his or her psychometric skills. In the work of @Bahrami2010, this model is called ’Coin flip’.

#### Results {#results .unnumbered}

$$\begin{aligned}
P_{RR}(c) &= \frac{1}{n}\sum_{i=1}^{n} P_i(c)\end{aligned}$$

After the differentiation, one obtains the slope and the bias : $$\begin{aligned}
s_{RR} & \approx \frac{s_1+\ldots+s_n}{n}\\
b_{RR} & \approx \frac{s_1b_1+\ldots+s_n b_n}{s_1+\ldots +s_n} \end{aligned}$$ The relative error both for $s_{RR}$ and $b_{RR}$ is $O(s_1^2 b_1^2) + \ldots + O(s_n^2 b_n^2)$. Note that $P_{RR}(c)$ is not normal .

Voting {#s:vot}
------

#### Model {#model-1 .unnumbered}

Each participant makes her or his own decision. The majority vote determines the decision of the group. In a case of equal votes for two outcomes, a coin is flipped.

#### Motivation {#motivation-1 .unnumbered}

People may have no access to their accuracy (or they cannot communicate it reliably); thus, a good strategy is to take voting as the final consensus result.

#### Results {#results-1 .unnumbered}

$$\begin{aligned}
&P_{Vot}(c) = \sum_{k=1}^{\lfloor \frac{n-1}{2} \rfloor} \sum_{\vec{i}} \left[ 1-P_{i_{1}}(c)\right]\cdots \left[ 1-P_{i_{k}}(c)\right] P_{i_{k+1}}(c)\cdots P_{i_{n}}(c)\\
 & +\left[ \frac{1}{2} \sum_{\vec{i}} \left[ 1-P_{i_{1}}(c)\right]\cdots  \left[ 1-P_{i_{n/2}}(c)\right] P_{i_{n/2+1}}(c)\cdots P_{i_{n}}(c)  \right]_{\mbox{if $n$ is even}},\nonumber\end{aligned}$$

where sum over $\vec{i}$ denotes sum over every permutation of participants. We obtain (derivation in \[s:appvot\]) $$\begin{aligned}
s_{Vot} &\approx
\frac{s_1+\ldots+s_n}{n}\times
\left\{
\begin{matrix}
\frac{n}{2^n} {n \choose n/2} & \hbox{if $n$ is 