 Each instance \(x\) of the facts \(\mathbf{x}\) defines a type (reference class) of tasks: those tasks in which the facts are \(x\). Some instances of the facts \(\mathbf{x}\) make it easy to form correct judgments: instances \(x\) where the evidence is transparent, witnesses are honest, laboratory tests are correct, etc. Here individuals \(i\) are competent: \(P(R_{i}|x)&gt;\frac{1}{2}\). Perhaps some other instances of the facts \(\mathbf{x}\) make it hard to form correct judgments: instances \(x\) with misleading evidence, etc. Here voters are not competent: \(P(R_{i}|x)\leq\frac{1}{2}\). Whether misleading instances exist—i.e., whether CC fails—depends on the facts variable \(\mathbf{x}\) used. If all common causes are packed into \(\mathbf{x}\) (presumably to ensure Conditional Independence CI), then almost inevitably certain instances \(x\) of \(\mathbf{x}\) represent misleading circumstances, in which voters \(i\) have low competence \(P(R_{i}|x)&lt;\frac{1}{2}\). Ironically, if one packs much less information into the facts \(\mathbf{x}\), possibly even reducing \(\mathbf{x}\) to the state (often a variable with just two instances), then one may well rehabilitate Conditional Competence, whilst sacrificing Conditional Independence. This is the dilemma.