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(i) the author nowhere left variant readings;
(ii) every manuscript (except the original) was copied from a single source;
(iii) no two copyists originated the same error independently;
(iv) errors were not removed by conjecture;
(v) every relevant manuscript (i.e. a manuscript that survives or leaves extant progeny) except the original introduced at least one new error, at a point where no relevant manuscript had yet erred;
(vi) of the errors introduced by a given relevant manuscript, at least one can be identified by critics as an error.

These assumptions concern the original (i), the genealogy (ii), scribal behaviour (iii-v), the length of the text analysed (v) and the investigator's judgment (vi). Assumptions (v) and (vi) can usually be relaxed but never wholly dropped.[1]

In any passage where the manuscripts are divided between the truth and one false reading, the set of manuscripts presenting the false reading may be termed the "error set". On the above assumptions, the error is due to an ancestor[2] common and exclusive to the error set. In two passages that exhibit different error sets, consider the relationship between the two ancestors responsible. Either one derives from the other, or they are collateral. In the former case, the error set due to the earlier ancestor

includes the whole error set due to the later ancestor. In the latter case, the two error sets have no manuscript in common. Two error sets are therefore called "consistent" either if one includes the other or if they share no manuscript.[3]

From a series of mutually consistent error sets, the stemma is reconstructed thus. We list all the manuscripts across the page, and arrange the error sets underneath, so that any error set(s) contained in a larger error set appear(s) below it. Every error set is joined to that immediately above.

Of each manuscript we then delete every occurrence except the lowest. This procedure is applied in fig. 1b to the error sets generated by fig. 1a, namely AB, CD, A, B, D.[4]

The text of ω, the latest common ancestor of the extant manuscripts, is reconstructed on the principle that two manuscripts which agree reproduce the reading of their latest common ancestor. In fig. 1, the agreement of AC or BC suffices.

So far, P. Maas's approach[5] has largely been followed, but an alternative method was developed by J. Froger. We may regard any stemma as suspended from its topmost point, which represents the latest common ancestor of the extant manuscripts. Were it suspended from any other point, Froger observes (pp. 80, 118), the new stemma would generate the same patterns of agreement and disagreement, as long as the notion of error is left aside. These patterns thus admit a range of possible stemmata, which present the same enchainment[6] (i.e. network of lines connecting extant manuscripts and lost branch-points) but differ in orientation (i.e. choice of topmost point).[7] Froger therefore first seeks the enchainment,

on the basis of agreement patterns in two-way splits alone (p. 119). One extant manuscript is arbitrarily chosen as a fictitious original (p. 83). The "error" set in any passage now comprises all manuscripts disagreeing with that manuscript. Over different passages, these sets too are consistent,[8] and so Froger can proceed (pp. 84, 95) as in fig. 1, obtaining an enchainment suspended from the fictitious original. With the tradition of fig. 1, and with C as "original", the "error" sets become AB, A, B, D, whence the enchainment of fig. 2ab, arbitrarily orientated

with C on top. He now re-orientates, on the principle (p. 88) that if a group of manuscripts (or one manuscript) is caught in error, the topmost point cannot lie on their (its) side of the line that separates them (it) from the remaining manuscripts. An identifiable error in AB, and another in CD, would suffice to locate the topmost point; in fig. 2c dotted curves surround the areas eliminated. Fewer identifiable errors are thus required under (vi). This is an advance, because passages (which we may call determinate) where intrinsic criteria identify the original reading may be rare.

The remaining assumptions are no less necessary. Without (v) different manuscripts would appear identical. As for (i), if certain variants stood as alternatives in the original, unrelated manuscripts could agree in their choice between them. The basic principle that an error set has an exclusive common ancestor is ensured by (ii)—(iv), which imply that any error set comprises all the descendants of the manuscript responsible for the error and them alone. If (iii) fails, however, the error set may be augmented; if (iv) fails it may be diminished (Froger, pp. 108 ff.). The failure of (ii) has the same effect as that of (iv) or (iii), according as good readings or bad are transferred from the secondary source. Two or more such shifts may occur in a single passage. In different passages the error sets may be distorted in different ways, and cease to be mutually consistent. If few consistent variants remain, the above construction methods break down. The largest error sets are the likeliest to be distorted. In all

too many traditions, therefore, some small groups remain recognisable, but the passages where the manuscripts are more evenly divided exhibit a bewildering variety of inconsistent patterns of agreement, each occurring just once or twice.

In most traditions, authorial variation, coincidence in error and successful conjecture are exceptional, and instances can often be suspected on intrinsic grounds and excluded. It is therefore primarily the level of contamination that determines whether a stemma can be constructed. In the total absence of contamination there are but a few possible error sets, all mutually consistent. At the opposite extreme we could imagine a totally contaminated tradition, where the truth may survive in any one of the manuscripts uniquely and a fortiori in any combination, and the possible error sets are correspondingly numerous and in the main mutually inconsistent. (Such a tradition, comprising just three manuscripts, is considered in §4.1.) Real-life traditions fall between these extremes. Contaminated traditions were less pejoratively termed "open" by G. Pasquali.[9] Here an open tradition will be defined empirically as one for which no stemma can be constructed.

1.2. Before devising an alternative to the stemma, one must ask what the stemma ideally achieves. The answer seems obvious: the stemma sketches the history of the extant manuscripts, and that history establishes priority between rival readings. In other words the stemma has two functions, historical and evaluative; and the latter would seem to depend on the former.

Yet once the possibility of contamination is accepted, the history sketched by the stemma becomes just one of many possibilities. In 1928 J. Bédier complained that the same distribution of agreements and errors in manuscripts of the Lai de l'Ombre admitted either of the pedigrees in fig. 3.[10] Indeed for any stemma, however well it fits the patterns of agreement and error, any number of alternative pedigrees can be devised. The stemma may present a simpler history, argued Bédier, but not necessarily the true one, and therefore formed no sure basis for evaluation of rival readings (pp. 354 f). This objection to the stemma is weightier than Bédier's well-known argument that among the stemmata constructed by editors the proportion having just two branches is impossibly high; in

fact a heavy preponderance of two-branched stemmata is entirely to be expected.[11]

Here the answer to Bédier is that the evaluative policy stands even if the history falls. Consider how a stemma evaluates variants. In any variant passage, each rival reading is attested in a group of one or more manuscripts, and traced back to the latest common ancestor of that group. Suppose that one of these ancestors derives from another; we may call the manuscripts whose reading is traced to the earlier ancestor the superior group, and those manuscripts bearing the reading traced to the later ancestor the inferior group. Then the superior group prevails, the divergence between the groups being attributed to error in the later ancestor. This is the essence of stemmatic evaluation. In fig. 3a, for example, let ABDE agree against CG. The latest common ancestor of CG (=y) derives from that of ABDE (=v); hence ABDE's reading is older, and CG's may be put down to error in y. Now the reason that an exclusive common ancestor was posited for the inferior group at the construction stage is that that group were somewhere caught in an exclusive common error. Bédier's objection is that such an error is not conclusive proof of an exclusive common ancestor.[12] True; but the fact remains that the superior group has been known elsewhere to preserve the truth against the inferior group,[13] through whatever historical process, while the converse has never been observed. Hence, in passages (called indeterminate) where intrinsic considerations fail, readings exclusive to the inferior

group deserve no priority. This conclusion bypasses historical reconstruction and Bédier's objections thereto, and rests on direct induction from determinate to indeterminate passages.[14] The history and the evaluative policy must be derived from the determinate passages independently, and not, as commonly thought, in succession.