In this paper, we study the positive impact that the availability of ``Sense of Direction'' has on the message complexity of the Election problem in arbitrary networks of processors. We present a Theta(n log n) solution ; without sense of direction, this problem requires Omega(e + n log n) messages where e is the number of communication links. This result confirms and extends the evidence on the impact of sense of direction which, up to new, was established only for specific classes of topologies.