Overview
A Hobson's choice is a free choice in which only one thing is actually offered. The term is often used to describe an illusion that multiple choices are available. The best known Hobson's choice is "I'll give you a choice: take it or leave it", wherein "leaving it" is strongly undesirable.
The phrase is said to have originated with Thomas Hobson (1544–1631), a livery stable owner in Cambridge, England, who offered customers the choice of either taking the horse in his stall nearest to the door or taking none at all.
Origins
According to a plaque underneath a painting of Hobson donated to Cambridge Guildhall, Hobson had an extensive stable of some 40 horses. This gave the appearance to his customers that, upon entry, they would have their choice of mounts, when in fact there was only one: Hobson required his customers to take the horse in the stall closest to the door. This was to prevent the best horses from always being chosen, which would have caused those horses to become overused. Hobson's stable was located on land that is now owned by St Catharine's College, Cambridge.
From Wikipedia (CC BY-SA 4.0).