the feedback is provided, we can plot $x$ versus $c$ to get $\sigma$.

#### Results {#results-4 .unnumbered}

The final group decision follows the standard derivation of n classifiers collecting independent results with normal distribution (e.g., @Sorkin2001 and @Bahrami2010): $$\begin{aligned}
P_{DSS}(c) &= \frac{1}{\hbox{normalization}}\int_{-\infty}^{c} P_1'(x)\cdot\ldots\cdot P_n'(x) dx\\
s_{DSS} &= \sqrt{s_1^2+\ldots+s_n^2} = \sqrt{n} \times \sqrt{\frac{s_1^2+\ldots+s_n^2}{n}}\\
b_{DSS} &= \frac{s_1^2 b_1+\ldots+s_n^2 b_n}{s_1^2+\ldots+s_n^2}\end{aligned}$$ Note that, regardless of the distribution of the individual performances, the group performance outscores both Best Decides and Weighted Confidence Sharing.

Truth Wins {#s:tw}
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#### Model {#model-5 .unnumbered}

We assume that on each trial each member is in one of the two states: either they know the right answer or they are aware of their own ignorance. In the latter case, a random guess is made. It is sufficient to have a single group member perceive the stimuli correctly to get the correct group answer. We assume no bias, as there is no possible way to treat it consistently and it introduces false convictions.

#### Motivation {#motivation-5 .unnumbered}

For so-called Eureka problems, the signal-theoretic limit can be exceeded [@Hill1982]. The key is that the answer to such a problem has the property of demonstrability: it allows a single member who has the 