Experimental Design
Design overview
The experiment uses a 2x2 design crossing protocol type (sequential vs. simultaneous) with adversary probability (q=0 vs. q=0.1). Protocol assignment is between-subjects: participants are assigned to either the sequential or simultaneous protocol for their entire session. Adversary condition is within-subjects: in half of the sequential sessions, rounds 1-20 use q=0 (no adversary) and rounds 21-40 use q=0.1 (possible adversary); in the other half of the sequential sessions, the order is reversed (rounds 1-20 use q=0.1 and rounds 21-40 use q=0). This counterbalancing controls for order effects in the sequential arm. Within each protocol arm, the adversary order is counterbalanced across sessions. In the simultaneous arm, one session uses q=0 followed by q=0.1, and the other uses q=0.1 followed by q=0.
Task and signal structure
Participants act as members of a three-person blockchain validation committee. In each round, the committee votes by majority rule to validate (Yes) or reject (No) a block. The block is legitimate (good state, theta=G) or illegitimate (bad state, theta=B) with equal prior probability 1/2. Each participant receives a private binary signal: white (good signal) or black (bad signal), where Pr(white|G)=1 and Pr(white|B)=1/2. In the sequential protocol, participants vote one at a time and observe prior votes. In the simultaneous protocol, all participants vote without observing others.
Adversary treatment
In q=0.1 rounds, each participant's vote is independently replaced by an adversary's vote with probability 10%. The adversary votes against the socially correct outcome. Participants are informed of this probability but do not observe whether replacement occurred until the end-of-round results screen.
Payoffs
+1 point if the participant voted Yes, was not replaced, and the group correctly validated a legitimate block; -1 point if the participant voted Yes, was not replaced, and the group incorrectly validated an illegitimate block; 0 otherwise. Points are converted to cash at $0.50 per point.
Sessions and randomisation
Sessions are conducted in the UQ experimental economics laboratory using oTree software. Within each session, participants are randomly re-matched into groups of three each round. In the sequential protocol, voting order is randomly assigned each round. Participants are assigned to one of eight sessions. The six sequential sessions each enrol 30 participants, while the two simultaneous sessions each enrol 21 participants. Within each protocol arm, the adversary order is counterbalanced across sessions.
Primary hypotheses (all two-sided at alpha=0.05, Bonferroni-corrected threshold alpha*=0.010)
• H1a: Pr(approved|B, Simultaneous, q=0) > Pr(approved|B, Sequential, q=0)
• H1b: Pr(approved|B, Simultaneous, q=0.1) > Pr(approved|B, Sequential, q=0.1)
• H2: Pr(rejected|G, Sequential, q=0.1) > Pr(rejected|G, Simultaneous, q=0.1)
• H3a: Pr(approved|B, Sequential, q=0.1) > Pr(approved|B, Sequential, q=0)
• H3b: Pr(rejected|G, Sequential, q=0.1) > Pr(rejected|G, Sequential, q=0)
Statistical analysis
Primary statistical tests are two-sample z-tests for proportions at the group-round level. A linear probability model (LPM) is estimated as the primary regression, with probit as a robustness check. A Fisher combined probability test across all five hypotheses (k=5) serves as a global test of the theoretical model, achieving greater than 99% power at the planned sample size.