Rails Multiple Input Field in Form to One Integer Attribute in Model

From a UI perspective this seems broken... users will be able to associate any model year & name with any manufacturer, even if that manufacturer did not produce that model year & name.

Assuming you will introduce some javascript to handle that, from a rails perspective you will get undefined behavior with two :bat_id fields in the same form. I think you need this:

<h3>Select Brand</h3>
<%= f.collection_select :manufacturer_id, Manufacturer.all, :id, :manufacturer, include_blank: true %>
<h3>Select Bat</h3>
<%= f.collection_select :bat_id, Bat.all, :id, :model_year_and_name, include_blank: true %>

Alternatively you can just create one dropdown containing a composite field, like this:

<h3>Select Bat</h3>
<%= f.collection_select :bat_id, Bat.all.sort {|a, b| a.manufacturer_model_year_and_name <=> b.manufacturer_model_year_and_name}, :id, :manufacturer_model_year_and_name, include_blank: true %>

and then in your Bat model introduce something like this:

def manufacturer_model_year_and_name
  "#{self.manufacturer.name}: #{self.model_year_and_name}"
end

As discussed in your other answer, you shouldn't need to store the manufacturer_id on your review model.

I would recommend creating a Manufacturer select that isn't accessed in your Review model, but is simply used to filter the list of bats on the form.

The best way to do this is probably to add some custom data attributes to the Bat select.

<%= collection_select :manufacturer, :manufacturer_id, Manufacturer.all, :id, :manufacturer %>
<%= f.select :bat_id, Bat.all.map{ |b| [b.model_year_and_name, b.id, {'data-manufacturer' => b.manufacturer_id}] } %>

Then use some javascript to filter the Bat select when the Manufacturer select is changed.

Unfortunately you cannot just set display: none to an option element to hide it. This does not hide the option in many browsers. So the best method is to use a bit of jQuery to clone the original select every time the manufacturer select is changed, and remove any option that isn't associated with the selected manufacturer. Like so:

// rename the original select and hide it
$('#bat_id').attr('id', 'bat_id_original').hide();

$('#manufacturer_id').on('change', function() {
    $('#bat_id').remove(); // remove any bat_id selects
    $bat = $('#bat_id_original')
        .clone() // clone the original
        .attr('id', 'bat_id') // change the ID to the proper id
        .insertAfter('#bat_id_original') // place it
        .show()  // show it
        .find(':not(option[data-manufacturer="' + $(this).val() + '"])')
            .remove(); // find all options by other manufacturers and remove them
});

You might need to change a few things to get this to work in your installation, but you can view a static demo on jsFiddle here: http://jsfiddle.net/JL6M5/

You will probably need to reject the manufacturer_id field on form submit, avitevet already pointed out this answer which should help there: Rails: Ignoring non-existant attributes passed to create()