This is already starting to happen. Legislatures in five states have scheduled referendums for this year, two of them on amendments providing a right to abortion (California, Vermont); two on amendments declaring that their constitutions do not contain a right to abortion (Kansas, Kentucky); and one establishing that infants born alive have a right to medical care (Montana).

Kansas shocked many political observers on Tuesday with a landslide win for abortion rights supporters, when voters refused to open the door to a complete ban on abortion. But the outcome is not as surprising for those who track public opinion, which shows that Americans of all political stripes strongly favor compromise policies on abortion. It’s a reminder that the public’s views on an issue are not always reflected in the stance of a state’s political leaders. The result may also serve as a cautionary tale for lawmakers: Pursuing abortion policy that goes too far in either direction risks a backlash.

Citizens are taking the lead in other states: abortion rights groups in Michigan appear to have collected enough signatures to qualify an initiative guaranteeing abortion rights, while in Colorado anti-abortion groups are petitioning for a proposal that would unconditionally ban abortion.

Initiatives allow citizens to propose their own laws, while veto referendums allow them to repeal laws passed by the legislature. Running either sort of campaign is expensive. Signature requirements vary by state but usually range from 5 to 10 percent of eligible voters, so about 40,000 in a sparse state like Wyoming and about 1 million in California for constitutional amendments.

Collecting signatures is time-consuming and can’t be done by grass roots volunteers. It usually requires hiring a signature collection firm, which can easily cost into the millions of dollars. Campaigns on social issues have had some success in raising money from small contributors, but most campaigns rely on a deep-pocketed individual or organization to front the costs. In Michigan, abortion rights activists spent over $1.6 million collecting signatures according to the latest campaign finance reports, almost 90 percent of which came from the ACLU. Sometimes the investment is for naught, as happened to an Arizona group this year that managed to collect only about half of the necessary 350,000 signatures.

In some states, sponsors will have to decide whether to seek a constitutional amendment, which typically requires more signatures but can’t be overruled by state judges, or an ordinary statute. Once a measure qualifies, even more funds are needed to run the campaign itself, especially to advertise.

Using referendums has some advantages over the more traditional legislative path. Most important, it allows citizens to overrule their elected representatives if they dislike the state’s policy choice. Opinion surveys on abortion tell us that most Americans favor a compromise policy somewhere in between what the activists on both sides want — legal abortion in the early stages of pregnancy, with increasing prohibitions as the fetus becomes viable. If legislators take abortion policy in an extreme direction, a real risk in this age of hyper-polarized parties, initiatives and referendums let voters steer policy back toward the center.

Some worry that voters would support extreme policies, but the historical record gives reason for cautious optimism. In the last two decades, Colorado, Mississippi and South Dakota — all deep red states — rejected by large margins ballot measures that would have banned abortion in almost all circumstances, and there is no recent example of voters approving an extremely restrictive policy. The Kansas vote is a case in point: It’s a red state but voters rejected the idea of moving toward a complete ban on abortion — they want to keep the current middle ground policy that allows abortion in the early stages and restricts it later on. There is also no example of voters approving an extremely permissive policy either, although California will be a test case in November; citizens will vote on a legislative proposition that appears to allow abortions without any restrictions related to viability, going further in the permissive direction than any Western nation. Europe’s record with national referendums also points to adoption of centrist policies when voters are involved.

Another advantage of referendums is that they can bring about more durable solutions. A loss in the legislature leads the losers to redouble their efforts to take control, while a referendum loss can only be undone by persuading the voters to change their minds. A comparison between the United States, which legalized abortion by judicial fiat in 1973, and Italy, which did it by referendum in 1981, is illuminating: Abortion never became the contentious policy in Italy that it became in the United States. Although the political temperature rises during the course of a campaign, citizens seem more willing to accept the legitimacy of a decision made by their fellow citizens than one made by political elites.

There is a risk, however, that legislatures will sponsor extreme proposals as a way to boost turnout by their bases. This cynical use of democracy may exacerbate divisions instead of giving voters an option to steer a middle course.

Congress could also get involved. In principle, lawmakers could simply pass a national abortion law that strikes a balance between the two extremes, although it’s hard to see an appetite for compromise in either party.

But there’s also a way to bring in the people’s voice at the national level. Although the initiative and referendum are unavailable at the national level, Congress could call an advisory vote asking citizens their preferences and using that information to construct a consensus policy. While this might seem fanciful to many Americans, in most countries, governments do call national referendums on important issues from time to time, and two-thirds of Americans tell pollsters they would like to vote on issues as well. We shouldn’t dismiss out of hand a practice that works well for other democracies. Ultimately, our system is only strengthened when the people have a say in how they are governed.