"My father cares more about the environment than the economy" Vs "My father cares more about the environment than he does the economy"
Does the first present an illogical comparison? I.e. Comparing the father's caring with the economy.
You certainly have less potential ambiguity in the latter sentence than the former one, but the former isn't wrong. Both are perfectly clear in practice, and I would be very surprised if anyone gave it a second thought if you went with the shorter version, even in the context of a conversation about this very topic. For example, did you notice how I started this answer? :)
With the conjunctive, "than", one can combine just a word which is the target of the comparison, or a phrase or clause which shows more detailed information. In other words, just putting the one and only word as a target of comparison is meant to denote the "omitted" version-ellipsis- of such clauses.
Taking your examples, as other repliers said, "My father cares more about the environment than the economy" is equal to "My father cares more about the environment than he does the economy". Then when one explicates this in a syntactic way, the structure is like this; "My father cares more about the environment than (he does) the economy" Therefore, in this context, in the "than" clause, the parts of the subject and the verb which the main clause has in common(that is, the subject and verb of the main clause(My father, to care about) are equal to those of the than clause(he, to do)), are omitted because of their commonness and the rest is left alone, for it is the main target of the comparison(in this case, what is compared is the object of "my father's" attention.)
This structure can be applied to many more interpretations. "He's taller than I (am)." (attention; in this case, in colloquial ways, this "I" can be replaced by "me") "This airline is cheaper than any other airline (is)." "This book is better than I expected (that it is)."(the focus of the comparison is put on the difference from the expectation.)
What you should be careful about is, the possibility of the use of "than" as pseudo-relative. Take an example; "My uncle had drunk more than was good for him." In this case, "than" serves as a subject of the relative clause, but it doesn't denote something clearly. Of course it means "My uncle had drunk more than the quantity that was good for him.", in other words, he'd drunk very excessive amount. Thus this "thus" means "quantity of liquor". For another example; "I have more mail than I can read in one hour." In this case, of course this "than" functions as an objective of the relative clause, whose sense is "mail".
I agree with Lemma except that probably, you'd either stop at '…than about the economy' or go on to the more formal '… than he does about the economy'
Does that make sense?