IT took him two days. But Jair Bolsonaro this week eventually admitted his time as president of Brazil was coming to an end.

The right-wing populist, who became something of an international pariah thanks to his reckless drive to ‘develop’ the Amazon, has not exactly conceded defeat in Sunday’s run-off presidential election.

And he has certainly not congratulated his socialist opponent, the usually mononymous “Lula” – Luiz Inácio Lula da Silva.

However, Mr Bolsonaro has, reports say, told his country’s Supreme Court that “it is over” even if some of his supporters were protesting as he did so.

The former military officer has often been described as the “Donald Trump of Latin America”.

The insult is not entirely without merit. There are emerging differences, though, between the two men. Subtle if crucial ones.

Mr Bolsonaro this week urged truckers who had set up roadblocks in his name to go home. He is not – touch wood – talking of a stolen election.

His US counterpart is still bleating about his 2020 defeat being unfair. And so are many Republicans standing for office, local and national, in Tuesday’s mid-term.

President Joe Biden this week again took direct aim at “election deniers”. Democracy itself, he told Americans, “is on the ballot”.

He is right. There has been no evidence of result-changing mass electoral fraud in the United States.

Those saying there is, let’s be blunt about this, are lying.

That does not mean it is not worth asking about about the health of America’s voting system. Or any state’s. We should be all over this like wasps on a popsicle.

There are international independent scholars – a whole army of them – who monitor election integrity. And they do not rank America’s especially highly, at least among its liberal democracy peers.

In fact, in the global league table of election integrity the United States comes 59th out of 169.

That is 11 places behind Brazil. Both nations – the two biggest in the Americas -– have what observers would normally call free and fair elections. Both, as these figures suggest, could do better.

Who tops the table?

Well, according to the independent Electoral Integrity Project that would be – no prizes for guessing – Finland, Denmark, Sweden, Norway and Estonia.

The UK? We rank a respectable but unimpressive 34th, just behind Poland, Israel and Australia and just ahead of Japan, Italy and Jamaica.

This stuff matters. Democracy only works if everybody respects the rules of the game.

In the United States that is no longer true. Most Republicans, perhaps as some kind of demonstrative oath to Trumpism, claim to believe in fake mass “fraud”.

Many Democrats, somewhat more credibly, warn of voter suppression, especially of African-Americans. But almost everybody people who wants a vote get one and all votes get counted right.

So is what causes the low score? Gerrymandering, for starters.

Most American states allow partisans to draw the boundaries of districts for local and national elections.

The result? Crazy maps. What we would call constituencies or wards in America can have the most bizarre and convoluted shapes.

How come? So that they favour one party over another. That means there are not very many marginals in the US. And lots of safe seats, designed to be so.

Sorry, America, your districting system sucks.

Here in the UK these things are done by independent non-partisan commissions, supported by small publicly funded secretariats.

So Boundaries Scotland, as an example, has just started reviewing Holyrood constituencies. There are no party hacks anywhere near the process. We take this for granted. But it is a big deal.

The US also lacks a single watchdog for elections, any equivalent of the UK’s Electoral Commission. Instead it has 13,000 local bodies.

Sure, there is some federal regulation on campaign finance (another big weakness in the US system).

And a small commission was set up to help states with kit and cash after the knife-edge 2000 presidential was won by a few hundred Florida ballots.

But a nation which sees itself as a great democracy is actually just not that great at nuts and bolts of voting. And nobody seems very eager to fix that, even after the controversies in 2000 and 2020.

America still has no national electoral management body (EMB) or boundaries commission.

And there is not much prospect of getting them, despite the efforts of independent academics like Pippa Norris.

The political scientist, once of Edinburgh University but, these last three decades, of Harvard, is one of the great forces behind comparative election integrity studies.

Speaking at a briefing last month organised by the US State Department non-partisan Foreign Press Centers, Prof Norris sounded pretty downbeat about her adopted home.

“The problem in the States is not just about having election deniers in office; it’s the fact that both sides in these disputes believe equally that they’re defending American democracy,” she said. “So there’s no way out.”

She added: “Both sides have dug themselves in. We’re like in the First World War. We’re in the trenches on both sides. There’s no No Man’s Land anybody is willing to come forward on.”

Prof Norris has no problems with disagreement.

“But when you can’t agree on the rules of the game and when we don’t have an umpire that’s neutral, like an EMB, then you end up in conflict and confrontation and potentially even violence,” she warned.

“People have been talking about a civil war. I don’t believe that that’s what’s going to happen, but incidences of violence are entirely possible because they’ve already happened.”

America is an open society, a democracy with a free press and the rule of law and some strong, resilient institutions.

It also has a scary mix of men with guns and polarised, tribalistic politicians and media commentators who are as high as kites on often opaque funding.

That is why come Tuesday it matters that losers at the very least do what Mr Bolsonaro did.

And, however reluctantly, admit that it is over.