What is "eclecticism?" In simplest terms, it is the process of compiling a text from multiple sources. This is in contrast to the notion of editing from a "proof text," in which one follows a chosen text unless there is an overwhelming reason to do otherwise.
In New Testament criticism, there are basically three approaches: "Thoroughgoing" eclecticism (also known as "radical" eclecticism), "Reasoned" or "Rational" eclecticism, and "Historical/Documentary criticism." The first two approaches are always eclectic, compiling a text from multiple sources, and the third may be eclectic also.
In simplest terms, thoroughgoing eclecticism consists of taking all manuscript readings and choosing the best based solely on internal criteria. Historical/documentary criticism consists of choosing readings based solely on their manuscript attestation, by some means such as preparing a stemma or counting text-types or just following the best manuscript. And reasoned eclecticism consists of splitting the difference: Evaluating variants based on both their attestation and their intrinsic merit.
It will be evident that this is actually a continuum: All editors are eclectic to some extent, and all use internal and external evidence to a degree. But the extent varies greatly, and sufficiently that it is reasonable to speak of three camps.
Currently, reasoned eclecticism is the dominant force in New Testament criticism; those who engage in other forms of criticism are a relatively small minority, who can find some difficulty in having their work respected.
It has not always been so. It is noteworthy that this sort of eclecticism is not considered proper in most areas of Classical Textual Criticism. In Shakespeare criticism, for instance, the standard method for editing is to take a particular proof text (usually the First Folio, but sometimes one of the quarto editions), and follow that except where the evidence of some other source is overwhelming. In other words, all modern Shakespeare critics are historical/documentary critics, generally of what would in New Testament circles be considered the most extreme type.
And this method has been followed in New Testament criticism, though the matter is rarely described in that way. The edition of Westcott and Hort, to a significant degree, is compiled using B as a proof text. Tischendorf's eighth edition is almost as strongly influenced by . Few other editions are so strongly dependent on single manuscripts, but there is a lot of D in the Clarke text of Acts, and the recent Majority Text traditions could almost be treated as being taken from a single proof text of that text-type.
It should be noted that the three categories of eclecticism described above are not actually methods of editing the New Testament text. They are, rather, approaches to creating a method. Historical/Documentary criticism, for instance, says, "determine the relationships between the manuscripts and reconstruct the text based on that." If you determine that the best manuscripts are the Alexandrian, you get the edition of Westcott & Hort; if you determine the Byzantine are best, you get Hodges & Farstad; if you treat all types equally, you'll probably get something like Von Soden.
Similarly, the approach of Thoroughgoing Eclecticism is to "determine the best rules of criticism and determine the best text based on that." Since editions based on this principle are very few, we cannot show how different forms of the method produce different texts -- but it's easy to imagine the results. Take just one rule, "prefer the shorter reading." Some critics swear by this rule, other reject it almost completely. Suppose there were two editors, one of whom considered the shorter reading the primary evidence of originality while the other considered the longer reading universally best. Imagine how different their texts would be!
Reasoned Eclecticism splits the difference, saying, "Determine the relations between the manuscripts and the best rules of criticism, and proceed from there." As it turns out, most recent editors have agreed, at least in outline, on both the best manuscripts and the best rules, so the modern editions compiled based on Reasoned Eclecticism (i.e. Bover, Merk, and UBS) are all fairly similar. But this is not inherently so; Harry Sturz would probably qualify as a Reasoned Eclectic, but had he edited a text, it probably would not have looked much like Merk or Bover -- it would certainly have had more Byzantine readings, and possibly some other surprises.
It is quite difficult to offer examples where all three methods produce divergent results, particularly if one uses the Westcott & Hort text as the "standard" for historical-documentary criticism. If we take Hodges & Farstad as the standard instead, we have slightly better luck -- though still limited, simply because there are so few places where different editors adopt three different readings.
One I know of is Matthew 22:7. Here the UBS text reads
o de basileus wrgisqh
The Kilpatrick edition, the first text to be compiled based on thoroughgoing eclecticism, reads
akousas de o basileus wrgisqh
kai akousas o basileus ekeinos wrgisqh
The Kilpatrick reading is supported by 33 (alone or nearly),
and is adopted apparently because it best explains the at least
six different readings in this passage:
akousas de o basileus
o de basileus
kai akousas o basileus ekeinos
ekeinos o basileus akousas
kai akousas ekeinos o basileus
o de basileus akousas
The UBS editors probably preferred their reading because it is supported by several good witnesses -- B L 1 700 892* 1582 -- and because it could easily have given rise to certain other variant readings, notably the reading o de basileus akousas of Q 13.
And Hodges and Farstad preferred their reading because it had the best support from the Byzantine manuscripts: E F G (K) Y P etc.