Creating a Multi-Level Associative Object Using AJAX

If you want to pass a complex value, your best path is probably to jsonify it. Something like

$.post( MyAjax.ajaxurl, {
    action: 'my_action',
    someValue: JSON.stringify({
        one: 'Some Value One',
        two: 'Some Value Two',
        three: 'Some Value Three',
        four: 'Some Value Four',
    })
} );

and then on the server side you decode the value with

$someValue = json_decode($_POST['someValue']);

At this point $someValue should be the array you wanted to pass.