Experimental Design Details
The group bargains over the division of 100 Points worth a total of 20 EUR. The game is repeated 20 times with random rematching. 10 games are played under complete information (breakdown values commonly known), 10 under private information (breakdown values known only privately). Three rounds are randomly chosen for payment.
Responder disagreement values are equal to either 10 or 45 points with equal probability. Proposer breakdown value is zero (always commonly known). The game lasts for at most two periods. If the first proposal fails, breakdown occurs with probability 1/6 or 5/6 (a treatment parameter, between subjects). If the second proposal fails, breakdown is certain. In addition to the the proposer subjects' proposal, a computer generated proposal is presented for a vote in round 1. Following voting on both proposals, one is randomly chosen to count. This is to observe voting on five specific proposals that we introduce exogenously:
Three (pairs of) proposals where a one subject (e.g. B) should expect to be pivotal:
Unanimity: (44,10,46), (34,20,46), (24,30,46)
Majority: (90,10,0), (80,20,0), (70,30,0)
These proposals come in "pairs" where subject B is offered the same amounts, respectively, under both rules. In every case, subject B should expect to be pivotal: Under unanimity, because the other is offered 46 and should therefore vote "yes", under majority, because the other is offered 0 and should therefore vote "no". We intend to compare acceptance rates by B between rules within these pairs.
The main prediction is that B is less likely to vote "yes" on these proposals under unanimity rule. For example: Both "types" (10 and 45) should vote "no" on (44,10,46) given unanimity rule. Under majority rule, both types should vote "yes" on (90,10,0) when the continuation probability is 5/6 and (only) low types (10) should vote "yes" when the continuation probability is 1/6.
One proposal (same under both rules) which should fail under unanimity rule and pass under majority rule:
(60,20,20)
One proposal (same under both rules) corresponding to a "fair" split:
(34,33,33)
Predictions:
Under unanimity, responders vote "no" unless breakdown value = 10 and continuation probability = 1/6
Under majority, responders vote "yes" unless breakdown value = 45 and continuation probability = 1/6
These and similar predictions come from our theoretical analysis. (Bayesian equilibrium in sequentially weakly undominated strategies.)
In addition to these Hypotheses we intend to investigate voting behavior on proposals that arise endogenously. Overall, the method will be to compare the frequency of "yes" votes between rules while controlling for parameters and the likelihood of being pivotal.