Order fairness in distributed ledgers refers to properties that relate the order in which transactions are sent or received to the order in which they are eventually finalized, i.e., totally ordered. The study of such properties is relatively new and has been especially stimulated by the rise of Maximal Extractable Value (MEV) attacks in blockchain environments. Indeed, in many classical blockchain protocols, leaders are responsible for selecting the transactions to be included in blocks, which creates a clear vulnerability and opportunity for transaction order manipulation. Unlike blockchains, DAG-based ledgers allow participants in the network to independently propose blocks, which are then arranged as vertices of a directed acyclic graph. Interestingly, leaders in DAG-based ledgers are elected only after the fact, once transactions are already part of the graph, to determine their total order. In other words, transactions are not chosen by single leaders; instead, they are collectively validated by the nodes, and leaders are only elected to establish an ordering. This approach intuitively reduces the risk of transaction manipulation and enhances fairness. In this paper, we aim to quantify the capability of DAG-based ledgers to achieve order fairness. To this end, we define new variants of order fairness adapted to DAG-based ledgers and evaluate the impact of an adversary capable of compromising a limited number of nodes (below the one-third threshold) to reorder transactions. We analyze how often our order fairness properties are violated under different network conditions and parameterizations of the DAG algorithm, depending on the adversary's power. Our study shows that DAG-based ledgers are still vulnerable to reordering attacks, as an adversary can coordinate a minority of Byzantine nodes to manipulate the DAG's structure.