How can I make a check_box_tag to post a ‘false’ or ‘0’ parameter when unchecked?

check_box (w/o _tag) helper adds hidden field to address your problem for you:

<%= check_box 'object', 'boolean_attribute', {}, 'true', 'false' %>

# result:
<input name="object[boolean_attribute]" type="hidden" value="false" />
<input id="object_boolean_attribute" name="object[boolean_attribute]" type="checkbox" value="true" />

UPD: Dealing with nested resources (Product accepts_nested_attributes_for :line_items)

= form_for @product, url: '' do |f|
  %p
    = f.label :title
    = f.text_field :title

  = f.fields_for :line_items do |li|
    = li.check_box :approved
    = li.label :approved, li.object.id
    %br
  = f.submit

Checking 2 of 3 checkboxes gives me the params as this:

{…, “product”=>{“title”=>”RoR book”, “line_items_attributes”=>{“0″=>{“approved”=>”0”, “id”=>”47”}, “1”=>{“approved”=>”1”, “id”=>”48”}, “2”=>{“approved”=>”1”, “id”=>”51”}}}, “commit”=>”Update Product”, “action”=>”action1”, “controller”=>”test”}

params as YAML for readability:

product:
  title: RoR book
  line_items_attributes:
    '0':
      approved: '0'
      id: '47'
    '1':
      approved: '1'
      id: '48'
    '2':
      approved: '1'
      id: '51'

See? No hidden fields but checked/unchecked states are clearly distinguished.

Having this params allows me to use one line of code to update associated line_items:

@product.update_attributes params[:product]

I hope it helps.