Why does the "e" in judge vanish in the word "judgment"?

Solution 1:

Words have entered the English vocabulary in waves. English spelling has also been standardized in waves, most conspicuously by dictionary editors like Samuel Johnson. Differences in spelling between words that seem like they ought to obey the same rules can arise because of when they entered the language.

The spelling of some words also froze in the history of English because they were already extremely prominent in written form, as may be the case with a word that may have been very common with judges and lawyers who might naturally standardize the spelling of a word due to its frequency in use.