Comparing two committed values Given two commitments on different values, Can a third party compare those two commitments to know which one is the higher value?
If there's a trusted third party who needs to do the comparison (and you don't care if the trusted third party knows the committed values), then it's actually quite simple.

Take your favorite public key encryption algorithm; remember that a public key encryption algorithm can be represented by $E_{pub}(x, r)$, where $pub$ is the public key, $x$ is the value being encrypted and $r$ is a random value; this random value makes the encryption nondetermanistic.

Now, have the trusted party generate a public/private key pair, and have him publish the public key.

To commit a value $x$, Alice would select a random value $r$, and publish the value $E_{pub}(x, r)$.  Assuming that $E$ is a secure public key encryption system, no one can recover $x$ without the private key (and we assume that only the trusted third party knows that private key).

The open the commitment $E_{pk}(x, r)$, Alice would reveal the values $x$ and $r$; anyone can verify that those values (along with the global public key) generate the commitment.

And, because the trusted third party has the private key, he can examine $E_{pk}(x, r)$, recover $x$, and check if it is a sane value, and check how it compares to another commitment.