How does the Sort Order of Products in Subcategories work?

Take a look at Mage_Catalog_Model_Resource_Category_Indexer_Product::_refreshAnchorRelations specially these lines:

$position = 'MIN('.
            $adapter->getCheckSql(
                'cp.category_id = ce.entity_id',
                'cp.position',
                '(cc.position + 1) * ('.$adapter->quoteIdentifier('cc.level').' + 1) * 10000 + cp.position'
            )
        .')';

cc and ce are the same catalog_category_entity table and cp is catalog_category_product table.

A product can be in more than one child categories so the product position is a minimum between multiple values.
So basically the product position in the parent category is the minimum between the positions relative to each categories from the table catalog_category_product following this formula:

(child category position + 1) * (child category level + 1) * 10000 + ( product position in catalog_category_product + 1)  

[EDIT]
Conclusion: products in a category with a position higher in the tree will be shown before the ones below.