know), and the communication and the decision-making process (usually Bayes-optimal). We briefly define the assumptions of each model and justify it in psychological terms. We give results in terms of the effective psychometric function, $P_{model}(c)$, the effective slope, $s_{model}$, and sometimes the effective bias, $b_{model}$ (as for a few models the bias is poorly defined). Whenever calculations of $P_{model}(c)$ are not straightforward, we give some insight into the underlying mathematics.

We investigate the following models:

-   \[s:rr\] Random Responder,

-   \[s:vot\] Voting,

-   \[s:bd\] Best Decides,

-   \[s:wcs\] Weighted Confidence Sharing,

-   \[s:dss\] Direct Signal Sharing,

-   \[s:tw\] Truth Wins.

Random Responder {#s:rr}
----------------

#### Model {#model .unnumbered}

The trial decision of a random group member is taken as the group decision.

#### Motivation {#motivation .unnumbered}

Random Responder serves as one of the reference models, and it is not expected to be fulfilled in most of realistic settings. Random factors determine the collective decision, i.e., communication is seen as ineffective within framework of this model. Sometimes the decision is not based on any evidence and people may have very misleading impressions of their own accuracy. Additionally, their decisions may depend more upon a group member’s charisma or persuasive skills than 