"I think him to be about 50" or "I think he is about 50"?

I have two options. Which one is correct?

a) I think him to be about 50.
b) I think he is about 50.

If both are correct, should I avoid one or the other?

It explains in this book that while "believe him to be" is a phrase commonly used in English (as is "consider him to be"), "think him to be" is not, and, further, that there is no apparent logic for why this should be so.

So the correct answer is (b), but if you're learning English as a second language, you shouldn't feel bad for not getting this right.

The vast majority of native speakers do not say *I think him to be about 50. This isn't some arbitrary idiomatic quirk, as has been suggested elsewhere - it's a subtle distinction based on the precise range of meanings covered by words such as think, believe, assume, judge, know, etc., and the implications of (pro)noun with "to be" + adjective constructions such as to be about 50.

I think you are beautiful gets 11,200 hits in Google Books, whereas I believe you are beautiful gets only 7 hits (and some of those seem to be from non-native speakers). Contrast this with I think you are honest (8240 hits), and I believe you are honest (3740).

GB "estimated results" behave very oddly with I think you to be honest - the first page says there are over 5000 results, but scrolling through you find there are only 11 (less than half-a-dozen, once you ignore the duplicates). By contrast, I believe you to be honest really does have over 2000.

Superficially, to think [sth] and to believe [sth] seem equivalent, but as the above examples clearly show, there's something else involved. Specifically, you can cause [sth] to be "true" (from your point of view), simply by "thinking" it. In the case of belief, [sth] is already objectively true or false, and you're either right or wrong depending on whether what you believe corresponds with reality. If you have an esoteric/solipsistic world-view I suppose you might think God [in]to be[ing] real, but in normal English you believe God to be real (or not, as the case may be). And your belief itself has no effect on His existence or lack thereof.

Why such a massive shift in verb preference simply dependent on whether the proposition being considered is phrased as you are honest, or you to be honest? We've already seen how think can imply a level of "interaction" with the "thought" that doesn't arise with believe. Now consider the different meanings of I expect you to be honest and I expect you are honest. Although the latter is relatively uncommon phrasing, I'm sure most people will understand it to be an "objective" statement of belief, whereas the former says what you would like to be true.

Since we commonly use the same format with "I want/would like/require/etc. you to be honest", obviously (pro)noun + "to be" + adjective associates strongly with constructions where the fact of [noun] being [adjective] is to some extent affected by our own attitude. But using the verb to think here is inherently problematic, because it highlights that uncomfortable split between personally bestowed/interactive assessment and objective belief.

I know this is already a long answer, but here's just one more set of GB results to ponder. I think they are explained by the fact that because "it" is more "impersonal" than "you", the potential for any implied "subjective interaction" with its "rightness" doesn't bother us so much.

• "I think you to be right" 4 results.
• "I think it to be right" 2220 results.
• "I think you are right" 888,000 results
• "I think it is right" 1,960,000 results.

TL;DR: Native speakers don't say they think [noun] to be [adjective] because this creates a "disjunct" between the verbs & phrasings we use for "wish fulfilment" and those we use for "objective assessment and statement of likelihood". If we intend the former, we say we think [noun] is [adjective]. If the latter, we believe [noun] to be [adjective].

There's a dedicated chat room if you want to see more of this issue being kicked around, or (please) contribute to the ongoing discussion and help find a clearer definition of why we avoid this usage.