The day after Britain’s referendum on E.U. membership, David Cameron observed, “Over 33 million people from England, Scotland, Wales, Northern Ireland and Gibraltar have all had their say… The British people have voted to leave the European Union and their will must be respected.”

But what exactly did last week’s referendum reveal about what these voters want? For instance, how big of an economic hit is the typical “Leave” voter willing to tolerate in order to ditch the E.U.? Do they consider “Brexit” worth pursuing even if it causes Scotland to break off? And what should come next — new bilateral trade agreements or protectionism? Further cuts in government spending or reinvestment in the National Health Service? Deregulation or tighter controls on the economy?

Here’s the problem: Most referendums do not allow for specifying alternatives, giving and weighing reasons, or ranking preferences. And they give no indication of what tradeoffs the electorate is willing to tolerate, or guidance on how to proceed with the vast number of decisions that must be made to implement the people’s will.

Referendums commit leaders to a mandated outcome, regardless of the costs and consequences. And this makes it tougher for democratically elected legislatures to deliberate, compromise and forge consensus.

This is what legislators are supposed to do

We entrust our elected legislators and executives with political power on the basis of their political outlook or electoral platform. And they then have the flexibility to decide what costs are acceptable in the pursuit of popular policies.

Although elections have been described as referendums on candidates or parties, particularly when incumbents run for reelection, there’s a key difference. Electoral hopefuls may promise certain substantive outcomes, but nevertheless retain significant room to maneuver once they are in power.

In contrast, a referendum that establishes a clear and unequivocal mandate is often costly for elected politicians to override. (But it’s not impossible, as Greece’s Syriza government showed after their bail-out referendum in June 2015.)

Democratic theorists from Edmund Burke to John Stuart Mill have argued that the discretion retained by elected officials in addressing their constituents’ demands is a key virtue of representative democracy. Furthermore, there are institutional constraints on this discretion. Most notably, incumbents must answer for their accomplishments at the end of their period in office.

This means that citizens who view European integration as a runaway conspiracy can mobilize and lobby their representatives to address their concerns — or vote them out for being pro-integration. And these elected officials have a corresponding duty to communicate what they consider to be the advantages and disadvantages of pursuing integration, at least if they hope to stay in office.

But decision-making by referendum breaks these feedback loops between representatives and constituents, and eliminates the flexibility representatives need to govern in the face of pluralism, conflict and contingency.

Is Britain in or out?

Britain now finds itself in this type of predicament. Some leaders in the Leave camp, including Boris Johnson, indicated that they regarded the referendum as a bargaining strategy rather than a binding decision. Using the logic of two-level games, Johnson reasoned that a “no” vote would enable the British government to credibly threaten to leave the E.U., get greater concessions out of its E.U. partners, and ultimately obviate the need for a “Brexit.”

E.U. Commission President Jean-Claude Juncker called Britain on this bluff, pushing instead for a swift start to exit negotiations. German Finance Minister Wolfgang Schäuble curtly pronounced “In is in; out is out.” As Abraham Newman observed here at the Monkey Cage, Germany is particularly anxious to undercut such a strategy, whose cumulative effect would be to dismantle the uniformity and effectiveness of the E.U.’s single market framework.

The referendum result leaves Britain’s elected politicians with less rather than more direction. They cannot ignore the explicit will of voters without risking a backlash. But they also can’t hope to sufficiently improve the terms of Britain’s relationship with the E.U. and ask for a second poll. So there’s deep turmoil in the ranks of both major British parties.

Most important, the next British government faces impossible tasks — extricating Britain from the E.U. (a constitutional curveball as well as a foreign policy challenge), forging new relationships with the bloc, renegotiating scores of foreign trade deals, managing the domestic economic fallout, and deflecting a possible second push for Scottish independence. These challenges are bound to lead to some unpopular choices.

It is easy to see why the Conservative Party painted itself into this tight corner. The promise of a referendum temporarily quelled intra-party strife and staunched the loss of votes to the far right.

Still, a consolidated Tory stance on E.U. membership would have clarified the choices available to voters and avoided the present muddle. After all, this is an important part of what parties are supposed to do.

Funneling the complex and conflicting preferences of voters with regard to E.U. membership, public spending and immigration through an up-or-down referendum instead has distorted the public’s voice rather than amplifying it.

This has happened elsewhere in the E.U.

Other E.U. member states have had punishing experiences with referendums before. For instance, voters in France and the Netherlands in 2005 defeated the draft Constitutional Treaty that was to reform the E.U.’s institutional structure. But which of the nearly 450 Treaty articles did “no” voters find unacceptable? Were they spooked by the specter of a supranational “Constitution”? Did they want to halt the European integration process, or even to reverse it? Or were they simply expressing dissatisfaction with their respective leaders?

Here’s what the E.U. did next. They simply repackaged the Constitutional Treaty’s most urgent provisions into an ordinary treaty, which was ratified by parliamentary vote in most member states.

Yes, it’s counterintuitive – but having a direct say over a particular decision may leave voters with less control over long-term political outcomes than when they select their representatives on the basis of their policy promises or party platforms.

One reason for this is that political decisions are rarely discrete, one-off choices. They generate knock-on effects on other areas of policy, and their implementation requires a cascade of future decisions and trade-offs.

The more consequential the policy choice, the more momentous these reverberations are likely to be. The most effective way for citizens to maintain influence over these choices all the way down the line is by controlling those authorized to make them — that is to say, their elected representatives.

No doubt the European integration process bears blame for disrupting this relationship – for instance, by whittling down the power of national legislatures. But the fallacy here is thinking that ad hoc referendums can remedy this systemic, long-term institutional erosion. (Ironically, Britain’s decision to stay out of European monetary union has allowed it to retain a greater degree of democratic control over its budgetary powers relative to its continental counterparts.)

This is not to say that voters cannot be trusted with such technically complex matters as fiscal policy or membership in multilateral institutions. But if democracy is about giving citizens control over political decisions, a referendum is not nearly as effective a democratic mechanism as many tend to assume. In fact, easy resort to a referendum can make political decision-making less democratic. In this case, honoring the referendum outcome will lead to costly choices that citizens neither intend nor prefer. Ignoring it will deepen the popular sense of disaffection with the democratic process.

Turkuler Isiksel is James P. Shenton Assistant Professor of the Core Curriculum in Columbia University’s Department of Political Science. Her book, Europe’s Functional Constitution: A theory of constitutionalism beyond the state, is out from Oxford University Press this month.