The &filter should use field,criteria,mode so if it should only work on those who have West checked you should write this:
&filter=`West,2,1|East,1,1|South,1,1|North,1,1`
So it sais: Select a document that West is checked and East isnt checked and South isnt checked and North isnt checked.
You could also create a snippet that does this and goes through the children of parent=5 and echoes out a commaseparated list with all the children IDs and put them in a &documents parameter. Something like this:
[[Ditto? &documents=`[!FindExclusive? &district=`West` &parentid=`5`!]`]]
In the Snippet-code you could write something like this (only pseudo-code under here):
$children = get all children from $parentid;
$documents = new Array();
foreach $children['id']{
Get the checkboxes from this child
Check if only the $district checkbox is checked
if it is true then fill inn the id in $documents-array
}
echo implode(',',$documents);
This will generate a commaseparated list of documents that only has West checked. And you could use the same snippet for East, North and South.