PARIS — In the eyes of the rest of the world, American democracy is a wonderful thing: The wonder is how it can work.
As US voters used punch cards, levers, touch screens, and paper ballots to elect their new president Tuesday - while lawyers stood by to challenge the results - voters in younger democracies marveled at the anachronistic complexity of the US system, and took pride in their modernity.
Since 1950, 95 nations have adopted this form of government. As the professed beacon and chief promoter of democratic rights around the world, the US has funded programs and sent electoral observers to pass judgment on the fairness of the process.
But since the contested election of 2000, the US system is seen by these new democracies - and older ones - as less credible.
Whether they use ticks on ballot papers, buttons on touch-pads, or hand-held bar code readers, foreign voters enjoy one advantage over their US counterparts: Within each country, voters cast their ballots using just one method, and those ballots are counted uniformly.
"If you don't have uniformity and harmonized laws, if there is no equality in the way you treat each vote, you are bound to have conflicts which don't arise when there is the same treatment for all votes," says Joram Rukambe, an elections expert with the International Institute for Democracy and Electoral Assistance (IDEA), an inter-governmental body in Stockholm.
In no democracy can all voting mistakes be eliminated, say electoral experts. But if voters' trust in their system is strong, they can put up with the occasional irregularity.
In the US, since the bitterly contested result of the 2000 presidential election was decided by the Supreme Court, that trust is no longer universal, says Mr. Rukambe. "When the popular vote and the electoral college vote are in conflict, very fundamental questions are raised about who won," he says.
In Europe, on the other hand, "you have elections with a high level of trust and confidence that they are working after years of experience," he adds.
Even new systems in young democracies can generate that trust. In Brazil, for example, which emerged from military dictatorship in 1985, all of the country's 121 million voters use electronic touch-pads in all of their elections.
Voters key in the number that corresponds to the candidate they support, check the photograph of the candidate that appears, and hit the "confirm" button. The "electronic urns" are small and can run on car batteries, which makes them usable in remote parts of the Amazon jungle.
Results of national elections are known within five hours of the polls closing, says Armando Cardoso, an official with the Supreme Electoral Court.
Brazilians trust their system: Since it was first used in 1996, no major election result has been challenged. "The security of confidence in the electronic urns has not been questioned," says Mr. Cardoso.
Challenges are rare also in Japan, where a long history of resolving disputes by consensus, and detailed rules on how to deal with contested ballots, sort out most problems.
For national elections, Japanese voters put a mark next to the name of the party of their choice, and then must write the full name of their preferred candidate. Though this raises problems of illegible scrawl, vote counters are flexible: they will register a vote even if they can make out only the candidate's first or last name, for example. Nor does any vote go to waste: If two candidates have the same name, an incomplete ballot will be shared between them proportional to the number of valid votes each has received.
No such confusion is possible in the world's the largest democracy, India. Earlier this year, 387 million voters there turned out for national parliamentary elections, all using electronic voting machines for the first time.
The simple Indian machines, carried by donkey or Indian Air Force helicopter to the more remote parts of the country, required voters just to punch the button next to the name and symbol of their party of their choice.
The elections were widely regarded as freer and fairer than previous votes, partly because of the voting machines. However, "technology by itself is not enough," says M.J. Akbar, editor of the Asian Age and a veteran political observer.
Improvements in Indian elections are due also, he adds, to "the increasing impulse to clean up the system."
The world's biggest Muslim democracy, Indonesia, has faced steeper challenges. In the last round of the recent presidential elections, 2,000 challenges to the results were brought before the courts.
But the courts handled them quickly and fairly, international observers said, and nobody challenged the overall result.
That is extraordinary, given the complexity of arranging elections for 145 million voters spread over 13,000 islands. Ballot papers were distributed by boat, ox cart, canoe, and helicopter to 500,000 polling stations, where voters punched their ballot papers with a nail (thus eliminating the chances of a hanging chad). European Union election observer Glyn Ford called it "the largest and most complex election ever," and it has been entered in the Guinness Book of World Records.
In Western Europe, voters tend to stick to their traditions, and all but the Dutch and the Belgians have spurned electronic voting machines.
Instead, voters generally mark their ballot papers with a cross beside their favorite candidate before folding it or putting it into an envelope, as in Britain and Germany. Or, as in France and Spain, they choose a ballot paper with their candidate's name already printed on it, and put that in an envelope, and then into the ballot box.
Almost everywhere in Europe, votes are counted by hand, first at the polling station itself, and then at a regional center, and then again in a central office, if need be.
Though Britain is exploring what a spokesman for the Department for Constitutional Affairs calls "new types of voting that are more convenient and suited to modern-day lifestyles," the government has gone no further than pilot schemes of all-postal vote elections.
Neither have any European countries yet begun experimenting with Internet voting. "That is very complicated and a lot of security problems have to be solved," says Dirk Inger, a spokesman for the German Interior Ministry.
The simplest system - ballot papers counted by hand in the presence of the candidates or their representatives - appears also to be the least problematic: European countries are rarely troubled by challenges to election results.
Only one challenge was raised in Britain during the last elections held there for the European Parliament. And 170 complaints were lodged with the courts at the last French legislative elections, from 64,000 polling stations.
Judges are particularly closely involved in French elections, visiting polling stations on behalf of the Constitutional Council (the ultimate arbiter of electoral disputes) and chairing all the regional vote-counting committees.
If the results from one polling station are contested, all that station's votes are sent immediately to the Constitutional Council, where they are recounted by a judge.
That, says Council official Stéphane Cottin, means that "Florida could not happen here, because everything is under a judge's control right from the start."
Another key difference between the US and almost every other democracy, electoral analysts point out, is the way countries from Japan to India, and from Ghana to Brazil, put their elections in the hands of independent and neutral officials. Only in the US could partisan figures such as Florida Gov. Jeb Bush have had any influence over a vote count.
It is perhaps local customs that count as much as any law when it comes to resolving electoral disputes.
At presidential elections last year in Somaliland - a region seeking independence from Somalia - the incumbent and his challenger ended up in a Florida-style virtual tie, 205,595 votes to 205,515. Opposition supporters cried foul and rioted, but the two sides eventually sat down for talks.
Soon enough, the traditional tribal system kicked in, and tribal elders convinced the politicians that Somaliland could not afford a messy postelection battle if it wanted to earn the world's respect. The opposition candidate stood down - and the lawyers had no work.
• Abraham McLaughlin in Johannesburg, South Africa; Bennett Richardson in Tokyo; Eric Unmacht in Jakarta, Indonesia; Andrew Downie in Rio de Janeiro; and Scott Baldauf in New Delhi contributed to this story.