Delegation of rights is a common practice in the real world. We present two identity-based threshold proxy signature schemes, which allow an original signer to delegate her signing capability to a group of n proxy signers, and it requires a consensus of t or more proxy signers in order to generate a valid signature. In addition to identity-based scheme, privacy protection for proxy singers and security assurance are two distinct features of this work. Our first scheme provides partial privacy protection to proxy signers such that all signers' identities are revealed, whereas none of those t participating signers is specified. On the other hand, all proxy signers remain anonymous in the second scheme. This provides a full privacy protection to all proxy signers; however, each valid signature contains a tag that allows one to trace all the participating proxy signers. Both our proposed schemes are secure against unforgeability under chosen message attack, and satisfy many other necessary conditions for proxy signature.