Referendums can be wonderful things. They can help to strengthen democracy, empower voters on important matters, and confer legitimacy upon decisions already taken by politicians. If you want to know what the voters think, then what could be more democratic than simply asking them?

The trouble is, sometimes they can go badly wrong. Sometimes they don’t just tell us what ‘the people’ think, but only what an ‘energised few’ thinks. If very few people vote, it becomes highly doubtful that the result bears any claim to be representative of the broader public.

That concern should give you an early clue about this article: it is not about Brexit. In June’s referendum, 72% of voters participated in the vote. Say what you like about the Brexit result, and say what you like about the campaign preceding it, but you can’t attack its legitimacy on grounds of turnout. More people voted on 23 June than in any general election in the UK since 1992. In the last 24 hours, however, we have witnessed two very different referendum outcomes.

Colombia’s rejection of a peace deal with Farc came as a big shock, if not to Colombia’s political leaders, then certainly to the international community. By a razor-thin margin of 0.5%, voters yesterday judged the deal too steep a price for peace. A preliminary look at the results suggests that it was people living in the regions most affected by decades-long violence who were most likely to back a deal. By contrast, those living in parts of the country that were more insulated from conflict were more likely to reject it. The future of the peace deal and, indeed, peace itself, is at risk.

Closer to home, voters in Hungary last night rejected the EU’s migrant quota plan. Having been accused of weakness and inaction in the face of the migrant crisis, the EU’s quota plan was designed to provide the leadership, coordination and solidarity that critics had accused the organisation of lacking. It was supposed to help take pressure off the pinch points of entry in Greece and Italy. But at a time when the EU remains under immense pressure, and when the migrant crisis shows no immediate signs of resolution, Hungary’s vote makes a coordinated response at the EU-level much, much more difficult.

Both sets of results have very different consequences. The result in Hungary is arguably just another punctuation mark in the fraught story of the EU’s response to crisis. The result in Colombia, meanwhile, has much more profound consequences for its own future. Both sets of results, however, share a fundamental problem: they both have weak claims of legitimacy.

In Hungary, 98% of those who participated in the referendum voted in line with the government’s recommendation: to reject the EU’s quota plan. But Hungarians were deeply divided about the controversial issue, and more than half of those eligible to vote opted to stay at home. Knowing that a valid result required a turnout threshold of 50%, many of those who supported the quota ban decided to boycott the poll – precisely to reduce the legitimacy of the outcome. In Colombia, it is remarkable that on such an important question only 37% of those eligible to vote cast a ballot. While many Colombians will undoubtedly want to see the back of a guerilla conflict lasting over half-a-century, perhaps not enough were prepared to take the next step of actively backing a deal that, by definition, required compromise.

Therein lies the real challenge of referendums. They are blunt instruments that require voters to come firmly down on one side over the other. There is no room for nuance. At the same time, however, governments sometimes need to make sure they have (most of) the public on board. If Colombia didn’t hold a referendum, perhaps its peace deal would have been more vulnerable in the long-term from popular backlash. Far more disagreeable in its motives, the Hungarian government opted for easy life by appealing to populism in the short-term over playing its part in long-term collective leadership.

Wherever both countries now head, their respective governments will need to understand not simply what the voters told them in yesterday’s referendum results. They face the much harder task of working out what the majorities of voters who didn’t cast a ballot were telling them.