Republican presidential candidate Ted Cruz is today in hot water after psychological data from tens-of-millions of US voters was collected from Facebook without their knowledge or consent, it has been reported.

According to documents seen by The Guardian, a little-known start-up company called Cambridge Analytica, which is backed by a "leading Republican donor" called Robert Mercer, paid researchers at the University of Cambridge to compile detailed psychological profiles on US Facebook users through an online survey.

The Guardian alleges that, in the main, the data subjects did not know they were being profiled, and Cruz - along with other presidential candidates - paid for the findings.

According to the publication, "In the race to advance data-driven electioneering strategies pioneered by successive Obama campaigns, Cruz has turned to Cambridge Analytica for its unparalleled offering of psychological data based on a trove of Facebook 'likes', allowing it to match individuals' traits with existing voter datasets, such as who owned a gun."

It alleges that the technology model used by Cambridge Analytica involves one person, called a 'seeder', taking a paid personality quiz and agreeing to the quiz's creator collecting a wide range of data, such as likes, birthdays, location and so on. However, the program also went on to collect the same data from the respondent's Facebook friends without their knowledge.