals have been waiting to catch a break. Ever the optimist, I hope they may have just got one, from an unlikely source, the Democratic Unionist Party. They are a Northern Ireland-based Protestant party that is usually at the margins of national British politics. Thanks to the outcome of the latest general election, they may be in a position to force the British Conservatives towards a more trade and immigration friendly Brexit.

In April, Prime Minister (for now) Theresa May called a snap election. She didn’t need to face the electorate until 2020, but decided to gamble, thinking that she would increase her working majority of Conservative MPs. Instead, as we discovered yesterday after the polls closed, she did the opposite, reducing the slim majority that David Cameron won in 2015 to a mere plurality. This was against one of the most radically left-wing opponents in decades, Jeremy Corbyn.

This was a dismal failure for the Conservatives but the result is a relatively good sign for liberals. I feared that Theresa May’s conservative-tinged anti-market, anti-human rights, authoritarian corporatism was exactly what centrist voters would prefer. It turns that Cameron’s more liberal conservativism actually won more seats. Not only is an outward-looking liberalism correct, de-emphasizing it turns out not be a popular move after all.

Without a majority, the Conservatives need to form a coalition or come to an informal agreement with another party. This seems likely impossible with Labour, the Scottish Nationalists or the Liberal Democrats who have all campaigned heavily against the Conservatives and disagree on key issues, such as whether Britain should leave the European Union at all. This leaves the DUP.

In terms of ideology, the DUP is far to the right of most British Conservatives. Their opposition to gay marriage, abortion, and occasional support for teaching creationism, means that they have more in common with some Republican Christian groups in the United States than the secular mainstream in the rest of the United Kingdom. Historically, at least, they have links with pro-unionist paramilitaries that have terrorized Irish Catholic separatists.

There is, however, one way in which the DUP are comparatively moderate. While content with the UK leaving the European Union, they want to keep the land border between Northern Ireland and the Republic of Ireland (an EU member) open. Closing it would reduce critical cross-border trade with an economically dynamic neighbor and re-ignite violent tensions between the Protestant and Catholic communities in Northern Ireland.

How could this be achieved? Leaving the EU while keeping a relatively open trading and immigration relationship is similar to the so-called Norway Option. Norway is within the single market but can exempt itself from many parts of EU law. In return, it has no direct representation in EU institutions. If the EU could accept such an arrangement, then the DUP may be able to make Conservatives commit to it.

Of course, the DUP will extract other perks from their major partners as part of any deal. But their social policy preferences are so far to the right of people in England, Wales and Scotland that this will hopefully have to take the form of fiscal subsidies to their home region (economically damaging but could at least avoid infringing civil liberties).

It might seem paradoxical that an extreme party may have a moderating influence on overall policy. However, social choice theory suggests that democratic processes do not aggregate voter, or legislator, preferences in a straightforward way. Because preferences exist along multiple dimensions, they are neither additive nor linear. This can produce perverse and chaotic outcomes, but it can also generate valuable bargains between otherwise opposed parties. In this case, one right-wing party produces an authoritarian Brexit. But two right-wing parties could equal a more liberal outcome.

That’s the theory. Has something like this ever happened in practice? Arguably, Canada is an outstanding example of how a minority party with many internally illiberal policy preferences produces liberal outcomes (see the fascinating Vaubel, 2009, p.25 for the argument). There, the need to placate the separatist movement in Quebec involved leaving more powers to the provinces in general, thus keeping Canada as a whole much more decentralized than Anglo-Canadian preferences alone could have assured. Will the DUP do the same for Britain? We can but hope.