even} \\
\frac{n}{2^{n-1}} {(n-1) \choose (n-1)/2} & \hbox{if $n$ is odd} 
\end{matrix}
\right.\\
 &\approx \sqrt{\tfrac{2}{\pi}} \times \sqrt{n} \times \frac{s_1+\ldots+s_n}{n}\label{eq:svotas}\\
b_{Vot} &\approx \frac{s_1b_1+\ldots+s_n b_n}{s_1+\ldots +s_n}\end{aligned}$$ The $P_{Vot}(c)$ is not normal . The relative error both for $s_{Vot}$ and $b_{Vot}$ is $O(s_1 b_1) + \ldots + O(s_n b_n)$. Note that the addition of an odd member to a group does not increase its average performance. The formula is an asymptotic expression for large $n$, which utilizes the Wallis formula. For $n=2$, the Random Responder and Voting models yield the same results.

Best Decides {#s:bd}
------------

#### Model {#model-2 .unnumbered}

The most accurate member of the group makes the decision. This model is called [*Behavior and Feedback*]{} in @Bahrami2010. In this model, we will focus on the case with no bias, $b=0$. Nonzero bias would make the result difficult to state in explicit form; see for further explanation.

#### Motivation {#motivation-2 .unnumbered}

In some experimental settings, members of the group can determine, who is the most accurate (e.g., when feedback is present). Group members can then let that individual make the final decision. Studies by @Henry1995 suggest that, at least in some types of tasks, participants can identify the most proficient member, so 