Randomization Method

All randomization takes place using Javascript code implemented through Qualtrics.

1) In the main task (described in Part 2 above), the levels of bias that individuals will see are {-10, -5, -1, 0, 1, 5, 10}. There are three levels of complexity levels for each bias level, and 2 expressions for each complexity level above 1. For example, for bias level = 0, we have complexity level 1 = "0%", complexity level 2 = "4 ∗ (2 – 2)/(2 ∗ 2)%" or "6 ∗ (3 – 3)/(2 ∗ 3)%", and complexity level 3 = "2^2 – 4 + 4 ∗ (2 – 2)/(2 ∗ 2) – 8 + 4 ∗ 2%" or "2^3 – 8 + 6 ∗ (3 – 3)/(2 ∗ 3) – 12 + 4 ∗ 3%." All other bias levels are analogous to this.

We will not have a full factorial design when it comes to the crossing of Bayes' posteriors with biases. For the reasoning behind this, consider the following: if Bayes' posterior were, say, 99%, then stating that the computer was underestimating by 5% would imply the true value was 104%, an impossibility. Thus for each value of Bayes' posterior, the code picks from all aforementioned bias values such that the information given is between 0% and 100%.

2) In the willingness to pay section, we will oversample bias = 0, so that it is selected 50% of the time in expectation (and one of the values -10, -5, -1, 1, 5, 10 are selected the other 50% of the time). Furthermore, we will only select from complexity level 1 with 50% probability and complexity levels 2 and 3 with 50% probability.