participants know their $z$-scores on a given trial but are unaware of their own parameters $s$ and $b$. This model was first introduced by @Bahrami2010. It is possible that, in an experimental trial, each participant can estimate and effectively communicate their relative confidences, by using a coarse real-world approximation of one’s $z$-score, e.g., ’I lean towards 1st’, or ’I am almost sure it is the 2nd’ [@Fusaroli2012]. The study by @Bahrami2010 suggests that this model most accurately describes dyad performance.

Given relative confidences $\vec{z}=(z_1,\ldots,z_n)$, the group has to determine whether to choose the first or the second option. If there are only two participants with different opinions, the one with the stronger confidence (for a given trial) decides. This can be written as follows: the group chooses the first option if $z_1+z_2 \leq 0$, the second option otherwise, yielding an optimal strategy [@Bahrami2010]. In the general case of $n$ participants, we use the Bayes optimal reasoning. We calculate the probability that the stimulus is positive (and thus the second answer is correct) given the $z$-scores provided by each participant: $$\begin{aligned}
p(c>0|\vec{z}) = \int_{c=0}^\infty p(c|\vec{z})dc
= \frac{\int_0^\infty p(\vec{z}|c)p(c)dc}{\int_{-\infty}^\infty p(\vec{z}|c)p(c)dc},\label{eq:whenposit}\end{aligned}$$ where $p(c)$ is the probability of a discrimination task with $c$. The 