The polarisation of politics in the Western world has created new challenges to existing political norms. Declining support for established political parties has been paralleled by a growth of alternative, more extreme, parties and politicians. This week we take a look at what voters in the US, UK and Europe are telling pollsters on the big issues.

Mr Trump won a remarkable victory, but he entered office with an approval rating of 45%, a record low for an incoming US President. His rating now stands at 40% compared with an average of 61% for previous Presidents at this stage in their administration.

Mr Obama's rating one month into his first presidency, eight years ago, was 64%. However, Mr Trump enjoys strong support among Republicans. More than eight in ten Republican voters approve of his performance, with a steady rating of around 87% since January.

Betting odds proved an alternative, if fallible, way of thinking about politics. The odds were spectacularly wrong over the UK referendum and the US elections, but they do track the views of those who are prepared to back their views with money. On Sunday, UK bookmaker Ladbrokes' betting odds implied a 52% chance of Mr Trump being impeached before the end of his term in 2020.

Last June the UK voted by 52% to 48% to leave the EU. 28% of the eligible electorate did not vote. Public opinion does not appear to have changed much in the intervening eight months. Removing "don't knows" a YouGov poll shows a pretty steady 52% of voters saying it was the right decision to leave the EU and 48% disagreeing.

Since the EU referendum, the Scottish National Party has renewed calls for a further referendum on Scottish independence. Perhaps surprisingly, while an overwhelming 62% majority of Scots voted to stay in the EU, and the Scottish National Party favours EU membership, there has been no real rise in support for independence since last June. Among those who express an opinion, support for the Union has risen from 47% in June to 55% in February – back, exactly, to where it was in the September 2014 referendum on independence.

Last week's UK by-election success for the Conservatives in Copeland highlights the improvement in the fortunes of the Conservative Party since June's referendum. Its support across the UK has risen by 8 percentage points since last June while Labour's support has fallen by 6 percentage points. The latest Guardian/ICM poll puts national support for the Conservatives at 44%, close to the peaks last seen in the summer of 2008. Labour support stands at 26%, its lowest reading since 2009 when the UK was in recession.

Public satisfaction with Mrs May's performance as UK Prime Minister, at 53%, compares favourably with the position of her two predecessors, David Cameron and Gordon Brown, six months after taking office. In the last 20 years only Tony Blair has enjoyed a better rating at this stage in a parliament.

Jeremy Corbyn's satisfaction rating, at 24%, has fallen since he took over as Leader of the Opposition. The last time a Labour leader was as unpopular at this stage in his leadership was Michael Foot in 1982.

The UK Independence Party played a decisive role in the campaign to leave the EU but since the referendum its support has waned. UKIP is currently polling 13% of the national vote, down from 16% before the referendum. But it seems premature to be writing UKIP's obituary. It remains the UK's third largest party in terms of the share of the vote and its current support is in line with the average of the last five years.

The Liberal Democrats took 23% of the vote in the 2010 General Election, their best showing in a General Election since 1983. But the coalition years took a heavy toll on support for the Lib Dems. Over the last five years support for them has averaged around the 9% mark.

2017 is the year of important elections in three leading EU member states.

The Netherlands goes to the polls on 15th March. The latest polls show Geert Wilders' far-right, Dutch nationalist PVV party in the lead with 28% of the vote. Mr Wilders is fiercely opposed to immigration and favours holding a referendum on EU membership. In second place is the ruling centre right VVD party lead by the current Prime Minister, Mark Rutte, with 25% of the vote. On Sunday, bookmaker PaddyPower's odds implied a 71% probability of Mr Wilders' Party winning the most seats and votes.

However, the PVV would need to forge a coalition with other right-wing or centre-right parties to achieve a majority. Mr Rutte has said there is a "zero chance" of his party forming a coalition with the PVV, virtually eliminating the prospect of Mr Wilders entering government. Mr Wilders' best hope may be to win a sizeable number of seats which could enable him to exercise influence over policy.

France's elections take place on 23rd April and on 7th May. The latest polls for the first round of voting show Marine Le Pen's right-wing, nationalist Front National in the lead with 26% of the vote. Ms Le Pen has stepped back from her earlier support for leaving the euro area altogether and now appears to favour a renegotiation of France's EU membership rather than departure from the Union. The possibility of a Le Pen victory is affecting financial markets with the euro and French government bonds softening on improvements in her poll position.

Francois Fillon of the centre-right Republicans and the centrist Emmanuel Macron with his newly founded party, En Marche!, each poll 19%.

Were Ms Le Pen to make it to the second round the polls currently suggest that Mr Fillon or Mr Macron would probably defeat her. This was the fate of Marine's father, Jean-Marie, the founder of the Front National who lost to Jacques Chirac in the second round of the Presidential election in 2002.

Yet Ms Pen remains a serious contender for the presidency. Roughly 40% of French voters currently say they will support Ms Le Pen in the second round. This is reflected in the betting odds. On Sunday, PaddyPower odds put Mr Macron as the frontrunner with a 45% chance of winning, followed by Ms Le Pen at 33% and Mr Fillon at 27%.

Germany goes to the polls on 24th September 2017. Angela Merkel's ruling centre-right CDU/CSU coalition leads the opinion polls with 31% of the vote, followed closely by the centre-left SPD, which has seen a sharp rise in popularity this year. Sunday's PaddyPower betting odds imply a 69% probability of CDU/CSU being the largest political grouping.

Even if the CDU/CSU wins the largest number of Parliamentary seats it may need to form an alliance with the SPD to govern. This explains why the betting markets see a high probability of a CDU/CSU win but only a 50% probability of Mrs Merkel remaining Chancellor. The markets give the SPD's Martin Schulz a 44% probability of taking over from Mrs Merkel as Chancellor in September. 

Another feature of German politics is the rise of the right-wing, nationalist AfD, which now polls 11% of the vote. The AfD has an anti-immigration and soft Eurosceptic stance, and has benefited from a popular backlash against immigration. In the 2013 federal election it won 4.7% of the vote, lower than the 5% threshold for seats in the Bundestag. It now holds seats in 10 of the 16 state parliaments. A big shock would come from the AfD gaining a significant number of seats in the Bundestag.

It would be a mistake to think that alternative political parties and politicians only achieve change by taking power. UKIP's influence on the outcome of the UK EU referendum shows that insurgent parties can shift policy with little or no parliamentary representation.

In a similar vein, during last year's US campaign Hillary Clinton went back on her previous support for free trade and adopted a more sceptical stance in response to the rhetoric of Donald Trump and Bernie Sanders.

The challenge from right wing parties in Europe may also be shifting the centre of gravity of mainstream politics. In Germany, Chancellor Angela Merkel has recently called for a ban on burqas or veils worn by Muslim women. Austria's centrist government has announced a ban on full-face veils in public places. The Netherlands' centre-right Prime Minister Mark Rutte recently warned migrants in an open letter in Dutch newspapers "to be normal or be gone".

So what conclusions can we draw from the polls? Having gone through the numbers with my colleague Debo two things stood out to us.

The first is the unexpected success of the UK Conservatives - albeit one greatly aided by the problems of the Labour Party and UKIP. Eight months after the referendum the Conservatives are riding high in the polls, Mrs May is pretty popular among voters and the House of Commons has voted to start the process of leaving the EU. Public opinion on Brexit has remained much as it was on 23rd June and in pro-EU Scotland support for the Union has risen.

We were also struck by the scale of the challenge to established parties posed by right wing, Eurosceptic parties in the Netherlands and France. The most likely outcome is that neither Geert Wilders nor Marine Le Pen enter government. But such outcomes cannot be ruled out; moreover, a strong showing in the polls for their parties, and for the AfD in Germany, would increase the influence of the right within Europe.

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