Tuesday’s US presidential election is routinely billed as a straight fight between the Democrats and the Republicans. It’s not: there is also host of no-hoper candidates from parties you’ve never heard of, and never will again.

But there is one that’s been getting global coverage for months, and by all accounts is very popular. It’s Nota – None Of The Above.

With about two-thirds of American voters saying they trust neither Hillary Clinton or her Republican rival Donald Trump, Nota would probably win by a landslide if it could put up a candidate.

And not just in the United States. Around the world, disenchantment with the choice of candidates is rife – as is frustration with the ability of voting systems to bring about change.

From Australia to Latvia, Poland to Japan, barely half of those eligible to vote in national elections now bothers to do so.

When Chile ditched compulsory voting in 2012, turnout plunged from about 90 per cent to 40 per cent of those registered.

In some countries, voter disengagement has reached the point where even legal compulsion makes no difference.

Last year’s elections in Greece, the cradle of democracy, resulted in barely half the population bothering to turn out despite voting being mandatory.

It seems that 2,500 years after its emergence in Athens, the democratic process is in crisis.

Yet the real surprise is that the disenchantment didn’t set in far earlier. For despite its familiarity, the process of voting has long been known to be fundamentally flawed.

In 1950, American PhD student Kenneth Arrow proved mathematically there’s no way of ranking candidates that’s guaranteed to give fair outcomes every time. No matter how you try to order the preferences of voters, if there are more than two candidates, voters can end up feeling cheated.

Arrow went on to win a Nobel Prize for what is now called the Impossibility Theorem. But even before its emergence, critics noticed that some voting systems were less fair than others. And it’s generally agreed that the worst of the lot is the one used by many democracies, including the US.

Known as the plurality rule, or First past the post (FPTP) system, it’s easy to understand, simple to implement – and prone to unfair results.

That’s because the winner doesn’t even need a majority of the total vote to secure victory – merely more votes than any of the other candidates.

So, if a nation is asked to choose between three candidates A, B or C, who duly get 45, 40 and 15 per cent of the vote respectively, candidate A wins – despite 55 per cent of voters wanting someone else.

All too often, this injustice is then amplified when the outcome of local elections based on FPTP is fed into a system for deciding who runs the country as a whole.

In 2012, America’s use of such a system – the electoral college – led to Barack Obama gaining re-election despite having the support of 28 per cent of eligible voters nationwide. That’s because that 28 per cent resulted in far more local victories than his rival, Mitt Romney.

Things can get even worse if people seeking a change from the “usual suspects” opt to support a more radical candidate.

Many Americans are still bitter about the impact of political activist Ralph Nader’s decision to run in the 2000 US presidential election.

Despite winning less than 3 per cent of the total vote, Nader is widely held to have diverted enough votes away from Democrat Al Gore to split the party’s vote, allowing George W Bush to win by a whisker.

Such anomalies have left many voters feeling they simply cannot make themselves heard, or bring about change. That, in turn, has led to attempts to remedy the problem with other voting systems.

Yet none of them have the power to evade Arrow’s theorem. For example, proportional representation gives voice to small parties but often at the cost of creating coalition governments in thrall to a handful of radicals that few voters support.

So, are democracies forever condemned to searching merely for the least-bad voting system? Not necessarily. Like all mathematical results, Arrow’s Theorem only holds under certain conditions, and these are now being challenged.

One major loophole centres on the effect of minority candidates on the final election result. Arrow’s proof assumes, roughly speaking, that such candidates are irrelevant - which as Nader proved, is clearly not always true.

This has led political scientists to focus on what happens to Arrow’s theorem by allowing voters to support more than one candidate.

One such system is the so-called Approval Voting, where voters can tick as many boxes on the candidate ballot-sheet as they like.

The winner is simply the candidate who is picked most often but, in contrast to FPTP, voters no longer have to make invidious choices, or reject a minority candidate for fear of “wasting” their vote. There’s also less incentive for either voters or candidates to indulge in tactical voting or targeting key areas.

Perhaps the biggest asset of Approval Voting is that it gives voters a more nuanced means of expressing their views, thus encouraging them to turn out. And lower turnouts are the single biggest threat to the democratic process.

But some theorists insist a far bigger loophole in Arrow’s proof has been overlooked: its insistence that a voting system must involve ranking candidates.

As anyone who has watched a gymnastic competition or checked out product reviews knows, there’s another way of deciding winners. Don’t rank them – score them.

Applied to election candidates, the result is Range Voting, where voters can give a score to as many candidates as they want, the winner being the one achieving the highest average.

Amazingly, this simple switch from rank to scores blows apart Arrow’s proof, and according to some results in the nearest thing yet to the ideal voting system. Computer simulations by mathematician Dr Warren Smith, of the Election Science Foundation, New York, suggests no other system meets the criteria of fairness in so many different situations.

Initially sceptical, even Arrow himself is now enthusiastic about the potential of Range Voting.

Yet even if it really is the best way to reflect the will of the people, its adoption will ultimately require the support of politicians. And therein lies the biggest challenge: how to persuade them that ditching the system that gave them power isn’t like turkeys voting for Christmas.

Robert Matthews is visiting professor of science at Aston University, Birmingham.