Can we use bash's conditional operator with assignment operators after colon?

[Bash reference manual](http://www.gnu.org/software/bash/manual/bashref.html#Bash-Conditional-Expressions) explains the arithmetic operators as follows.

- conditional operator `expr ? expr : expr`
- assignment `= *= /= %= += -= <<= >>= &= ^= |=`


Fisrt, this code seems to work well.

`a=1; ((a? b=1 : 2 )) #seems to work`

But when I use assignment operators after `:`, I got 'attempted assignment to non-variable' error.

`a=1; ((a? b=1 : c=1)) #attempted assignment to non-variable error`





Why can we use only assignment operators before colon?