The voters of the world have had quite a year: They rejected Colombia’s peace deal; split Britain from the European Union; endorsed a Thai Constitution that curtails democracy; and backed the Hungarian government’s plan to restrict refugees, but without the necessary turnout for a valid result.

Each of these moves was determined by a national referendum. Though voters upended their governments’ plans, eroded their own rights and ignited political crises, they all accomplished one thing: demonstrating why many political scientists consider referendums messy and dangerous.

When asked whether referendums were a good idea, Michael Marsh, a political scientist at Trinity College Dublin, said, “The simple answer is almost never.”

“I’ve watched many of these in Ireland, and they really range from the pointless to the dangerous,” he added.

Though such votes are portrayed as popular governance in its purest form, studies have found that they often subvert democracy rather than serve it. They tend to be volatile, turning not just on the merits of the decision but also on unrelated political swings or even, as may have happened in Colombia, on the weather. Voters must make their decisions with relatively little information, forcing them to rely on political messaging — which puts power in the hands of political elites rather than those of voters.

“This is a tool that’s risky, but politicians keep using it because they think that they’ll win,” said Alexandra Cirone, a fellow at the London School of Economics. But often they do not win, and instead of resolving political problems, the referendums create new ones.

Looking over the research on these votes, it becomes clear why many experts are skeptical.

‘Short cuts’ to hard answers

Voters face a problem in any referendum: They need to distill difficult policy choices down to a simple yes or no, and predict the outcome of decisions so complex that even experts might spend years struggling to understand them.

Voters typically solve this problem by finding what the political scientists Arthur Lupia and Mathew D. McCubbins have termed “short cuts.” The voters follow the guidance of trusted authority figures or fit the choice within a familiar narrative.

When a referendum is put forward by the government, people often vote in support if they like the leadership and vote in opposition if they dislike it, according to research by Lawrence LeDuc, a political scientist and professor emeritus at the University of Toronto.

“A vote that is supposed to be about an important public issue ends up instead being about the popularity or unpopularity of a particular party or leader, the record of the government, or some set of issues or events that are not related to the subject of the referendum,” LeDuc wrote in a 2015 paper.

In Colombia, for example, most regions that voted for President Juan Manuel Santos in 2014 also voted for the peace deal, and vice versa.

Voters may also cope with complex issues by shoehorning them into existing ideological beliefs.

This dynamic plays out in virtually every referendum — especially those with higher stakes.

Imposing a narrative

Politicians or other powerful actors will often reframe the referendum into simplistic, straightforward narratives. The result is that votes become less about the actual policy question than about contests between abstract values, or between which narrative voters find more appealing.

In Britain’s debate over whether to leave the European Union, or “Brexit,” neither side emphasized the specifics of membership in the bloc, instead framing the vote as a choice about which values to emphasize. The “Remain” campaign presented membership as a matter of economic stability. The “Leave” campaign emphasized immigration.

It worked. People who voted to remain expressed great concern about the economy, but not much about immigrants. People who voted to leave said they were very concerned about immigration, and less so about the economy.

In Colombia, Santos presented the referendum as a vote on peace, but the opposition presented it as a decision on whether the country’s largest rebel group, the Revolutionary Armed Forces of Colombia, known as the FARC, was entitled to leniency. Neither narrative fully portrayed the question of whether the peace deal would be worthwhile.

Colombia, Cirone said, also highlighted that “in contexts where the referendum addresses a historical political issue, it may be hard for voters to separate past experiences with what is best for the country in the future.”

In Thailand, the military-led government held a referendum in August to approve a new constitution that would entrench its power and curtail elements of democracy. But the military also promised elections only after the constitution passed, in effect selling an anti-democratic document as the pro-elections choice. The measure passed.

Democracy for the powerful

Though presented as putting power in the hands of the people, referendums are often intended to put a stamp of popular legitimacy on something leaders have already decided to do.

“It doesn’t have a lot to do with whether this should be decided by the people,” Cirone said. “It has to do with whether a politician can gain an advantage from putting a question to the people.”

For example, David Cameron, until July the British prime minister, held the vote on whether to depart the European Union expecting that it would bolster his decision to stay in the bloc and would thus silence British politicians who wanted to leave.

The Thai military restricted news coverage of the draft constitution, ensuring that there was no counternarrative that might portray it as a threat to democracy. By giving the appearance of popular input, the military in fact dampened it.

Prime Minister Viktor Orban of Hungary most likely devised his country’s referendum — on whether to reject EU requirements for accepting refugees — to pre-empt inevitable objections in the bloc to his anti-migrant policies and to bolster his political standing at home. In both cases, it was about using the vote as an instrument to strengthen himself.

High-risk, high-reward votes

This stamp of popular legitimacy, though, can sometimes be a good thing, settling contentious national disputes that might otherwise lead to political turmoil or even to armed conflict. But it is precisely because the stakes are so high that the risks are, as well.

Northern Ireland’s Good Friday peace deal in 1998 was followed by two referendums, one in Northern Ireland and one in the Republic of Ireland. That gave communities a sense of having been included, and marginalized anyone who wanted to keep fighting, making a relapse into conflict less likely.

This shows an important way referendums are different from regular elections: They succeed only when the nation perceives the vote as reflecting popular will. That works best if turnout is high and one side wins in a landslide, as happened in Northern Ireland’s 1998 vote.

But in Colombia, turnout was just 38 percent, and the vote was split almost perfectly down the middle, meaning a few thousand people swung the outcome. Even if the referendum had passed, it would have failed to give the peace deal popular legitimacy.

That problem can be solved by requiring high turnout and a landslide victory for a referendum to be binding, Cirone said. But in a puzzling decision, neither Colombia nor Britain required more than 50 percent of the vote for either side to win.

A low-turnout, close result like Colombia’s can risk deepening political disputes rather than bridging them. Leaders have to choose whether to accept a result that does not demonstrably reflect popular will, or reject the result and risk a political backlash or a constitutional crisis.

‘Russian roulette for republics’

National referendums can also be extremely volatile, driven by factors unrelated to the issue’s merits and outside anyone’s control.

Opinion polls are often misleading, because people do not form their opinions until immediately before the vote. Tellingly, they often abandon those views just as quickly.

Marsh of Trinity College Dublin said he had found, in some cases, that “most people can’t remember any arguments for — this is about a week later — they can’t remember any arguments against, and they’re not really quite sure why they voted yes or no.”

He added, “That doesn’t inspire me, really, with referendums.”

The ambient noise of politics can also distort popular will: Whether one party is up or down in the polls, whether intraparty infighting over the vote spills into public, and how the news media portrays related issues all play a role.

Votes are also subject to random factors, including the weather. In Colombia, turnout for the referendum may have been depressed by a hurricane that hit the day before, forcing evacuations in some areas.

“The idea that somehow any decision reached anytime by majority rule is necessarily ‘democratic’ is a perversion of the term,” Kenneth Rogoff, an economics professor at Harvard, wrote after Britain’s vote to leave the European Union.

“This isn’t democracy; it is Russian roulette for republics,” he added.

© 2016 The New York Times Company