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The people are fed up with widespread corruption, high crime and economic woes.
As has happened in other parts of the world, electors have rejected the ruling elites and the establishment and backed an outsider.
So often, however, such optimism turns sour with time. The populist takes over threatening to "drain the swamp" or deal to corruption and the opposite occurs. Legal protections and constitutional balances are undermined and human rights suffer. Democracy is weakened, or worse.
A sound argument can be made that the likes of Brazil needed a shake-up.
Policies were not working and fresh approaches were needed. The country was only feebly recovering from a 2014-16 recession and the ruling left-wing Workers Party took the blame.
But just look at the Philippines under President Rodrigo Duterte, or Hungary ruled by Prime Minister Viktor Orban, or Poland’s Jarosaw Kaczynski, or for that matter the "leadership" of Donald Trump.
Mr Bolsonaro spent little time before carrying out some of his rhetoric. Executive orders were last week issued targeting the country’s indigenous groups, descendants of slaves, the LGBT community and non-governmental organisations.
His is clearly right-wing, socially conservative and pro-business. If that is what Brazilians want, then so be it. But what a shame a shift to more business-friendly policies and stricter law and order is accompanied by extreme and dangerous positions and by the likely gutting of environmental protection.
Mr Bolsonaro will, for example, loosen gun laws so people can defend themselves.
He has likened indigenous communities in protected territories to animals in zoos. During his campaigning, he revelled in ranting offensively about blacks, indigenous people, gays and women. He praised the former military dictatorship as well as torture. The so-called "tropical Trump" outdid his northern friend.
President Trump, meanwhile, tweeted after Mr Bolsonaro’s inauguration that "The USA is with you".
Crucially for the world as a whole, it would appear more of the Amazon is under increased threat. Responsibilities for delineating indigenous territories have already been shifted from the Justice Ministry to the Agriculture Ministry and Mr Bolsonaro has promised to put business interests ahead of environmental protection. Given the monstrous threats from climate change, this is disastrous.
The Amazon is often described as the lungs of the planet and Brazil is the world’s fifth-largest nation by area and population (about 220 million people). What happens there is crucial. Brazil is also ranked ninth in the world in GDP, significantly ahead of the next three, Canada, Russia and Korea.
The relationship between the United States, the EU and Brazil will be important. Should Mr Bolsonaro prove, despite his assurances, to undercut Brazilian democracy, he should know that that is unacceptable. The EU, the largest foreign investor in Brazil, might be able to reject agricultural projects from cleared Amazon land.
Mr Bolsonaro is alongside the United States in being critical of growing Chinese influence. Not surprisingly, he has little time for left-wing Venezuela and Cuba.
Sadly, extreme populists are surging to popularity in several parts of the world. Sadly, the initial optimism of many of the people is misplaced. Even as Mr Bolsonaro encourages an economic surge, the costs will be severe and longer-term damage to the nation critical.