We present various types of new electronic voting schemes, including two-way, multi-way and multi-selection election schemes, which guarantee privacy, universal verifiability, and robustness. Initially, a voter registers a polynomial function, his public key, with the election committee. Each voter uses his polynomial function to cast his vote in various elections. The distinct feature is that each term of a polynomial function corresponds to a candidate in a multi-way election. Thus, the final tally is independent among candidates, and the time complexity for searching final results is O(n). In our schemes, each voter contacts the authorities only once; thus, our schemes are practical and suitable for large-scale elections. For robustness, we use the witness indistinguishable technique to construct the proof of validity. Security, then, is based on the discrete logarithm and decisional Diffie-Hellman assumptions.