Setting a cookie in WordPress plugin, cookie gets deleted automatically

I'm currently trying my hands on WordPress plugind developement for an exercise and came across some little snag.

The plugin is designed to display a simple poll in a widget on the front page. Once the visitor has voted, I use setcookie to drop a cookie containing his vote, and some simple code to change the widget so that it shows the results and the user cannot vote again until a new poll is proposed. The problem is, voting is still possible, the results are never shown. Looking at the logs with the developer's tools, I found that the cookie is deleted the second it lands on the client browser. Does anybody know why, and how I can correct that?

Here's the code. First, the action hook:

    public function __construct()
{
    parent::__construct('poll_plugin', __('Polls', 'poll_plugin'), array('description' => __('Simple poll widget', 'poll_plugin')));
    add_action('init', array($this, 'save_votes'));
}

Then, the actual action:

public function save_votes()
{
    global $wpdb;
    /*Cookie setting, 30 days expiration */
    if ( isset($_POST['option']) && !isset($_COOKIE['Poll_Votes']))
    {
        unset($_COOKIE['Poll_Votes']);
        setcookie('Poll_Votes', $choix, 30 * DAYS_IN_SECONDS, COOKIEPATH, COOKIE_DOMAIN);

        $choix = $_POST['option'];
        $id_choix = $wpdb->get_var("SELECT id FROM {$wpdb->prefix}poll_options WHERE label = '$choix'");
        $wpdb->query("UPDATE {$wpdb->prefix}poll_results SET total = total+1 WHERE option_id = '$id_choix'");
    };
    /*Testing the presence of a new poll */
    $vote = $_COOKIE['Poll_Votes'];
    /*If the cookie's value isn't found in the db, the poll's changed, so we reset the cookie*/
    if (is_null($wpdb->get_var("SELECT * FROM {$wpdb->prefix}poll_options WHERE label = '$vote'")))
    {
        setcookie('Poll_Votes', '', time()-3600);
    }
}

Quick note here, I already tried commenting the line designed to unset the cookie, it changed nothing.

The only other time where the cookie is mentioned is via the $_COOKIE global, in a isset().

And lastly, please forgive my english, I'm french :)

via Chebli Mohamed