Breakdown of Hann heldur að fólkið dæmi sig.
hann
he
halda
to think (believe)
sig
himself/herself/themselves (acc)
að
that (conjunction)
Questions & Answers about Hann heldur að fólkið dæmi sig.
Why is sig used here instead of hann, since it's in a different clause than the main subject?
This is a classic "long-distance reflexive." Usually, sig refers to the subject of its own clause (which is fólkið here). But because the second clause describes the main subject's (Hann) own thoughts, the reflexive pronoun reaches across the clause boundary to refer back to him. That's why it translates to "him" rather than "itself" here.
Does the subjunctive verb dæmi have anything to do with using sig across a clause boundary?
Yes, they are directly connected! Long-distance reflexives almost always require the subordinate clause to be in the subjunctive mood. The subjunctive signals that the event is happening inside the main subject's head, creating a grammatical "bridge" that allows sig to look past fólkið and point all the way back to Hann.
Why is the verb dæma in the subjunctive mood here in the first place?
The main verb halda means to think or believe. Using halda að (to think that) expresses a subjective opinion or thought, which always triggers the subjunctive mood in the following clause. So, the regular present tense (indicative) dæmir becomes the present subjunctive dæmi.
If fólkið means "the people," why isn't the verb plural?