... Although they should. I blogged about this in November of 2003, for those of you keeping track, but I figure I can resurrect a word gripe after two years and two months.
A gantlet is, according to Webster's New World: "A former military punishment in which the offender had to run between two rows of men who struck him with clubs, etc. as he passed." In other words, an ordeal.
A gauntlet is, according to the same source, "a medieval glove." It was sometimes thrown down to challenge someone.
Therefore, you "run the gantlet" and "pick up the gauntlet."
The AP Stylebook has made its preference known in this matter. The gamut / gantlet /gauntlet entry reads quite clearly. The words mean different things, so we should use them in the appropriate circumstances.
But people don't say "run the gantlet." They say "run the gauntlet." They don't write it correctly either. Dictionaries don't make the matter any clearer; Merriam-Webster's defines gantlet as a variant of gauntlet.
Urg. It feels like the "literally" debate all over again, but with a less-popular word.