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Zkp that prove that the ciphertext is a reencryption of a cipher from an ensemble of cipher

So I had a question about ZKP protocol, I had to create one by myself and I am not sure if it is valid.I’ll try to explain, if you need any precisions, don’t hesitate to ask. In an election system, the voters are allowed to copy the vote of a deleguate. They need to do ::Listen

So I had a question about ZKP protocol, I had to create one by myself and I am not sure if it is valid.I’ll try to explain, if you need any precisions, don’t hesitate to ask.

In an election system, the voters are allowed to copy the vote of a deleguate. They need to do so without any exchange of information with the deleguate in order to avoid the deleguate to get any information of who votes for him.
The protocole here is an attemp to make them able to proove that they copied a vote from a deleguate, a valid vote. Here is a capture of my protocol so far.

I did this protocol from a suggestion of my assistant, but as it is my first time concepting a new Sigma protocol i have no clue if he is valid.
Can you tell me if this protocol is valid or close to valid ? Any help in that sense would be greatly appreciated ! I can join the proof of completness, special soundness and zero-knowledge of this proof (even tho I did them really fast) if you need them.

Thanks a lot !