With the first round now over, Brazil's presidential elections evoked intense emotions that even a Greek Tragedy could not conjure up. There was the drama of protesters in 2013 whose expectations of greater support for education and jobs led to disaffection with the Labor government of President Dilma Rousseff. And then there was tragedy. Just two months before the October first round, Eduardo Campos, the candidate of the Socialist Party, died in a fiery plane crash. Marina Silva, his running mate, took on the mantle of leadership. And there was irony. Pundits and pollsters who had thought that Silva was the rising star to defeat both the incumbent and the pro-business Social Democrat, Aecio Neves, were proven wrong. When the polls closed Sunday night, Neves came in second.

A runoff election in what was described as a very tightly competitive campaign will mean that Rousseff, who won 42 percent of the vote, will compete with Neves. And Silva's role will be to see whether she has enough political clout with her suppporters to push Neves, who came in second, with 34 percent of the vote, over the top if she endorses his candidacy over that of Rousseff. Silva received 21 percent.

If this sounds too much like inside baseball, it probably is, except that as we approach election season in this country there are lessons we can learn from our Brazilian neighbors. The first is that the wisdom of pollsters must be considered, but not used to anoint any one candidate. Public opinion is volatile. When the votes were counted Sunday night, the biggest losers were Brazil's pollsters and the many Washington pundits who were betting on a slam-down second round between Rousseff and Silva.

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Unreliable polling data makes guessing the final outcome more of a parlor game, given how unreliable polling was in round one. Chalk it up to Brazil's young democracy. No Nate Silver has come to the rescue of the political parties this time. Brazilians relied too much on the inadequate polling data that led them to believe that Silva would surge. The pundits were so convinced of this that there were endless commentaries about her rise and what it would mean in Brazil. (Even The Economist website devoted its take on the election to this fatal flaw right after the results of the first round.)

The second lesson is that pocketbook issues matter. The Labor Party's 12-year run launched social programs that lifted millions from poverty to the middle class. The Bolsa Familiar ensured that millions would get to school, raising the expectations of an emerging group of citizens who now want even more. The corruption scandals of Labor, however, coupled with the stagnant economy of the past two years, have also created even more dissatisfaction among Labor's supporters.

For voters, the choices were stark. Do voters want four more years of the same social welfare policies that have only taken citizens to the edge of being part of the middle class? Or do they want a government that will end corruption, endorse a less protectionist trade policy, and invest in education and infrastructure? More than 10 points separated Dilma's votes from those of Neves, whose more free-market business approach took the more industrial regions of the country. Silva's voters were limited to those in Brazil's northeast, her base for the Green Party, and in Acre, her native state.

Silva's Cinderella story is not to be discounted. Rising from extreme poverty, the daughter of rubber tappers in the Amazonian state of Acre, she became a leading voice of Brazil's environmental movement, eventually joining the Labor government of former President Lula da Silva (no relation) as minister of the environment. She later broke with Labor and ran as a Green Party candidate in 2009 against Lula's handpicked successor, Rousseff. She lost. But Silva's story is far from over as she may hold the key to the future of the presidency in Brazil. A poll conducted the day before the election showed that 71 percent of her supporters would vote for Neves in a runoff. Now Brazil's next president hangs in the balance as voters wait to see whom she will endorse.

The bigger question that you may be asking as your eyes glaze over these details is: Why should this election matter to the United States? The answer is simple. Brazil, the second-largest state in the Western Hemisphere, is a strong democracy with a tradition of respect for international law. It works through international organizations like the United Nations, where its police and military have continued to support peacekeeping operations in Haiti and around the world. Just as the United States is a leader for the countries of the Global North, so Brazil has assumed leadership in the Global South. This is important in a world experiencing dynamic changes in the governance, security and trading relationships.

If the Oct. 26 runoff election results in a Labor victory, with Rousseff serving another four years, then both the U.S. and Brazil will need to continue a rebuilding of trust between both countries. Last fall, after revelations about National Security Agency eavesdropping on Rousseff's cell phone conversations, she cancelled a much sought-after state visit to Washington. The fallout from this event still haunts the bilateral relationship. Both countries will need to work even harder to rebuild trust as regional events, including the Summit of the Americas scheduled for Panama in 2015, will reach a tipping point with the inclusion of Cuba as part of that process. The U.S. will need to work with Brazil, the leader of the South American Union, to reach some form of accommodation.

A victory of the Social Democrats, with Neves returning that party to office, would present another opportunity to revisit efforts to expand free trade agreements to the Southern Hemisphere. Neves, the grandson of Brazil's first democratically elected president after the military dictatorship ended in 1985, would be more open to working with U.S. investors. His party's record of economic reform, led by former President Fernando Enrique Cardoso, could usher in a period of greater focus on such priorities as building infrastructure and going beyond the social programs of the Labor Party. Most important, Neves has also promised an end to the endemic corruption that has plagued his Labor Party colleagues for years.

South America has not been the focus of much attention in Washington. The reasons are obvious when you have a hemisphere that is more peaceful and not stockpiled with nuclear weapons. There may be challenging governments in the region who dislike United States policies on counterterrorism and narcotics, but these nations do not threaten other states. If anything, Brazil and its neighbors have united together in their own subregional arrangements precisely to create a countervailing force to a region once dominated by the United States.

Of all the countries in South America, Brazil, as the largest and richest, is also poised to lead in the decades to come. As part of the so-called BRICS (Brazil, Russia, India, China and South Africa), Brazil is finding its voice as a leader of the Global South, a position that dominates its own foreign policy. These types of relationships with other emerging economies are also an important part of the evolution of a region that is no longer the poor, underdeveloped neighbor that we often wrongly think of when we talk about South America.

While foreign policy issues are not a feature of this presidential election in Brazil, it seems certain that no matter who wins this race in round two, the winner will want to ensure that the long-term relationship with the United States evolves in a way that benefits respective interests. Those include the mutual respect for democratic governance, protection of the environment and support for international law. Fortunately, all those seeking the presidency share these common values, and any change will benefit us all.

Mendelson Forman is a senior adviser at the Stimson Center and a scholar-in–residence at the American University School of International Service in Washington.