(Karen Bleier/AFP/Getty Images)

Bertram J. Levine and Michael Johnston are, respectively, political science professors at Rutgers University and Colgate University.

Labor Day has come and gone, and we are now into the heart of the 2014 election campaign. This year’s races are the first to be run under the combined effects of the Supreme Court’s decisions in McCutcheon v. Federal Election Commission, eliminating aggregate limits on individual contributions to federal candidates, and Citizens United v. FEC, allowing corporations to make unlimited expenditures on behalf of federal candidates. Already, the Associated Press reported, spending on this off-year election has topped $1 billion — and it may exceed $4 billion by the time the votes are in. Welcome to the new normal.

Ironically, the court’s decisions, along with the resulting activities of megadonors such as Sheldon Adelson and the Koch brothers, have only added to the appearance of corruption that plagues our electoral process, something that has worried the justices ever since the landmark Buckley v. Valeo decision of 1976. Is there a better way?

Since the enactment of the Federal Election Campaign Act in 1971, the United States has relied on a combination of contribution limits and transparency — public reporting of contributions and expenditures — to safeguard the political process. But now contribution limits have been rendered largely impotent by the court because of the majority’s contentious reading of the First Amendment: “Money is speech” writ large.

That leaves transparency: mandatory disclosure of contributions in excess of $200. Reformers might take some comfort from the fact that the court has left reporting requirements intact. Sunlight, we are told, is the best disinfectant. But has transparency ever been an effective corruption-fighting tool? Many people deeply involved in electoral politics don’t think so. As former Minnesota representative Tim Penny once put it: “There’s no tit for tat in this business, no check for a vote. But nonetheless the influence is there. Candidates know where the money is coming from.”

Indeed, if we think about all the ways transparency helps contributors and candidates put pressure upon each other, it is clear that reporting contributions can make matters worse. Suppose, then, that we turned out the lights? What if we let Adelson and Shaun McCutcheon spend their money on politics but not take credit for their “generosity”? What if we made all campaign contributions and independent expenditures anonymous — and made sure they stayed anonymous?

To be sure, anonymity for contributors is not a new idea. In their 2002 book “Voting with Dollars,” Bruce Ackerman and Ian Ayres convincingly argued for making it impossible for candidates to verify the sources and amounts of contributions to their campaigns. Under their approach, contributors could boast of their largess, but candidates would have no way of knowing whether a contribution was actually delivered. Sadly, the Ackerman-Ayers system has not taken root, and federal law continues to make it possible for anyone — powerful incumbents included — to learn precisely who has given how much to whom.

The problem is not just how much money we allow into the system, or even how few individuals provide it. An equally serious, and somewhat ironic, issue is that transparency makes the appearances problem worse. If incumbents could not know the sources of contributions to their war chests, they could not “thank” their benefactors with policy “favors,” nor could they extract contributions through intimidation. Donors wanting to support challengers — who are routinely out-spent by solid margins under the current system — would not need to worry about reprisals from incumbents.

How would such a system operate and, most important, be policed? Contributions could be made directly to the Federal Election Commission, to be disbursed periodically to candidates in aggregate. And to make sure big donors don’t break their silence — even in private — fines, and even prison sentences, would be imposed on violators. This would not be as impractical as it may seem, because it would be largely self-enforcing: Given the value of personal connections in politics, donors would think twice before making trusted friends in Congress a party to a felony.

Such a system might lead to fewer donations, but it is hard to see how fewer quid pro quo-driven contributions would harm the process.

Could all this pass constitutional muster? We believe so. Like the court, we value First Amendment rights immensely. But it is a basic tenet of constitutional law that fundamental liberties, including speech, can be limited where doing so serves a compelling state interest and when remedies are narrowly crafted.

As noted, the court has already identified combating the appearance of political corruption as a compelling interest. As for the narrowness of our proposed remedy, advocates of less-restricted giving have argued for years that contributions don’t just encourage or facilitate political speech but rather are speech. So let’s run with that idea: Even anonymous contributors, by giving money to candidates of their choice, will have spoken.

Let’s just make it harder for them to trade that support for personal favors.