Somewhat cryptic title, but a simple question.

> I start with the (logical?) assumption that kanji makes writing Japanese
> shorter than using romaji. How shorter is it compared to English written in
> Latin script, on average? For example, how many pages would an average 100
> page book in English (Latin) have in Japanese (kanji+kana)?

Are there some studies concerning this topic?
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kanji rōmaji english-to-japanese
Japanese language "compression ratio"
In computer encodings, a kanji or kana usually takes 16 bits, not 8 bits, and
even as much as 24 bits for really obscure kanji. In Weibo (the Chinese clone
of Twitter, i.e. Evil Censorship Profiteer), Chinese chars count as two ASCII
chars. Chinese (especially literary Chinese) is even more dense than Japanese
though.

From a linguistic perspective (not a computer storage perspective), Japanese
is very much the _opposite_ of dense. This is mostly due to Japanese words
being long:

> 緑 vs. green: 3 vs. 1 moras (グリーン is four...)
>
> 日本 vs Japan: 3-4 vs 2 moras

This is even more apparent when you factor in the agglutinative grammar of
Japanese:

> さゆりちゃんが来たので、とてもうしくなりましたね。 (22 syllables)
>
> I'm so happy that Mary came. (8 syllables)

This is part of the reason why Japanese is spoken so quickly, and why it likes
dropping pronouns so much. Nobody wants to say `私達は、あなた達と私達の昼ごはんをゆっくり食べました`
(36 syllables) for `We ate our lunch with you slowly` (8 syllables).

(Side note: earlier forms of Japanese were thought to have been spoken
**much** more slowly, due to the fact that the phonology was complex, and
things took less cruft to say.)
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An alpabet has roughly log(60)～6bits informations and a Kanji has roughly
log(3000)～12bits informations.

> Here we assumed that every character has equal frequency.  
>  More acculate estimates would be  
>  -Σ((probability of a character X)×log(probabily of a character X)  
>  (sum over every character X).  
>  If all the character have equal frequency, this sum becomes to log(total
> number of characters).  
>  If we include the space character into the sum above, the sum becomes
> smaller because the frequency of the space chacter in alphabetical texts is
> very high.

So a kanji character has as twice informations as that of an alphabet.  
Since each kanji character has twice width as that of an alphabet, and English
texts have many spaces, I estimate the total length of japanese texts would be
0.7～0.8 of English texts.

> We assumed the very important fact that  
>  'texts written in English and corresponding texts written in japanese have
> equal informations'  
>
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This is not an answer, but I will post it in the hope that it may resolve part
of your confusion. I am afraid that you seem to be mixing “shorter” in the
sense that it uses less _characters_ and “shorter” in the sense that it uses
less _area_ in typical typesetting (hence less pages in typical books,
assuming that the size of a page is similar in books in English and books in
Japanese).

I think that it is fair to say that text in Japanese tends to use less
characters than the corresponding text in English, because the writing system
of Japanese has more characters to choose from. However, for the same reason,
characters in Japanese tend to be more complicated than those in English, and
therefore characters in Japanese take more area when printed than those in
English. Therefore, it would not be surprising if books in Japanese sometimes
have more pages than the corresponding books in English.

Your comparison of the number of pages of novels in English and Japanese is
interesting (from your comment):

> I already did something on my own, comparing Anna Karenina, Crime and
> Punishment and Catcher in the Rye in Japanese and English (using Amazon book
> data). Interesting enough, the Japanese version of The Catcher in the Rye
> had more pages than the English one.

Although comparing three pairs of books is clearly not enough to draw any
conclusion, what you observed may have something to do with the fact that
_Catcher in the Rye_ is originally written in English and translated into
Japanese, whereas _Anna Karenina_ and _Crime and Punishment_ are originally in
Russian and translated into both English and Japanese. I would try to see if
the comparison gives the opposite results in case of novels originally written
in Japanese and their translations into English.

I have been always thinking that there may be a tendency that text translated
into some language is longer than text originally written in the same
language. I do not have any evidence for this hypothesis, but if this tendency
really exists, a hypothetical reason is as follows: A text (especially text in
novels) in some language is often written in such a way that it is natural in
that language, and probably natural text can often be concise. Translation
tries to reproduce the content and/or the atmosphere of the original text in
another language, which forces less natural way of using the language.
Therefore I think that it is a plausible possibility that translation often
sacrifices conciseness. Of course, this is just a hypothesis yet to be tested,
unless someone has already thought the same thing and tested it. [Edit:
PhoenixFox has already mentioned a similar point in a comment on user54609’s
answer, so it is at least not just me.]
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