agent’s performance on the task.

For each agent, we can then determine his or her psychometric function: the probability of the agent choosing the second answer as a function of the stimulus, $P(c)$. An ideal responder would be described by the Heaviside step function: $P(c)=0$ for all negative stimuli, and $P(c)=1$ for all positive stimuli (i.e., choosing the second interval if and only if $c>0$).

Because responders make errors, the actual decision rule and probability are different. One way to describe such a response is derived from signal detection theory [@Sorkin2001]. According to it, for a stimulus $c$, a participant perceives stimulus $x$, which is a normally distributed random variable centered around $c+b$ and with variance $\sigma$, and decides basing on the sign of $x$. Two models described in this paper (Weighted Confidence Sharing and Direct Signal Sharing) use this mechanism explicitly. The modified realistic decision rule of an agent states that if the observed stimuli $x$ is negative, an agent decides to select the first patch (therefore interpreting the difference in contrast as negative), in the case of positive value, the second option is selected.

In particular, psychometric curves which are cumulative of the normal distribution: $$\begin{aligned}
P(c)&=H\left(\tfrac{c+b}{\sigma}\right),\qquad\hbox{ where}\label{eq:pdef}\\
