cumulative Gaussian function. Moreover, when there are no biases, for all decision-making considered in this paper, the maximal slope is at $c=0$.

A question arises about the relation between the psychometric curve parameters and the expected rate of errors. To assess the average amount of incorrect answers we could expect from a responder, we introduced the following quantity, $$\begin{aligned}
W(\sigma,b) &= \int_{-\infty}^{0}P(c)dc + \int_{0}^{\infty} \left[ 1-P(c)\right]dc\\ 
 &= \sqrt{\frac{2}{\pi}}\sigma \exp\left(-\tfrac{b^2}{2\sigma^2}\right) + b\left[ 2H\left(\tfrac{b}{\sigma}\right)-1 \right]\label{eq:penaltyres},\end{aligned}$$ where we integrated the error function [@AbramowitzStegun1965]. For a uniform distribution and range of stimuli, $(-r,r)$ for $r \gg (\sigma + |b|)$, the rate of the incorrect responses is given by $W(\sigma,b)/(2r)$. The average number of wrong answers is always reduced when lowering either width or bias, regardless of the other parameter’s value. This fact further justifies the choice of the slope as the proper effectiveness measure. When there is no bias, simplifies to $W(\sigma,0)=2/s$; thus, the rate of the incorrect responses is $1/(r s)$.

Information-sharing models {#s:communication}
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In this section, we discuss different models of information sharing for $n$ participants. It is important to underline that the models incorporate the process of perceiving (what the subjects may know), the state of mind (what the subjects 