  In this paper a new multi-candidate electronic voting scheme is constructed
with unlimited participants. The main idea is to express a ballot to allow
voting for up to k out of the m candidates and unlimited participants. The
purpose of vote is to select more than one winner among $m$ candidates. Our
result is complementary to the result by Sun peiyong$'$ s scheme, in the sense,
their scheme is not amenable for large-scale electronic voting due to flaw of
ballot structure. In our scheme the vote is split and hidden, and tallying is
made for $G\ddot{o}del$ encoding in decimal base without any trusted third
party, and the result does not rely on any traditional cryptography or
computational intractable assumption. Thus the proposed scheme not only solves
the problem of ballot structure, but also achieves the security including
perfect ballot secrecy, receipt-free, robustness, fairness and
dispute-freeness.
