ar_q.rb

User.includes(stamp: [:contact]).where(:user_type => 'franchisee').joins(:stamp).joins(:children).group("users.id, stamps.status").count("stamps.status")

ar_q.sql

SELECT COUNT(DISTINCT stamps.status) AS count_stamps_status, users.id, stamps.status AS users_id_stamps_status 
FROM "users" INNER JOIN "stamps" ON "stamps"."stampable_id" = "users"."id" AND "stamps"."stampable_type" = 'User' 
INNER JOIN "users" "children_users" ON "children_users"."parent_id" = "users"."id" 
LEFT OUTER JOIN "contacts" ON "contacts"."id" = "stamps"."contact_id" 
WHERE "users"."user_type" = 'franchisee' GROUP BY users.id, stamps.status

arel.rb

    users     = Arel::Table.new(:users)
    stamps    = Arel::Table.new(:stamps)
    contacts  = Arel::Table.new(:contacts)    
    children  = users.alias

    query = users.where(users[:user_type].eq('franchisee'))
    query = query.join(stamps).on(users[:id].eq(stamps[:stampable_id]))
    query = query.join(contacts).on(contacts[:id].eq(stamps[:contact_id]))
    query = query.join(children).on(users[:id].eq(children[:parent_id]))
    query = query.join(stamps).on(children[:id].eq(stamps[:stampable_id]))
    query = query.group users[:id], stamps[:status]
    query = query.project(users[:id], stamps[:status].count.as("count"), stamps[:status], contacts[:first_name], contacts[:last_name])

arel_sql.sql

SELECT "users"."id", COUNT("stamps"."status") AS count, "stamps"."status", "contacts"."first_name", "contacts"."last_name" 
FROM "users" INNER JOIN "stamps" ON "users"."id" = "stamps"."stampable_id" 
INNER JOIN "contacts" ON "contacts"."id" = "stamps"."contact_id" 
INNER JOIN "users" "users_2" ON "users"."id" = "users_2"."parent_id" 
INNER JOIN "stamps" ON "users_2"."id" = "stamps"."stampable_id" 
WHERE "users"."user_type" = 'franchisee' 
GROUP BY "users"."id", "stamps"."status"