correct answer to easily convince the rest of the group of its correctness [@Laughlin1975]. People know if they see the ’right’ stimuli (and all errors are due to guessing, not to false observations). This model has received much attention in group decision theory, e.g., in @Davis1973. It is appropriate in situations when the correctness of a solution can be demonstrated. However, we do not expect this model to be applicable to tasks similar to that of @Bahrami2010. This model serves as a control and an explicit example of a result beyond one provided by the Direct Signal Sharing model. We included it with the aim of generalizing the models to different decision situations.

#### Results {#results-5 .unnumbered}

The probability that the responder knows with certainty the right answer is $$\begin{aligned}
R(c) = \left| 2 P(c) - 1 \right|.\end{aligned}$$ That is, we have a reversed formula saying that, when a responder knows the answer with probability $R(c)$, the responder answers correctly with probability $R(c)+(1-R(c))/2$ (as there is the chance to answer correctly by a random guess). The probability that at least one person knows the correct answer is $$\begin{aligned}
R_{TW}(c) &= 1 - \left[ 1-R_1(c)\right]\cdot\ldots\cdot\left[ 1-R_n(c)\right].\end{aligned}$$ Consequently, $$\begin{aligned}
P_{TW}(c) &= \frac{\mbox{sign}(c)R_{TW}(c) 