Fresh SI: Okada & Sawa on the implications of collective agency arising from majority voting

In a new working paper, Akira Okada and Ryoji Sawa examine an evolutionary model in which the policy followed by a collective is determined by majority (or supermajority) voting by individuals. They look at the kind of policies that emerge under given voting rules.

A voting rule can be considered a way of forming a collective intention. In fact, it can be a strong way of forming a collective intention as the wishes of individuals in a minority are disregarded. It follows that, in this sense, the weakest voting rule is the one that requires ALL individuals to agree: the unanimity voting rule.

Under the unanimity rule, the only way a new policy x can defeat a status quo policy y is if every individual voting weakly prefers x to y. This is exactly the Coalitional Better Response rule found in Newton and Angus (2015, paper, video).

Okada and Sawa find that when their voting dynamic is perturbed uniformly, in the long run Condorcet winning  policies tend to emerge. When perturbations depend on payoffs (specifically, logit) Borda winning policies tend to emerge.

For more, see the paper.

SI: Nax and Perc on the replication of coalitionally beneficial behaviour by individual mistakes

In this paper published in Scientific Reports, Heinrich Nax and Matjaz Perc discuss naive learning in public goods games. They examine a situation in which simultaneous mistakes by multiple players can end up benefiting the mistake making players. For example, it could be the case that 3 players make mistakes and play a myopically suboptimal action, but that because they make mistakes simultaneously they gain payoff from these mistakes.

Hence, profitable coalitional moves are replicated by the mistakes of individuals. To replicate coalitional moves by larger numbers of players will require a larger number of mistakes and so such moves will be relatively less likely. This is similar to the assumption made in Newton (2012, paper, web), although in the cited paper it is an assumption, whereas in Nax and Perc it emerges endogeneously as described above.

A Nash equilibrium is k-strong if there exists no profitable coalitional deviation for a coalition of any size up to and including k  (see the paper under discussion or Newton & Angus, 2013). The authors show that behaviour under naive learning depends on the k-strength of the equilibria in their model (i.e. on the value of for which equilibria are k-strong).

Read the full paper here.