The most common and most likely answer to this crossword clue is the 7 letter word GUESSES
I've seen this crossword clue in The Guardian
G
U
E
S
S
E
S
Buddy explains!

The straight part
We know that "Ill-informed judgments" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case ill-informed judgments = guesses.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does GUESSES mean?
GUESSES verb- To reach a partly (or totally) unqualified conclusion.
- To solve by a correct conjecture; to conjecture rightly.
- To suppose (introducing a proposition of uncertain plausibility).
- To think, conclude, or decide (without a connotation of uncertainty). Usually in first person: "I guess".
- To hit upon or reproduce by memory.
- A prediction about the outcome of something, typically made without factual evidence or support.