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What is the **universal standard** used by Japanese natives to assign ordering
to a group of kanji that might be as simple as:  
[決、元、川、湖]

As a non-native, my thinking is that I can use the index# of the [Nelson
Character Dictionary](http://en.wikipedia.org/wiki/The_New_Nelson_Japanese-
English_Character_Dictionary):

  * Every kanji has a kangxi radical or is the radical itself.
  * Kangxi radicals have an already decided ordering.
  * Within a group of kanji with the same kangxi radical, the tie-break is stroke count.
  * _I don't know the final tie-breaker._

Nelson index# seems like a really good way to create an ordering, right?

But, there is zero chance that Nelson influences Japanese at all. It is just a
view of the Japanese language intended for non-Japanese to use. So, for
official Japanese bookkeeping, what is the universal standard for ordering
kanji?

Basically, as the 3rd largest economy in the world, Japan cannot have chaotic
record keeping. There must be a universally recognized way to order kanji. I'd
like to know what it is. Maybe it is as simple as a look-up table.
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kanji
Using the Nelson index# as a means to order kanji? What do natives use?
If you want an ordering of 漢字 by themselves, each 漢字 dictionary will tell you
what ordering they use for 漢字, as pointed out in the comments. As far as I can
tell, this is usually very close (if not identical) to the Nelson system
(which of course comes from the Kangxi dictionary of the 18th century).

A total order on 漢字 would likely be unpractical, because there are many
variant characters which should be considered. (Even other variant characters
may be newly discovered in old documents.)

The 常用漢字 table has been revised several times, as has the 人名漢字 table. It would
be unwise to attach much importance to the ordering there.

Lastly, Unicode has a total ordering, which will not change, although new
characters may be added in the future. (Of course it is unlikely that newly
added 漢字 characters will ever find their use in modern Japanese, although I'd
kind of like if 変体仮名 make a comeback; at the moment there are very few
Unicoded 変体仮名.)

In any case, Japanese _words_ (including names) may be ordered by the あいうえお
(the "dictionary" ordering), i.e. the kana table. (Every name in the 戸籍 has a
registered kana reading, which doesn't change.) In daily life, therefore, it
is not necessary to insist on a total order of 漢字, because 漢字 usually come
with a reading. If you ask a computer to order 漢字 "alphabetically" it will
give you the Unicode (or JIS) ordering.
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answer
One way is to order by total stroke order, so in your example, the Kanji for
"river" would come first.
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