GREECE’S LONG-SUFFERING voters will go to the polls on Jan. 25 in a snap election that pits Prime Minister Antonis Samaras’s ruling coalition against the radical left-wing Syriza party led by Alexis Tsipras. Mr. Tsipras promises to replace the fiscal austerity imposed by foreign creditors with a free-spending populism that many Greeks, weary of double-digit unemployment, seem to support. The likelihood that creditors, led by Germany, would stop supporting Greece’s economy if Mr. Tsipras keeps that pledge, however, means that a vote for Syriza may be a vote for Greece’s abandonment of the European common currency, the euro — with all the risks that entails for Greece, Europe and the wider global economy.

Greece could probably face widespread bank failures and capital controls, while the rest of Europe could face financial stress as bondholders began speculating on which of Europe’s debtor countries would be next to go. University of California economist Barry Eichengreen, an expert on the euro crisis, told a recent conference of the American Economic Association that the potential fallout of a “Grexit” from the euro could be as dire as the bankruptcy of Lehman Brothers in 2008 — except that Mr. Eichengreen says it “would be Lehman Brothers squared.”

Right now, both German Chancellor Angela Merkel’s government in Berlin and Syriza seem to be approaching the situation the way German and Greek politicians have approached previous chapters in the European debt crisis: as a game of chicken. By broadcasting a take-it-or-leave it attitude to austerity, Germany seems to be trying to tilt the election to Mr. Samaras, whose victory it would presumably reward by tweaking the terms of Greece’s current bailout. Syriza’s defiant campaign seems designed to convince Greeks that they should send someone as inflexible as the Germans to the bargaining table.

Europe’s leaders need to move instead from brinksmanship to a policy that would emphasize the shared benefits of constructive behavior. Fiscal discipline and structural reform have indeed begun to yield growth and balanced budgets in Athens and must be continued whoever wins; the same goes for further stretching out of Greece’s debt. Yet none of that will be sufficient to reduce Greece’s debt load — now roughly 175 percent of national output — fast enough to ease the economic pain that so understandably troubles Greek voters.

Mr. Eichengreen proposes that, in addition to the more conventional forms of debt relief already contemplated, official creditors — the European Central Bank, International Monetary Fund and European governments led by Germany — sell their Greek bonds at a discount to the private sector, for the purpose of buying Greek firms, property and banks. These debt-for-equity swaps, modeled on smaller-scale experiments during the Latin American debt crisis, would present technical difficulties and would have to be phased in over several years, given the paucity of attractive investments in Greece. Still, if coupled with continued structural reforms, they could help shrink Greece’s manifestly unpayable debt more quickly — while giving German and other taxpayers a share of the eventual upside in return for their subsidy. Fresh thinking is a must, lest Greece’s economic crisis spark a populist political fire that could engulf Europe.