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Table 1 Ideal decisions and confidences

From: Group decisions based on confidence weighted majority voting

Scenario Individual Group  
A B C   
\(y^*_1\) \(c^*_1\) (%) \(y^*_2\) \(c^*_2\) (%) \(y^*_3\) \(c^*_3\) (%) \(y^*_g\) \(c^*_g\) (%)
I Fair coin 87 Fair coin 70 Fair coin 62 Fair coin 96
II Biased coin 76 Fair coin 51 Fair coin 51 Biased coin 75
III Biased coin 88 Biased coin 54 Fair coin 81 Biased coin 66
IV Fair coin 81 Biased coin 58 Biased coin 72 Fair coin 54
  1. In each trial, we applied one out of four scenarios (I–IV), which is defined by three stimulus sequences (A, B and C). Each of the three participants from a group viewed one stimulus sequence. Each individual stimulus sequence entails an ideal decision \(y^*_i\) and ideal confidence \(c^*_i\) that can be derived from probability computations. The ideal individual responses from each scenario determine the groups’ ideal decision \(y^*_g\) and confidence \(c^*_g\) (see “Methods” section for an example calculation corresponding to Scenario II)