text: But are there limits to how far authenticity can take a politician?
  During the course of his campaign Donald Trump has made statements that mainstream politicians would consider disastrous gaffes, alienating important parts of the electorate.
  "When Mexico sends its people," Trump told an audience in Arizona, "they're not sending their best. They're sending people that have lots of problems. They're bringing drugs. They're bringing crime. They're rapists..."
  It was a remark bound to alienate Hispanic voters. But others liked Trump for saying what he thinks.
  One recent poll shows him having 24% support for the Republican nomination - well ahead of second-placed Jeb Bush's 11%.
  One of Trump's key messages is that he is so rich that no one can buy him.
  Jeremy Corbyn, who has a record as one of the Labour Party's most rebellious MPs, argues that while many of his colleagues duck and weave, he is an honourable man committed to core principles on which he will not compromise.
  His ability to pack halls with huge crowds suggest it's a message that has great resonance.
  In Europe - especially in southern countries hit hard by the financial crisis - some insurgent politicians have broken through.
  Historically most European populist parties - which generally pit the people against a self-serving elite - have been on the right.
  But in recent years the left too has produced Spain's Podemas and in Greece, Syriza, which went from a protest party to forming the government, taking on the bureaucrats in Brussels.
  In the last UK general election Nigel Farage's UKIP won support by arguing that it was prepared to confront issues that the Westminster politicians were trying to dodge.
  And in Scotland the SNP swept to power, partly by running against what the party portrayed as a privileged and remote political establishment in London.
  There are a number of explanations for the increasing number of people who resent mainstream politicians.
  As well as a long-term fall in the levels of deference, sceptics point to spin doctors, focus groups, heavily managed public appearances and mainstream politicians' use of vacuous, scripted language.
  Campaign finance scandals also create mistrust.
  It is estimated that to run a successful re-election campaign a US senator needs to raise over $14,000 (Â£8,900) every day that he or she is in office.
  Aware that they are distrusted, some politicians try to connect with voters by emoting in public.
  When Hilary Clinton was performing worse that expected in the 2008 New Hampshire Democratic Party primary contest, she broke down in tears on TV.
  Analysts at the time said that moment helped her to secure victory in the state.
  But even if many mainstream politicians cast an envious glance at colleagues perceived to be authentic, there are limits to conviction politics.
  On both sides of the Atlantic the current phases of the electoral cycles means Trump and Corbyn are appealing for support from active party members.
  If either win they will face the daunting challenge of broadening their appeal to less politically committed voters.
  And even then authenticity does not always produce the results voters are hoping for.
  Jose Mujica of Uruguay is generally considered to have been one of the most authentic politicians of modern times.
  Having won the presidency in 2010 he turned down the chance to live in the presidential palace, staying instead in his modest home on the outskirts of Montevideo.
  A revolutionary fighter who spent over a decade in prison, Mujica stayed true to many of his ideals, giving away 90% of his presidential salary.
  Jose Mujica: The world's 'poorest' president
  But even some of President Mujica's allies said that their leader's undimmed idealism did not turn into as many practical reforms as they had hoped for.
  And for all Mujica's impassioned and heartfelt denunciations of consumerism, most Uruguayans were just as materialistic at the end of his term in office as they were at the start.
  Many admire authentic politicians. But those who stay true to their beliefs and manage to win power still face the challenge of turning their ideas into implementable policy.
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target: US presidential hopeful Donald Trump and UK Labour leadership candidate Jeremy Corbyn are demonstrating that whether you come from the left or the right, authenticity can win support.