Text Scholars who advocate the Byzantine Text Type, the Majority Text, and the Textus Receptus are so few that they could all sit in my living room, more or less comfortably.
Foremost on this list is Maurice Robinson who, with William Pierpont, published The New Testament in the Original Greek. This Greek New Testament represents what Robinson believes is the purest form of the Byzantine Text Type, and therefore, what he thinks is closest to the original Greek. There is much to be admired about this work, if one assumes that the Byzantine Text Type reflects the original texts of the New Testament writers. Robinson, however, despite his considerable efforts, has not been persuasive. Robinson teaches at Southeastern Baptist Seminary in Wake Forest, North Carolina and is a member of the Evangelical Textual Criticism blog, and is a most gracious member of the (informal) textual criticism guild.
Hodges and Farstad produced their text essentially by a majority vote, without asking which reading might be older. The title, The New Testament according to the Majority Text conveys that whichever reading is attested by a majority of manuscripts is most likely to be original.
The standard critical edition of the Greek New Testament is the Nestle-Aland/UBS text, or the lately produced SBLGNT (Society of Biblical Literature Greek New Testament). A third option is due out in 2018 from Tyndale House, the evangelical think tank/foundation in Cambridge England. These three will be relatively close to one another. If you don't like one of these, your only other options are the Hodges/Farstand or Robinson/Pierpont editions, unless you resort to out of print editions (which are out of print for good reasons).
If you decide to use one of these alternative editions, you should be aware that few Christian colleges and seminaries use them. You should also be aware that none of them have been used as the basis for a standard Bible translation in any language; certainly this is true for publishers of English versions. And you should also be aware that no Bible commentary series in any language is based on them.
We all should be circumspect about whom we trust to tell us which reading is God's word and which isn't. Indeed, the paramount importance of the text of the Bible is so great as to justify the learning of Greek and the science of textual criticism. Otherwise, we are absolutely dependent upon other people who have.
In the case of Hodges and Farstad, and in the case of Robinson and Pierpont, they are all godly men (Pierpont died a few years ago). On the other side, however, is a full, overwhelming array of evangelical scholars (and others, too) who are the giants in the field of New Testament. These scholars have judged these two critical editions as having failed in their effort to establish a viable edition that contains a more ancient textual tradition.
This reality in itself does not refute Byzantine priority or the Majority Text Type. However, for those who don't have the time or means to weigh the arguments carefully, this reality should make them more circumspect.
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