Post filtering is returning blank page

It turns out the cause of this lingering filter problem was to do with the way WordPress was set up as well as the argument of WP_Query. Once I changed the Your Homepage Displays setting to the latest posts and renamed front-page.php to be index.php, the filter began working and the blank page no longer showed.

Concerning the post filter, declaring the orderby parameter as part of the argument of WP_Query got it working. The code for the filter is as follows:

<form class="post-filters">
    <select name="orderby">
        <?php
            $orderby_options = array(
                'post_date' => 'Order By Date',
                'post_title' => 'Order By Title',
                'rand' => 'Random Order'
            );
            foreach($orderby_options as $value => $label):
                echo '<option '.selected($_GET['orderby'], $value, false).' value="'.$value.'">'.$label.'</option>';
            endforeach;
        ?>
    </select>
    <input type="submit" value="Filter">
</form>