The American people want the Democratic and Republican parties to solve our nation’s problems together, but bipartisan solutions become possible only if each side gives the other the benefit of the doubt. We should begin with two polarizing issues — voter fraud and migration. Biometric identification cards offer a solution for both.

More than 30 states require identification cards to vote. Republicans believe such ID cards are important to prevent electoral fraud. Democrats believe voter impersonation is not a problem, and the real reason for the IDs is to suppress the votes of poor, old people and minorities, who often lack cards and tend to vote Democratic.

The Supreme Court accepted that voter identification cards were a legitimate instrument for ensuring ballot integrity, but many state courts suspended the laws because they were implemented late with confusing rules and without easy access to cards. In fact, statewide IDs are of little help because most cases of double voting are by people with homes in two states.

The solution to the problem is for Democrats to accept that voter IDs are important, and for Republicans to accept that all eligible voters should receive free national biometric cards, which would have unique identifiers for each person based on fingerprints or an iris scan.

In the 1990s, Mexico provided biometric IDs to all of its citizens in just three years, using Kodak and IBM technology. Mexicans now use them for many purposes. If the U.S. were to provide such a card to all citizens, it would address Republican concerns about ballot integrity while assuring Democrats that everyone would have a card and could vote. Indeed, the process could add as many as 50 million eligible but currently unregistered people to voter rolls.

A dividend to this bipartisan solution is that it could also solve the most vexing part of the immigration issue. Because of the growing importance of the Latino vote, both parties want to move forward on immigration, and a small bipartisan group in the Senate has gained some agreement on border enforcement and greater access for high-skilled immigrants and low-skilled agricultural workers. This initiative and the president’s ideas are positive and encouraging signs of compromise, but they don’t solve the problem. And their ideas for addressing the hardest issue — legalization for the 11 million undocumented workers in the U.S. — are unlikely to make it through the congressional gantlet.

Democrats favor legalization because they believe it would be wrong to divide families or deport 11 million people. Republicans oppose amnesty because they fear that after the economy recovers, a new wave of illegal migration will begin, much as occurred after the 1986 immigration reform. Democrats suspect the real reason is that Republicans fear the new immigrants will vote Democratic.

The first step toward resolving this is for each side to give the other the benefit of the doubt. The Democrats should accept the Republican concern of the unintended effect of amnesty, and Republicans should accept the Democratic opposition to mass deportations.

There is a way to permit legalization without opening the floodgates. Although the U.S. has invested about $187 billion since 1986 to stop illegal migration at its borders or to deport those in the country, the borders can never be fully secure. The flaw in the system is in the workplace. The U.S. has relied on a system to check workers’ identities and residency — E-Verify — that is flawed, voluntary and used in few states.

The solution for elections — a biometric ID — would also help solve the illegal migration problem. With systematic and effective verification for all workers, undocumented people would not find work and would not come. Legal residents, who are not citizens, would have a card that would allow them to work but not vote.

A comprehensive immigration solution should not only include legalization and a workplace ID card, but also a North American investment fund to narrow the income gap between Mexico — the source of the vast majority of migrants — and the United States. The fund would connect North America with better transportation and infrastructure, promoting growth in Mexico that would reduce the incentive for people to migrate. As our second-largest market, Mexico’s growth is also good for us.

A biometric card has a permanent and unique means of identifying each person and therefore cannot be hacked or forged. More and more countries are using it. In the U.S., it is already used in passports; the FDA uses it to combat fraud in the food stamp program; and Disney World takes biometric information from guests’ fingerprints to ensure that a multi-day ticket is used by the same person. Some fear that a national ID could be used improperly, but arbitrary abuse is far more likely if there are multiple, flawed IDs rather than a single, secure one.

It would not be easy or cheap to implement, but Mexico did it, and the U.S. can, too. To assuage concerns, the president and Congress could set up a group to propose ways to ensure privacy, prevent identify theft and address any other concerns. Acting on these two issues in this way could not only prove bipartisanship is possible; it could solve two vexing issues.

Robert A. Pastor is a professor of international relations at American University and the author of “The North American Idea: A Vision of a Continental Future.” He wrote this article for the Los Angeles Times.