H(x) &= \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{x} \exp\left(-t^2/2\right)dt,\end{aligned}$$ result in a good fit for the experimental data [@Bahrami2010]. The parameter $\sigma$ can be interpreted as the participant’s uncertainty about the decision. The parameter $b$ is the bias (offset); it represents a tendency to choose a particular answer, see Fig. \[fig:psychometric\]. The $P(c)$ function, defined as above, can be viewed as a convolution of the step function (the correct answer) and the Gaussian distribution (the discriminative error).

![Plot of the psychometric function, with shown slope $s$ and positive bias $b$. []{data-label="fig:psychometric"}](psychometric_ns.pdf){width="60.00000%"}

For our purposes, we assume that bias is much smaller than the characteristic width parameter, i.e., $|b|\ll \sigma$.

Consequently, $\sigma$ becomes the main determinant of the effectiveness of discrimination. It is convenient to choose the maximal slope of the psychometric function $$\begin{aligned}
s &= \frac{1}{\sqrt{2\pi}\sigma},\label{eq:slopesigma}\end{aligned}$$ as the primary measure of the responding agent’s effectiveness.

Now, we can proceed to extending the @Bahrami2010 models. We would like to know how the performance of a group of $n$ people depends upon their individual cognitive performances. Therefore, we need to solve the explicit formulas for the propagation of slopes and biases when combining several responders within each of the different models of communication: $$\begin{aligned}
s_{model} &= 