Homomorphic crypto allowing anonymous yes/no votes?
A homomorphic cryptosystem has some operation $*$ on ciphertexts that correspond to some other operation $\circ$ on plaintexts, that is
$$\mathcal{D}(c_1 * c_2) = \mathcal{D}(c_1) \circ \mathcal{D}(c_2).$$
Typically, the ciphertexts you get by applying $*$ look like ciphertexts that are produced by the encryption algorithm. For Damgård-Jurik, $*$ is multiplication modulo $n^{s+1}$ and $\circ$ is addition modulo $n^s$.

A cryptosystem is secure if the ciphertext does not help you to say anything about the message encrypted.

Suppose you encode "yes" as $1$ and "no" as $0$. The voter will encrypt his encoded vote and send it to the server. Suppose the server receives ciphertexts $c_1, c_2, \dots, c_L$ that are all encryptions of $0$ or $1$. The server can now multiply the ciphertexts to get a single ciphertext, which by the above requirement will satisfy
$$\mathcal{D}\left(\prod_i c_i\right) \equiv \sum_i \mathcal{D}(c_i) = \text{number of "yes" votes.}$$
The server can therefore find the correct election result by decrypting the product ciphertext.

It does not really matter how many ciphertexts are submitted.

If the server is passive (honest-but-curious, will try to break confidentiality without deviating from instructions), the voters are honest and the cryptosystem is secure, the server cannot deduce anything about the votes from the ciphertexts (except the result, of course, since he decrypted a ciphertext containing the result). Damgård-Jurik is generally believed to be secure.

The interesting question is of course what happens when the voters aren't honest or the server tries to cheat. There's a lot of nice cryptography in the answers to those questions.