A US citizen is taking Cambridge Analytica to court to get access to data he says it holds on him.
Prof David Carroll filed his legal challenge on the same day Facebook announced it had banned the company from its network.
He also wants Cambridge Analytica to disclose how it came up with the psychographic profile it had on him.
Legal experts believe the case could set a precedent for how such companies collect data.
Prof Carroll, who is an associate professor at Parsons School of Design in New York, requested a breakdown of the data Cambridge Analytica held on him when it emerged the company had built profiles up to 240 million Americans.
He received some data points in March last year, including a set of scores ranking him:
Three out of 10 on gun rights
Seven out of 10 on national security importance
Unlikely to vote Republican
"I discovered the depth of accurate information they held about me, including modelling my political beliefs," wrote Prof Carroll.
But at the same time, he told the BBC he also found the information "hard to interpret".
He also felt that the data was incomplete, partly because the company itself had boasted that it had 4,00 to 5,000 data points on each voter.
Taking advice from lawyers, he decided to take legal action to require the company to hand over all the data he believed it had on him.
As the company named as Cambridge Analytica's data controller was based in the UK, Prof Carroll brought the case at the High Court in London.
He also filed a complaint with the UK's Information Commissioner's Office, reports BBC.
On the crowd-funding site where Prof Carroll is raising money to fund his case, he wrote: "We are fighting for a legal principle that, in an age of unlimited access to personal data, is fundamental: companies cannot use your data in any way they see fit.
"Your data is yours and you have a right to control its use."