In the Ultimatum Game, the proposer issues an ultimatum as to how they wish to split a prize with the responder. The responder either accepts or rejects the proposal. If it is rejected, both players leave empty-handed. The Dictator Game is a variant of the Ultimatum Game where the responder (the recipient) is not given this choice. Instead, they must always accept the proposal from the proposer (the dictator). These games highlight a tension between selfishness and fairness. In this work, we investigate factors that may help induce the evolutionary emergence of fairness in a simulated Dictator Game environment. We employ an Edge Weight Learning mechanism where the weights of the edges connecting the players determine the probability of interactions occurring. We compare multiple approaches that either account for proposal values or for utility. Each approach has two parts: (1) a logical condition to determine whether the edge weight will increase, decrease or remain the same, and (2) a formula to calculate the magnitude of change. Our experimental results show that proposal values are a better stimulus to incorporate into Edge Weight Learning than utility when it comes to promoting fairness.