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I use _The Kodansha Kanji Learner's Dictionary_ , which describes
pronunciation in romaji instead of kana. I never learned romaji in a
classroom, and generally only use it when reading this dictionary.

When "ō" is not proceeded by a consonant (like "tō" is), how does one know how
transcribe it into kana?

I first used "おう" (such as "tō": "とう"); however, through trial and error, I
came to realize that "おお" is more accurate. Then, I came across the kanji `扇`
in my dictionary as "ōgi", and realized that, if I typed "おおぎ" or "おうぎ", both
displayed the option of `扇`.

It's quite possible this is a "spellcheck" type safeguard (the Japanese
equivalent of "the" being typed out when "teh" is entered) because I have
checked around various online dictionaries (Wiktionary, Yahoo!dict) and it
turns out that in this case, `「おうぎ」` is indeed the correct transcription. Is
there a definitive way of knowing in other cases, solely by reading the
romaji?
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2011-12-08T18:11:00.517
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spelling hiragana rōmaji
How does one transcribe the romaji "ō"?
It depends. In most cases it is おう. But is some words, the "おお" form is
retained, such as "大【おお】きい", "多【おお】い", "遠【とお】い", etc.

For 扇, I'd believe if the dictionary doesn't have おおぎ, it should be incorrect.

(btw, from the transcription of おうぎ in classic Japanese (あふぎ) which is shown
in the dictionary, the transcription now can only be おうぎ.)
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2011-12-08T18:34:09.840
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If it's a kanji, and it's an ON reading of the kanji, it's almost certainly
オウ.

Ex. Tōkyō = とうきょう

With kun readings, you just have to know which one. I don't think it's an
especially common occurrence, so knowing the common cases (おおきい,
おおい、とおる）should be pretty sufficient.

Even if you get it wrong, you'll be understood.
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2011-12-08T22:49:32.917
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You seem to be considering the relation between the written and the spoken
forms in the opposite way. Indeed, the writing system of a language always
appears after the spoken form to transcribe it. But that is true only at the
beginning. As time passes, the spoken form undergoes language change faster
than the written form. As a result, when you see a discrepancy between the
written and the spoken forms, the written form is not the (exact)
transcription of the spoken form any more. It is the opposite: the spoken form
is rather the (rough) reflection of the written form (which is tied to the
original spoken form). There are both words that are written in kana as `おう`
(`[王]{おう}[位]{い}`) and `おお` (`[多]{おお}い`). They are the underlying forms. They
converge into the same pronunciation "ō" because of the phonological rules. It
is not the other way around. There is no mapping from the pronunciation "ō" to
the written forms `おう` or `おお`. But the mapping from the written forms `おう` or
`おお` to the pronunciation "ō" is simple: `ou → ō`.
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