Brexit: a comparison of dynamic voting games with irreversible options (Q2667240)

With the Bexit referendum of 2016 in mind, the authors introduce a tractable, dynamic framework of a polarized society that has to choose among a reversible option (called REMAIN) and an irreversible one (called LEAVE). In their model, a large electorate decides in each period \(t = 1, 2, \ldots\) between REMAIN (\(d_t = R\)) and LEAVE (\(d_t = L\)). The latter option ends the decision process. In each period \(t\), each agent \(i\) obtains a stage payoff of \(\pi_t^{i} \in \{0, 1\}\) from LEAVE and a stage payoff of \(\frac{1}{2}\) from REMAIN. If \(\pi_t^{i}\) = 1 (0), then agent \(i\) is a LEAVE-winner (loser) from a short-term perspective. The authors distinguish among two types of environments: the environment is REMAIN-friendly (LEAVE-friendly) if the probability of a future majority of LEAVE-winners is lower (higher) that 50\%. The existence of only two types of agents models a simple notion of extreme polarization, but in Appendix A the authors explain that their results continue to hold in less polarized societies. Two main scenarios arise: If the environment is REMAIN-friendly, and if discounting is not too high, it is socially optimal to never LEAVE. Otherwise, it is socially optimal to LEAVE in the first period with a sufficiently large supermajority of LEAVE-winners. The main findings of the authors are: 1. In environments where it is sometimes optimal to LEAVE, the irreversible option LEAVE is adopted too easily. Supermajority rules can lead to better decisions. 2. In environments where it is never optimal to LEAVE, an equilibrium where LEAVE is chosen quickly can coexist with one where LEAVE is never chosen. Requiring a sufficiently large supermajority for LEAVE avoids the existence of the welfare-inferior equilibrium. 3. There is an asymmetry in the potential welfare costs from non-optimal rules: a too low supermajority rule can have a much higher cost than a too high supermajority rule. 4. Welfare-inferior equilibria can often be avoided without fine-tuning if a final decision for either alternative requires winning by a certain margin.