Question: Four English translations of the New Testament, three of which are mainly projects of individual translators, have been published in the past ten years. Each one is more far more accurate and less idiosyncratic than Eugene Peterson's paraphrase, The Message. What is the base-text of these four new English translations?
Answer: The Byzantine Text. That is, the text which, in general, is supported by a large majority of the existing Greek manuscripts of the New Testament.
In case you're wondering what those four translations are, and where you can find them, here's a list:
The World English Bible - http://worldenglishbible.org/
The Analytical-Literal Translation of the New Testament, by Gary Zeolla - http://www.dtl.org/dtl/alt/index.html .
The English Majority Text Version, by Paul Esposito - http://majoritytext.com/ .
The Eastern Orthodox New Testament - http://www.orthodox-church.info/eob/purchase.asp .
The Byzantine Text on which the first three of these translations of the New Testament are based is similar to the base-text of the King James Version and New King James Version, with a difference: whenever there is a difference in the manuscripts, and one variant is supported by a strong majority of Greek manuscripts, that is the variant in the base-text of these three versions.
The fourth version, the Eastern Orthodox New Testament, is also translated from a base-text that agrees with the majority of Greek manuscripts far more often than the base-texts of the ESV, NIV, and NASB (etc.) do. Its base-text consists of the consensus-reading of a group of manuscripts that represents the text approved in the Eastern Orthodox Church. It has about 1,550 differences from the 2005 Robinson-Pierpont Byzantine Textform; most of them do not have a translatable effect. (The differences are specially concentrated in the book of Revelation.)
A cornucopia of resources about the Byzantine Text, including links to PDFs of the 2005 Robinson-Pierpont compilation of the Byzantine Text and Robinson's essay, The Case for Byzantine Priority, is ripe for plundering at
I do not subscribe to Byzantine Priority. And I do not think that the Byzantine Text, taken as a whole, is congruent to the original text. (Q: Does it convey the same message, book by book, as the original text? A: Yes, and it does so better than the Alexandrian Text.) To me, a reading that is supported by a large majority of twigs on a minority of branches of the transmissional tree does not have the same level of weight as a reading that is supported by a minority of twigs on a majority of branches. And some non-Byzantine readings (including some non-Byzantine readings that are longer than their Byzantine rival variants) have strong internal characteristics that commend them as original, compared to the Byzantine variant. Nevertheless, if you're looking for an English translation that is designed with the goal of reflecting the meaning of the text of the majority of Greek manuscripts, these four, collectively -- overlooking, for the moment, whatever quirks any one of them might contain -- should suffice.
Here's a diagram of what the transmission of the text of the Gospels would look like if the Byzantine Priority Theory were true.