There is a theory that security is increased by decoupling reward from transaction selection in pooled mining. The theory holds that by sharing only the reward, control over transaction selection shifts to miners with less hash power. This implies a reduction in the variance discount and therefore an increase the competitiveness of smaller mines. Because smaller mines can presumably operate more covertly than larger, this in turn implies that censorship resistance is increased.

The theory fails to recognize that control over transaction selection remains with the pool operator, and is therefore invalid. The sole benefit is variance reduction, but this is only realized by the receipt of payment. As payment is discretionary any condition may be attached. Such conditions may include censorship and identity. Member recourse is to leave the pool for another, just as with a coupled pool. As such decoupled pools and coupled pools are equally subject to co-option.

There is a related theory that transparency of a decoupled pool is greater than that of a coupled pool, facilitating flight of members to non-censoring pools, therefore limiting the dominance of censoring pools. Generously accepting the assumptions of greater transparency and independent miners operating against financial self-interest, we are still left with the fact of co-option. The state can still reserve for itself the ability to operate with the financial advantages of pooling and the theory is therefore invalid.

This fallacy is similar to the Relay Fallacy in that all financial advantage depends on otherwise independent miners granting control over that advantage to a single person.