php.php

$article_supplier = Shopware()->Db()->fetchAll("SELECT a.id article, s.name supplier FROM s_articles a, s_articles_vote av, s_articles_supplier s WHERE a.id = av.articleID AND s.id = a.supplierID GROUP BY (av.articleID)");

        foreach ($article_supplier as $a_s) {
            $sql = "UPDATE `s_articles_vote` 
              SET 
                `supplierName` = '" . $a_s['supplier'] . "'
              WHERE 
                `voteID` = '" . $a_s['article'] . "'
            ";

            Shopware()->Db()->query($sql);
        }

query.sql

UPDATE s_articles_vote av 
INNER JOIN (
SELECT a.id article, s.name supplier FROM s_articles a, s_articles_vote av, s_articles_supplier s WHERE a.id = av.articleID AND s.id = a.supplierID GROUP BY (av.articleID)
) AS s
SET av.supplierName = s.supplier
WHERE av.`articleID` = s.article
;