Theresa May, U.K. home secretary, during a news conference in Birmingham, U.K., on July 11. (Jason Alden/Bloomberg)

Referendums might be the closest we can get to a pure democracy, giving the voting public a direct say in how their country is governed. But they can also present problems when they butt up against the more established representative democracy found often in the Western world.

This can be seen right now in what is going on in Britain. A referendum on leaving the European Union was conducted last month. It gave a divisive but clear result: Britain had voted for Brexit. But now the knock-on effect of that vote is that the country is having a new prime minister put in place with little to no democratic say from the vast majority of the country's eligible voters.

And to rub salt in the wound, that new prime minister actually campaigned against a potential Brexit.

The topsy-turvy immediate political outcome of the Brexit vote has left many in the country gnashing their teeth. Their once-widely repeated British criticisms of the electoral system in the United States — in particular the long, confusing path to choosing a party's nominee (case in point: 2016) — suddenly look hollow when compared to the bizarre and strikingly undemocratic leadership contest that just occurred in their own country.

Of course, it all goes back to David Cameron. The British prime minister, fearing he wouldn't win reelection in 2015, had attempted to appeal to Britain's Eurosceptics by promising a referendum on the E.U. When Cameron ended up winning the general election comfortably, it bolstered his sense that he could win the vote to stay in the E.U., too. He could not. After a "remain" campaign that was widely criticized as lackluster, the "leave" vote triumphed.

The day the results were announced, Cameron told the British public that he would step down. In Britain, there are no regulated lines of succession for when a prime minister steps down — there is not an equivalent of an American vice president to move seamlessly into the role. This is in large part due to the different nature of government in the two countries. In Britain, the prime minister is the head of government rather than the head of state; their standing rests on their ability to command the support of a majority in Parliament rather than direct election.

This meant that the Conservative Party, of which Cameron was the leader, would need to have an internal leadership contest to determine who should lead the party in Parliament. By extension, that person would then lead the country.

That process contained a number of different stages. First, names would be nominated for the position. Then, assuming there were more than two candidates, Conservative MPs would hold a ballot among themselves. There would be a number of rounds of voting, with each candidate with the least amount of votes eliminated until there were only two remaining. These two candidates would then be put to a vote of the Conservative Party's general membership, who would vote on their new leader in September.

The end result of that process may have left many wanting in terms of democracy. Britain has more than 46 million registered voters out of a total population of 64 million. The total membership of the Conservative Party is around 150,000, and there are rules in place to stop new members from being eligible to vote in leadership contests. In theory at least, Britain's future would be decided by about 0.23 percent of the total population.

In practice, things may be worse than that.

The fun started before the leadership contest even began, with leading Brexit campaigner Michael Gove suddenly deciding to enter the race, prompting Boris Johnson, another high-profile Brexiteer and a favorite to win the contest, to preemptively drop out, apparently fearing the "leave" vote would be split. In the first round of voting there were five candidates. One was then eliminated and another dropped out. In the second round of voting, Gove came last and was eliminated. This left two female candidates, the well-established favorite Theresa May and the dark horse Andrea Leadsom, to be put toward the party membership for a vote in September. Britain geared up for a summer of more political campaigning.

On Monday, however, we discovered that that vote wouldn't happen. Leadsom, the country's energy minister and a vocal supporter of Brexit, announced that she, too, was dropping out of the race. Her decision came after widespread criticism of her comments about May's lack of children (May, Britain's home secretary since 2010 and a "remain" supporter, has said that she was unable to have children with her longtime husband because of health reasons). May became the only candidate to lead the country. Cameron has now announced that he will resign by Wednesday, paving the way for May to take office.

May isn't unelected, per se. Since 1997, she has been an elected member of Parliament, representing Maidenhead, an area near London. She kept her seat there in the 2015 election, winning a not-too-shabby 65.8 percent of the vote — more than current prime minister Cameron won in his own constituency of Witney. In procedural terms at least, there's nothing really wrong with what's happened: In Britain's general elections, voters vote for their local member of Parliament rather than the head of the party.

The thing is, everyone knows that's not how it works in practice. Although Britons may vote for their local MP, they are also swayed by the leadership of the parties and their platforms. To put it in context, 35,453 people directly voted for May in 2015. In the recent referendum, 17,410,742 voted to leave the E.U. Some polls had suggested that May would be neck and neck with Leadsom in September's leadership vote.

Given that, it's not surprising that many are now calling for a general election in Britain. In theory, the country isn't due to have one until 2020, but given the exceptional circumstances, it's possible one could be called soon. It may be in the Conservative Party's interests to hold it as soon as possible. The opposition Labour Party currently has its own leadership woes. The party is led by Jeremy Corbyn, an unrepentant old-school leftist who unexpectedly became leader last year. Corbyn — a reluctant "remain" campaigner at best — is abhorred by many of his own MPs and now faces his own leadership challenge, but he is popular with the party's membership. (With the general public? Who knows.)

What this all means is that Britain is now likely to have another election that will indirectly decide how the Brexit should happen — or perhaps even if it should happen at all. Whatever happens, expect many to be disappointed — and to wonder what their vote in the E.U. referendum was really all about, anyway.

More on WorldViews

What a real ‘Brexit Britain’ would look like

Brexit campaign wipes website clear, sparking speculation it is hiding its promises

Millions of Brits signed a petition for another E.U. referendum. They shouldn’t hold their breath.