Why would Lucilius want the enemy to think he is Brutus?

When Cassius says, "Three parts of him is ours already", he is talking about Brutus and means that Brutus is almost on Cassius and Cinna's side. What is the reason they so desperately want Brutus to join them? Cassius and Cinna desperately want Brutus to Join them because Brutus is well likes among the people.

Explanation:

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ok so like i went to wiki and looked up the (constitution x new "hammystan")and it showed me the picture it highlights new hampshire and says first and second session and than it says that they hit up the u.s and was like "ey dude that paper u sent us was adopted it bro thx" xd syays it all on wiki/the pic

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