'To be, or not to be . . .' is the famous line of one of William Shakespeare's most famous plays.

The double-minded theme of The Tragedy of Hamlet, Prince of Denmark, aptly reflects the Danish people's relationship with the European Union. In 1972 a good half of them voted Denmark into the EU. In 2000 a similar proportion of citizens voted against joining the euro.

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Recent events are set to remind Danes of this ambivalence.

The country’s parliament in February announced it was considering extending paying child benefit allowances to cover all EU citizens from the first day of work in Denmark and also to pay for children, not living with their working parent in Denmark.

The move comes after the European Commission last year demanded the rules be changed so that EU workers are entitled to benefit more from the welfare scheme, worth €2,300 a year for young children and €1,500 a year for teenagers.

Brussels wants EU workers to be eligible for the child benefit scheme after working just one day in Denmark, making them equal to Danish workers. Currently, the scheme only kicks in after EU citizens have worked and paid taxes in Denmark for two years.

A large majority in the Danish parliament want to keep the two-year rule despite the EU's demand. But Prime Minister Helle Thorning-Schmidt wants to enforce the change with or without the support of her parliament.

And so in February 2014 the old Hamlet play was repeated in the parliamentary hall, with one leader of the opposition, the Danish People's Party's Christian Thulesen Dahl, asking: "Do we have a minority government that is completely indifferent to what this parliament thinks?"

The Prime Minister's answer was yes.

"If there is no majority support for this bill, well then we will have to continue to manage in accordance with EU law," she said.

For her, EU obligations clearly take priority. But most Danes, and even some of Thorning-Schmidt's own social democrat party members, consider that ultimately it is the Danish Parliament and constitution that matter most.

"It is very hard to explain and thus to defend, for example, that Polish children who have never been to, and will never be coming to, Denmark are entitled to have Danish children's pay," said Bjarne Laustsen, a Social Democrat MP, who would like to see the case tried at the EU Court of Justice.

The child allowance covers around half the cost of a kindergarten in Denmark. But for parents who work in the Nordic country, but whose children live in a poorer EU state, the value of the benefit can be considerably higher.

Leftist politicians claim that employers could even use the lucrative child benefit to force EU workers working in Denmark to accept lower wages than Danes.

The pro-EU camp has indicated it is ready to go against the EU on the issue.

"In Denmark we have some of the most generous welfare benefits and therefore we also need to ensure that there is fairness in who contributes and who receives," said pro-EU Liberal spokesman Ellen Trane Nørby.

'Selfie' with Obama

Since becoming prime minister in Denmark in 2011, Helle Thorning-Schmidt has herself shot to global fame.

Her 'selfie' photo in December with US president Obama and UK leader David Cameron at Nelson Mandela's memorial service in South Africa brought her face to newspapers and social media wordwide.

But her international style has distanced her from her electorate.

What does a typical social democrat supporter – say a cleaner or a supermarket cashier - have in common with an English- and French-speaking, Gucci-styled power-woman?

Little it seems. The supermarket cashier has instead typically switched loyalty to the populist Danish People's Party. Support for Thorning-Schmidt's Social Democrats has dropped to 17.6 percent.

Thorning-Schmidt was always different.

When she was elected MEP in 1999, the European Parliament was known as the place for 'has been or never were' politicians. By starting her political career in Brussels and then making it to the top of Danish politics, Helle Thorning-Schmidt swam against the tide.

She became leader of the Social Democrats in 2005 and challenged Anders Fogh Rasmussen as prime minister. She beat his Liberal party in her second attempt and became Denmark’s first woman prime minister in 2011. Anders Fogh Rasmussen, for his part, left Danish politics to become Nato's secretary general.

Meanwhile, the media is awash with rumours and speculation that Helle Thorning-Schmidt could also be up for a new job in Brussels soon – perhaps president of the European Commission when the post comes up for grabs later this year.

She, of course, does not comment.

EU elections

The child allowance battle could end up being the main theme in the campaign for the May EU elections – it is the perfect topic for the three eurosceptic parties.

Ever since Denmark entered the EU, The People’s Movement against the EU has been active and has managed to send representatives to the European Parliament in every single election since 1979. Its MEPs sit in the Confederal Group of the European United Left/Nordic Green Left group.

The Danish leftist Red-Green Alliance is supporting the movement rather than presenting its own election candidates. This gives the movement a fair chance of regaining a seat despite running a completely unknown candidate at the top of its list, Rina Ronja Kari.

To improve her chances, veteran MEP Soren Sondergaard vacated his seat in the EU assembly in February, allowing her to take his place and gain some experience as an MEP prior to the elections.

On the right, the Danish People's Party is up for another big score in the EU elections. In national politics, the party has successfully balanced populism with support for Liberal-Conservative governments and is polled to get more MEPs elected than Prime Minister Thorning-Schmidt's social democrat party.

Its current MEP, Morten Messerschmidt, who won a landslide in the 2009 elections, is running again. He sits in the Europe of Freedom and Democracy Group, a faction currently dominated by the eurosceptic UK Independence Party.

For eurosceptic voters with no appetite for either the far-left or the far-right, the relatively new Liberal Alliance party provides an alternative. Opposed to the euro but pro-internal market and pro-free trade, the party appeals to young ultra-liberalists and business people.

It has financial backing from the Confederation of Danish Industry and from Saxo Bank's founder and CEO, Lars Seier Christensen, who currently lives in Switzerland. Christensen wrote the Danish introduction to 'Europe: The Shattering of Illusions’ the latest book by former Czech president and renowned critic of the EU, Vaclav Klaus.

For pro-Europeans there is an array of parties - five in total - to choose from on election day.

The Social Democrats are not likely to keep their current four seats in the European Parliament, won in 2009 at a time when the party was more popular.

The conservatives and the socialist SF party may each hold one seat by re-running their MEPs; Bendt Bendtsen and Margrethe Auken respectively.

The pro-EU liberal party, Venstre, has put together an eye-catching list of candidates including current MEPs, the well-known former TV journalist Morten Lokkegaard, and former head of commercial TV2 Radio, Jens Rohde.

The top candidate is former minister Ulla Tornas. The list includes another TV news-anchor journalist, Jens Myrthu, as well as retired top badminton player, Poul-Erik Hoyer, who is currently president of the Badminton World Federation.

In the 2009 EU elections, turnout was a relatively high 59.5 percent. A referendum held the same day on the equal right of Danish princesses and princes to inherit the old throne helped motivate people to go to the ballot boxes.

EU election day will see a referendum this year too. Danes will be asked whether they accept that the country should sign up to the European Union’s patent court. But the issue is unlikely to have the same pull-effect on voters as the future of the royal family had in the last EU election.

Danish voters will elect 13 MEPs to the 751-strong European Parliament on 25 May.