This paper presents an intuitive explanation about why and how Rawlsian Theory of Justice (Rawls in A theory of justice, Harvard University Press, Harvard, 1971) provides the foundations to a solution for algorithmic bias. The contribution of the paper is to discuss and show why Rawlsian ideas in their original form (e.g. the veil of ignorance, original position, and allowing inequalities that serve the worst-off) are relevant to operationalize fairness for algorithmic decision making. The paper also explains how this leads (...) to a specific MinMaxfairness solution, which addresses the basic challenges of algorithmic justice. We combine substantive elements of Rawlsian perspective with an intuitive explanation in order to provide accessible and practical insights. The goal is to propose and motivate why and how the MinMaxfairness solution derived from Rawlsian principles overcomes some of the current challenges for algorithmic bias and highlight the benefits provided when compared to other approaches. The paper presents and discusses the solution by building a bridge between the qualitative theoretical aspects and the quantitative technical approach. (shrink)