Hooper et al (2010) A theory of leadership in cooperative groups

Hooper PL, Kaplan HS, & Boone JL (2010) A theory of leadership in human cooperative groups. Journal of Theoretical Biology 265, 633-646.

Motivating questions:

• What evolutionary and behavioral processes lead con-specifics to be more vertically differentiated by social rank in some circumstances, but not others?
• Within our own species, why is it that some human groups exhibit relatively egalitarian distributions of social power, while others exhibit more recognizable distinctions between dominant and subordinate, leader and follower, chief and commoner, king and subject, or ruler and ruled?

•  Theory 1: Inegalitarian structure benefits the powerful. Lots of previous research assumes that rank differentiation between two individuals (or groups) is the result of competition between the two, and the more powerful are those who can claim those positions at the expense of the less powerful. Expected to arise when some individuals have a significant advantage over others that they can maintain. Theoretical work in this area includes models of economic defensibility, territorial circumscription, and reproductive skew.
• Theory 2: Inegalitarian structure may benefit everyone. Greater differentiation of social rank may be preferred over egalitarian arrangements by all parties as a solution to the key challenges of life in social groups, including conflict over resources, coordination failures, and free-riding in cooperative relationships.
• The existence of facultative, cooperation-facilitating leadership roles in otherwise egalitarian small-scale human societies – such as Amazonian poison-fishing leaders or Inuit whaling captains – supports this conjecture.
• However, most modern versions of this idea have relied on informal, group functionalist, or group selection arguments, a fact which has hampered their acceptance by biologists and biologically oriented social scientists.
• There has previously been little formal analysis establishing whether, and under what conditions, self-interested individuals would prefer the establishment of more hierarchical relationships over more egalitarian alternatives.

The argument:

• In some social, economic, and ecological circumstances, there are gains to cooperating in groups of significant size. Incentives for individuals to shirk or free-ride on the cooperative contributions of others, or simply the difficulty of coordinating action among multiple actors, however, can prevent the realization of these gains. These problems tend to become more serious as group size increases. While genetic relatedness, reputation tracking, and norm enforcement by regular group members can attenuate these problems in small or medium-sized groups, these effects likewise tend to diminish as the number of actors increases beyond certain limits.
• We propose that the effort of a leader can reduce the likelihood that cooperation fails due to free-riding or coordination errors, and that under some circumstances, un-coerced group members would prefer to cooperate in a group under the supervision of a leader who receives a share of the group’s productivity than to work in an unsupervised group. We suggest, in particular, that this becomes an optimal solution for individual decision makers when the number of group members required for collective action exceeds the maximum group size at which leaderless cooperation is viable. The transition to cooperation under leadership should thus occur when the benefits from being able to successfully cooperate at larger scales exceed the costs of having a leader.

NOTE: This is a good argument. It suggests that leadership evolves as an institution that facilitates cooperation among large groups. I think it’s complementary to our model. It doesn’t address who becomes leaders, or how the leaders represent the will of the people.

The model

Basic description: An evolutionary game theoretical model based on the public goods game in which the benefits of and scale required for cooperation are characteristics of the group’s ecological or economic niche. We analyze the conditions under which collective action is sustainable without reinforcement, sustainable under mutual monitoring by group members, sustainable under reinforcement by a leader, or ultimately unsustainable.

Mechanics.

Each generation, groups of size n are randomly formed from a very large population.

Every round, each group plays the public goods game (PGG) and can either cooperate or defect. Those who cooperate pay a cost c and generate a benefit b that is distributed to all group members.

The probability that a group persists and continues to play the next round is w.

After play ends, agents reproduce according to their final (total) payoffs and die.

Analysis

Pure game, no monitoring. ALLC can only invade and resist ALLD if b/n > c. That is, free unilateral contribution can only be sustained when its benefits are high relative to its costs and the group size is very small, which presents a major challenge to successful collective action in sizeable groups.

Mutual monitoring and punishment.

• Consider strategy mutual monitoring (MM) that always cooperates and pays a cot c_m to monitor other members’ contributions each round. If anyone defects, MM pays a cost c_s to reduce the defector’s payoff by s. Costs are expected to vary as functions of the socioecology and technology of production or competition.
• Two competing strategies: ALLC and reluctant cooperators (RC), who defect until they are punished, then cooperate in every subsequent round. Assume that ALLC is not sustainable, i.e., b/n ≤ c.
• Punishment is sufficient to discourage defection for RC is the cost of being punished exceeds the net cost of contributing to the public good, s > c – b/c.
• Monitoring (MM) can invade as long as the benefit from cooperation and the likelihood of another round are sufficiently high relative to the costs of cooperating, monitoring, and punishing.

Summary of dynamics:

• (a) Monitors are able to increase in the population when there are enough reluctant cooperators and few enough pure cooperators and monitors that monitoring yields a high differential benefit to individual monitors.
• (b) If monitoring is costly, pure cooperators gain an advantage over mutual monitors when there are few reluctant cooperators to defect, or at least enough willing monitors to neutralize the threat of their defection.
• (c) Reluctant cooperators, in turn, regain an advantage over pure cooperators when there are few enough monitors that defection is likely to go unpunished.
• Analysis shows that RC takes over when group sizes are large, especially if monitoring costs are higher.

Invasion of cooperation under leadership.

Model

• Each player is either willing or unwilling to join a hierarchical group.
• Those unwilling continue to operate in acephalous (leaderless) groups with one of the strategies defined above (ALLC, MM, or RC).
• Those willing to join a hierarchical group may either be willing to lead (L) or unwilling (UL). An individual willing to lead can act as a leader at tax rate t, which is an evolvable attribute of each willing leader.
• Each generation, individuals with hierarchical preferences are randomly sorted into groups composed of one leader and n normal group members. If there are no willing leaders, they play as non-hierarchical types.
• If there are multiple individuals willing to lead, we assume the leader is chosen by majority vote for the leader with the lowest tax rate. Assume the cost of appointing a leader is costless.
• Like mutual monitors, the leader pays a cost c_m to monitor each group member each round and reduces the payoff of a defector by s at a personal cost c_s.
• Non-leaders are either pure cooperator (H.ALLC) or reluctant cooperators (H.RC).
• A leader with access to the public good will extract his benefit directly – tbx per round, where x is the number of contributors to the PG.
• A willing taxpayer strategy (H.T) always pays the tax, and a reluctant taxpayer strategy (H.RT) does not pay until punished and then pays it every subsequent round. Assume that the leader can additionally reduce the payoff of non-taxpayers by s_t at a personal cost c_t.

Analysis:

• Because the benefits of contributing are diminished by taxation, the minimum punishment s for reluctant cooperators must be higher in the leadership case than in the mutual monitoring case, s > c – (1–t)b/n.
• The minimum punishment for reluctant taxpayers must simply exceed the cost of the taxes themselves, which depends on the tax rate and the magnitude of the public good produces: s_t > tb.
• For the leader to have a payoff advantage over acephalous defectors, he or she must receive a fraction of group proceeds that is greater than the ratio of the costs of monitoring and sanctioning to the taxable benefits.
• Hierarchical group members will proliferate when then the net benefits of cooperation exceed the costs of taxation and punishment by a leader.
• Preferences for acephalous versus hierarchical groups also depend on the cost of monitoring and sanctioning. In contrast to mutual monitoring’s strong dependence on low monitoring costs, leadership remains quite robust to increased monitoring costs as long as the benefits produced from cooperation are sufficient to cover them.

The evolution of strategies and the negotiation of taxation within a hierarchical population

• As long as the sanctions are sufficiently strong, tax-paying pure cooperators will always out-compete their more reluctant peers. Here the focus is on hierarchical groups dominated by tax-paying pure cooperators.
• Once chosen leaders are earning even slightly more than regular group members, the willingness to lead will increase in the population, if it is not already widespread. Among those willing to lead, those who are actually chosen as leaders will increase relative to those offering higher tax rates who are not, and who are therefore receiving the regular hierarchical group member’s payoff. Thus, selection will simultaneously work to prune the upper end of the distribution of tax offers.
• This process of competition among potential leaders will cause the tax rate offered by potential leaders to converge on that which yields equal payoffs to group members and leaders – an “egalitarian tax rate.”
• NOTE: This assumes that a leadership class does not emerge that colludes to keep tax rates high. However, it does allow for the co-existence of leadership and egalitarian norms.

In contrast to acephalous cooperation’s precipitous decline with group size, cooperation in hierarchical groups is remarkably robust even in very large groups. In fact, at this model’s market equilibrium, leadership becomes cheaper in larger groups as the cost of the leader’s compensation is split among a larger number of group members (although this would not necessarily be the case if the cost of monitoring one individual increased with group size).

Discussion

• We expect that in environments where the returns to scale diminish quickly, self-interested individuals will optimally form small groups in which unenforced cooperation and/or mutual monitoring are sufficiently stable to gain the benefits from cooperation, and the costs of leadership are unnecessary.
• When the potential benefits of cooperation reach the point of diminishing returns only at much larger scales, however, we expect that individuals who are willing to join large, hierarchically organized groups will out-compete those who are only willing to join either large acephalous groups dominated by defectors, or smaller, more cooperative but less productive acephalous groups.
• Members of acephalous cooperative groups may sometimes be capable of holding out against the invasion of hierarchical types even when there are very high returns to scale. Other potential processes theoretically capable of reinforcing cooperation include: costly signaling; group selection; conformist cultural transmission; recursive punishment of non-punishers; optional participation; and costless punishment of free-riders by withholding help in other cooperative domains. As the number of viable theoretical models aiming to explain large-scale human cooperation continues to grow, the answer will ultimately hinge on the empirics of cooperation in the real world.