Experimental Design
Our experimental design includes two treatments, with group sizes of 3 and 5 participants, respectively. Each experiment consists of 2 stages: the first stage involves individual decisions, and the second stage involves collective decisions (in groups of 3 or 5).
Baseline Condition (Group-size-3 condition)
In the first stage, using the methods of Choi et al. (2007, 2014), the decision maker’s (DM’s) task is to independently distribute points between two accounts, labeled BLUE(x) and RED(y). We can caculate the exchange rates(p) between BLUE and RED accounts. Thus, a decision obtains a tuple (x, p) whereby a DM selects a bundle (x, y) under the exchange rates (px, py).
Since measuring rationality requires a collection of such decisions, we include 25 tasks with randomly generated lines (Choi et al., 2014). After that, we measure the economic rationality of these 25 decisions, (xi, pi) (i=1,…, 25).
The second stage involves collective decision-making, including 25 rounds as well. At the beginning of each round, each group member makes an independent allocation choice following the method from Stage 1. They then proceed to an “deliberation” phase, such as structured discussion, silent voting, during which a collective decision is reached. Collective rationality for each group is measured using the same method as in the first stage. The design enables identification of whether collective choices satisfy rationality.
Group-size-5 condition
The Group-size-5 condition proceeds exactly as the Group-size-3 condition, except that each group consists of five members instead of three in the collective decision stage.