vicious circle; vicious cycle.
Both mean “a situation in which the solution to one problem gives rise to a second problem, but the solution to the second problem brings back the first problem.” “Vicious circle” is about 40% more common than “vicious cycle” in modern print sources.
And “vicious circle” is the phrase with stronger precedent to support it. The Oxford English Dictionary records it from 1792 in the sense “a situation in which an action and reaction intensify each other.” “Vicious cycle” isn’t recorded in the OED.
For information about the Language-Change Index click here.
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Quotation of the Day: “One piece of advice can be universally handed out, and it applies equally to speaking, understanding, reading, and writing. If in the course of any of these language activities, you run across words whose meaning or use baffles you, don’t by-pass them. Look them up in the dictionary and familiarize yourself with them.” Mario Pei, Language for Everybody 303 (1956).