Is it feasible to design a crypto scheme for centralised reporting of anonymized data?
Ok, here's what I got:


Someone selects two large primes $p$ and $q$ such that $n = 2pq + 1$ is prime, and $pq$ is large enough to make factorization infeasible; they select a value $g$ with order $p$ in $Z^*_n$ and a value $h$ with order $q$ in $Z^*_n$ (e.g. select a random $s$ in the range $[2, n-2]$ and set $g = s^{2q} \bmod n$ and $h = s^{2p} \bmod n$ and verify that neither $g$ nor $h$ are 1).  Someone (and it need not be the same someone) also selects a symmetric encryption key $k$.
The authority gets the values $q, n$ (and optionally the values $g, h, p$; the authority doesn't need them, but it wouldn't hurt security), the authority does not get $k$. Each "reporting party" gets the values $g, h, n, k$.
For a reporting party to convert original information $i$ into derived information, he first deterministically encrypts $i$ with the key $k$ (forming $E_k(i)$), selects a random value $r$, and computes $d = g^{E_k(i)}h^r \bmod n$, which is the derived information, which he can send to the authority.
For the authority to compare two derived information $d_1, d_2$ to see if they correspond to the same original one, he computes $(d_1 d_2^{-1})^q \bmod n$, if that is 1, then the original information is the same.


This works because $d_1 = g^{E_k(i_1)}h^{r_1}$ and $d_2 = g^{E_k(i_2)}h^{r_2}$, hence $(d_1 d_2^{-1})^q = (g^{E_k(i_1)}h^{r_1} \cdot g^{-E_k(i_2)}h^{-r_2})^q = (g^q)^{E_k(i_1) - E_k(i_2)}$, which is 1 if $E_k(i_1) = E_k(i_2)$, that is, if $i_1 = i_2$

As for your requirements:

1) The authority does not directly receive original information

2) The authority can compare two different derived information; it cannot otherwise reconstruct the original information; that is because of the symmetric key $k$; given $g^{E_k(i)}$, the attacker might be able to recover $E_k(i)$ (actually, he couldn't, however if the $E$ function was public without a secret $k$, he could, given the short range of possible $i$ values), however because he doesn't know $k$, that's as far as he could go.

3) Reporting parties are dynamic; all reporting parties are given the same information, and so adding more is not an issue; they cannot determine if other parties have contributed the same information; because they don't know the orders of $g$ and $h$, they cannot determine this.

4) Two or more parties cannot collaborate to subvert the system; because all reporting parties get the same information, two parties don't have any more power than one.

Now, a reporting party and the authority could collaborate to recover another reporting party's original information; this is actually inherent in the problem, and so is not an issue (at least as far as I'm concerned; you may consider it a deal-breaker, in which case you need to rethink the problem).  You could make it somewhat more difficult by replacing an invertible encryption function $E$ with a keyed hash $H$ (and assume that two different inputs just don't collide); however given the small range of the original information, it won't help that much...