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There might be some debate here. I personally prefer the second version, but the first is likely acceptable because one simple tense (simple past) is being compared to another (simple future): a reader can discern that how Mary walked is being compared to how Mary will [walk].

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Yes, the rule needs to be qualified.
When a helping verb such as has refers to a verb in a parallel form, do/did is typically not needed because the helping verb is sufficient on its own to imply the omitted verb. (Often, we don't even need the helping verb: John has eaten more cookies than Mary is sufficient to imply that John has eaten more cookies than Mary HAS EATEN.)

In the sentence here, to increase and has increased are not parallel verb forms. Thus, the helping verb has is NOT sufficient on its own to imply the intended comparison. To make the comparison clear, the SC above uses has DONE (which is standing in for has INCREASED).

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We should be skeptical: has done -- at least on the GMAT -- should be used to stand in for a verb in the same form, but no suitable antecedent verb appears in the preceding clause here.

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You're suggesting that a reader might make the following interpretation:

John has eaten more cookies than Mary has cookies.

I doubt that any reader would interpret the sentence this way.
The expectation is that the second clause will be parallel to the first.
Thus, the default interpretation here is that how John has eaten cookies is being compared to how Mary has eaten cookies.

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i received a private message regarding this thread.

here's the best -- and simplest -- way i can think to simplify this issue:
the helping verb “will” is the future-tense form of the helping verb “do”.

this should take care of all the problems regarding this issue all at once.

with this rule/adjustment, all of the following sentences are now in the same basket:
david looks better today than he did yesterday.
david looks better than his brother does.
david looks better today than he will tomorrow.

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vikram, go back and read rule #3 in that post again. it appears that you read the part in parentheses but missed the big boldface capitalized part right beforehand.
when you see “do” in the second part of one of these sentences, it is sometimes parallel to another form of “to do” -- hence the parenthetical comment -- but it's usually parallel to an ACTION VERB. for instance, note that the forms of “do”, in the example sentences on that thread, are parallel to the forms of “disappear” (an action verb).


this sentence is fine, although the second “look” is unnecessary (“will” is a form of “to do”, as noted above, and so is already sufficient).

this one is wrong.
if “will do” is acting as a full verb -- i.e., not a helping verb -- then the sentence is wrong because that verb no longer carries the meaning of “look”.
if “will do” is acting as a helping verb, then it's redundant (“will” and “do” are both forms of “to do”, so you don't need both of them).

for comparison purposes, here is one correct sentence for each of those types of constructions:

* do as a normal (non-helping) verb: Scott accepts more assignments than he will actually do.
(in this sentence, “do” does not stand for “accept”; it just means “do”, as in “complete the assignment”.)

* do as a helping verb: Scott accepts more assignments this year than he will next year.
(in this sentence, “will” is a form of the helping verb “do”. it stands for “will accept” all by itself.)

this one is correct. see above.

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Ron is a Director of Curriculum Development at Manhattan GMAT. He has been teaching various standardized tests for almost 20 years.

He wears white after Labor Day, gets 55% of his calories from protein, and takes standardized tests for fun.

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