The increasing institutionalisation of Online Dispute Resolution (ODR) reflects a structural transformation in contemporary systems of alternative dispute resolution. While early models of ODR were largely confined to facilitating communication, document exchange, and procedural coordination, recent platforms increasingly deploy algorithmic systems capable of predicting dispute outcomes, recommending settlements, and, in limited contexts, autonomously resolving disputes. This technological evolution raises fundamental concerns for arbitration law, particularly in relation to the principle of neutrality, which has historically derived its legitimacy from human judgment, ethical responsibility, and procedural accountability. This paper undertakes a doctrinal and socio-legal examination of whether algorithmic ODR systems can meaningfully satisfy the legal and constitutional requirements of arbitral neutrality. Drawing upon Indian arbitration jurisprudence, statutory obligations under the Arbitration and Conciliation Act, 1996, and international instruments such as the UNCITRAL Technical Notes on Online Dispute Resolution, the paper critically interrogates the widely held assumption that algorithmic decision-making is inherently objective or impartial. It demonstrates that neutrality in arbitration is not merely the absence of bias, but a normative construct shaped by discretion, contextual reasoning, transparency, and accountability. The paper further argues that claims of algorithmic neutrality are largely illusory, as such systems remain deeply influenced by human design choices, institutional incentives, and historically contingent datasets. The delegation of adjudicatory functions to opaque digital systems is shown to undermine due process guarantees, particularly the requirement of reasoned decision-making and the availability of meaningful judicial review. While recognising the efficiency and accessibility gains offered by ODR, the paper concludes that algorithmic systems cannot replace human arbitrators without eroding the normative foundations of arbitral justice. A carefully regulated hybrid framework, preserving substantive human oversight, is proposed as the only legally sustainable model for the future of digital arbitration.