Before revision:  Our main results are that the standard definition of error-free CRNs have equivalent computational power to  1) asymmetric and 2) democratic CRNs. The former have only "yes" voters, with the interpretation that the CRN's output is yes if any voters are present and no otherwise.
After revision:  Our main results are that the standard definition of error-free CRNs have equivalent computational power to 1) existence-based and ( 2) democratic CRNs. The former have only "yes" voters, with the interpretation that the CRN's output is yes if any voters are present and no otherwise.