The phrase "almost decisive for" is correct and usable in written English.
It can be used when discussing factors or elements that significantly influence an outcome but are not entirely conclusive.
Example: "The evidence presented was almost decisive for the jury's final verdict."
Alternatives: "nearly conclusive for" or "significantly influential for".
Let this set be called V, and let it be almost decisive for x against y.
Suppose that lineage J is almost decisive for some x against some y, i.e., there exists x, y in X such that A x, y).
A lineage J is picked out to denote A x, y) to mean that J is almost decisive for x against y, and denote D x, y) to mean that J is decisive for x against y.
If there is some individual J who is almost decisive for any ordered pair of alternatives, then a LTM satisfying conditions C1, C2, and C3 implies that J must be dominant.
Since V is almost decisive for x against y, and since every linage in V ranks x higher than y, and every lineage not in V does the opposite, we must have xPy.
Compare all the sets of lineages that are almost decisive for some pair-wise choice, which is not necessarily the same pair, and from them choose the smalles one (or one of the smallest ones).
Thus, for every pair of alternatives there is also at least one almost decisive set, since a decisive set is also almost decisive.
Indeed, if one takes this view, the above objection seems almost decisive against it.
The theorem now follows from the Lemma since a lineage almost decisive over some pair must be dominant.
In particular, almost all business angels believe that information related to governance relationships and the scientific curriculum are decisive for investment decisions.
Intrinsic resistance is often decisive for treatment failure; almost half of patients present with baseline resistance, rendering classical therapies ineffective.
