Is “that had been” omitted here?

Question

Among the biggest changes prompted by the scandal was political morality.

Is this omitted here?

Among the biggest changes that had been prompted by the scandal was political morality.

Answer 1

Many quite distinguished grammarians agree with your analysis: they call postposed modifiers like prompted by the scandal "reduced relative clauses", where the reduction is accomplished by "Whiz-deletion".

This analysis certainly results in an understandable paraphrase of the original utterance; but I myself do not believe that the construction is actually a result of reducing an underlying relative clause. I think the “rule” at work here is

A modifying phrase whose head is followed by additional elements must be placed after the modified element.

For instance, we speak of a grateful man and a very grateful man, but not ∗a grateful for help man; this modifying phrase must be postposed: a man grateful for help.

The rule seems to be based on our left-to-right parsing conventions: we prefer to arrange our utterances so each word signals what kind of term will follow. Modifiers before a head provide this signal, but modifiers after a head are ‘digressions’; it requires a little extra effort to pin down where the phrase ends.

Modifiers typically affected by this rule are

• participle phrases, because a participle in its ‘verb’-al aspect often takes postposed complements and adjuncts. Your prompted by the scandal is an example.
• preposition phrases, because a preposition is the head of the phrase and is usually followed by an object. Your by the scandal is an example—we do not say ∗by the scandal prompted.
• adjectives taking complements, like grateful for help above.

There are exceptions to this rule, such as ready-to-wear, off-the-cuff—but note that in writing we hyphenate such phrases, to overcome the parsing difficulty. Some, however, are so frequently used that they have ‘hardened’ into single words—inline, online, offline are some recent examples.