Facebook's troubles with Cambridge Analytica came to light in March, after a whistleblower, Christopher Wylie, revealed that the political firm sought to create "psychographic" profiles about social-media users and target them with messages that preyed on their hopes and fears.
The lawsuit was filed Wednesday by Karl Racine, the attorney general for the District of Columbia.
'Facebook's lax oversight and misleading privacy policies allowed, among other things, a third-party app to collect the personal info of users without their permission and sell it to Cambridge Analytica, a political consulting firm'.
"Furthermore, after discovering the improper sale of consumer data by Kogan to Cambridge Analytica, Facebook failed to take reasonable steps to protect its consumers' privacy by ensuring that the data was accounted for and deleted", the complaint states.
The DC lawsuit alleges that Facebook failed to properly monitor data-gathering by third-party apps and that its privacy settings aren't easy for people to use.
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The information of more than 340,000 District of Columbia residents was exposed but only 860 downloaded the quiz, Racine noted. The lawsuit accuses Facebook of violating DC's consumer protection law.
'We're seeking to hold Facebook accountable for jeopardizing and exposing the personal information of tens of millions of its users, ' Mr Racine said.
Privacy settings on Facebook to control what friends on the network could see and what data could be accessed by apps were also deceiving, Racine said.
After the suit was filed Wednesday, Facebook said in a statement: 'We're reviewing the complaint and look forward to continuing our discussions with attorneys general in DC and elsewhere'. It could presage even tougher fines and other punishments still to come for Facebook as additional state and federal investigations continue.
It turned out that Facebook had even developed a special tool which could turn access to private data on and off - even if a user had already disabled sharing of their information. In total, the effort allowed Cambridge Analytica to harvest insights on more than 87 million users around the world, including 71 million Americans, Facebook previously revealed.