  From social contracts to climate agreements, individuals engage in groups
that must collectively reach decisions with varying levels of equality and
fairness. These dilemmas also pervade Distributed Artificial Intelligence, in
domains such as automated negotiation, conflict resolution or resource
allocation. As evidenced by the well-known Ultimatum Game -- where a Proposer
has to divide a resource with a Responder -- payoff-maximizing outcomes are
frequently at odds with fairness. Eliciting equality in populations of
self-regarding agents requires judicious interventions. Here we use knowledge
about agents' social networks to implement fairness mechanisms, in the context
of Multiplayer Ultimatum Games. We focus on network-based role assignment and
show that preferentially attributing the role of Proposer to low-connected
nodes increases the fairness levels in a population. We evaluate the
effectiveness of low-degree Proposer assignment considering networks with
different average connectivity, group sizes, and group voting rules when
accepting proposals (e.g. majority or unanimity). We further show that
low-degree Proposer assignment is efficient, not only optimizing fairness, but
also the average payoff level in the population. Finally, we show that stricter
voting rules (i.e., imposing an accepting consensus as requirement for
collectives to accept a proposal) attenuates the unfairness that results from
situations where high-degree nodes (hubs) are the natural candidates to play as
Proposers. Our results suggest new routes to use role assignment and voting
mechanisms to prevent unfair behaviors from spreading on complex networks.
