Why did the 1611 Authorized Version translators choose to translate ἐλπίδος as "faith" in Heb. 10:23 when the majority of old and modern translations chose "hope"?
In Heb 10:23, all GNT's have ἐλπίδος including TR, NA28, UBS5, Byzantine text, etc. According to UBS5 there is no significant variation in the Greek text at the point.
Why the KJV translators rendered ἐλπίδος "faith" rather than "hope" is a complete mystery. Both Tyndale 91526) and Geneva (1560) Bibles correctly have "hope". The Latin Vulgate has "hope" as well.
This unjustified translation of the KJV translators has been noticed by others such as Ellicott:
Of our faith.—This rendering, apparently found in no earlier English version, is supposed to be due to oversight on the part of our translators. The true reading is “of the hope” (Hebrews 6:11; Hebrews 6:18-19).