"India's army, in numbers, is second only to China's and America's."

The odd sentence

India's army, in numbers, is second only to China's and America's.

appeared in the article Contest of the Century in the current issue of The Economist (August 21-27, 2010). Should the author have written third instead of second, or is it fine as it stands?

Second means also subordinate or inferior in position, rank, or importance; the New Oxford American Dictionary uses the following sentence as example:

It was second only to Copenhagen among Baltic ports.

The sentence doesn't mean that Copenhagen has the first position in the list of Baltic ports.

Similarly, I could write the following sentence:

His desire of being the next Bill Gates is only second to his desire of being the next Brad Pit, and his desire of being the new Paul Newman.

Looking at the Corpus of Contemporary American English, I found sentences like the following ones, where the comparison is made between one and more items:

In those early works the desire to belong was second only to drives like safety, hunger and reproduction.
Nixon himself harbored a deep distrust of the CIA, which he saw as a conspiracy of Ivy League liberals second only to those in the State Department.
She has personally raised more than $100 million, second only to Bill and Hillary Clinton, which she dispenses generously to her colleagues.
Second only to corn and soybeans in terms of U.S. cash value, these businesses—many small and family-owned—are busy greening up American streets and backyards.

In the sentence you wrote second is not referring to the position in a list; the sentence can be also written as the following one:

India's army, in numbers, is inferior only to China's and America's.

I agree that the sentence is a bit problematic. If we agree that

A is second only to B.

states that there is no other thing to which A is inferior in ranking, only B, which in turn logically strictly implies that B is ranked first and A is ranked second. Also, to clearly state - it is talking about absolute ranking within the scope of comparison. (Original quote might not be comparing all the countries in the world, but from the pool of compared countries, the rankings which are implied are absolute; due to the word "only").

So, if¹ we agree on the above logic and meaning, let us look at

A is second only to B and C.

Here we have a problem - if we decompose to “A is second only to B” and “A is second only to C” then we run into contradiction, according to the logic I presented this would imply that A is second and B and C are both ranked first.

However, if we skip this strict logic for a second, the only other interpretation that is possible is that A comes right after B and C, which are ranked higher than A². In this case however, as OP suggest, strictly logically we might be tempted to denote the absolute rank of A, which is indeed third, but that kind of notation is not so common (ngrams, keep in mind that expression “third only to” is represented only in portion of the results).

Still, though it is not as common as “second only to” there are quite a few instances, such as this:

third only to the Soviet Union and South Africa in 1985 in terms of output

This denotes absolute third place, stated exactly as OP intended, and after reading it a few times I come to opinion that it is quite natural and that the original should have been written like that:

India's army, in numbers, is third only to the China's and America's.

¹ If we don't agree see the usage in books.
² There would be no problem if the original quote was “India's army is second to America's and China's”, (second meaning inferior in rank) the problem occurs with introduction of the word “only”. As stated before “second only to”, as phrase, denotes absolute position; in the meaning of inferior in ranking there would be no problems to use it: “India's army is inferior in ranking only to America's and China's” is semantically perfectly fine.

My theory would be that the key here is the "numbers". Note the plural. The way I interpret this is as follows. If we take one number — say, the number of soldiers —, then India is second only to China (but not to the US). If we take a different number — say, that of nuclear warheads —, then India is second only to the US (but not to China). In other words, on some accounts India's army is second only to China's, and on others only to America's. So, I guess, the author just took a shortcut there by summing it up the way he did.

(Also, on a tongue-in-cheek side note, I can't help but notice that we have the idiom "second to none". Something in me says that if things can be second to none, they can also be second to two, or second to ten, or in fact second to any number.)

I'm with you, I.J. I think just about every reader of this sentence gets the point, but it is arguably an oxymoron. You see arguments in favor and against in all the other answers and comments here.

Whatever the final decision may be (if there can even be one), doesn't matter all that much. The fact that it engendered this much discussion, even amongst experts, is itself the problem. This seeming contradiction is going to make readers stumble over it, which in my book makes the whole thing at the very best inartful.

The author should have phrased the thought better.