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It's a fairly representative example of social acceptance models. Despite the far greater disparity in qualifications, talents, motivations and lifestyle, people will identify far better with celebrities/icons and role models than they will a political, social or economic expert.
A lot of this is down the subconcious perception of how people are making decisions. A lot of Beckham supporters will feel that, due to their social and educational status, they won't be able to understand what informs the experts. They feel excluded from that type of knowledge and informed decision making. However, the perception is that the likes of Beckham are making their decision on their feelings and emotional response to the issue and fans will have that connection of similarity.
You can mock it, but you've probably done the same thing yourself in previous situation.
The reality is that this issue is being decided by people who don't really know what they are voting for or against. They're voting on a gut feeling about what the EU is and what their choice would mean on a mainly binary good/bad basis. It's not surprising though. Both sides of the debate have avoided much in the way of concrete commitments and people mainly vote on definites.
I love that his opinion matters to more people than prominent economists.