  Statistical matching methods are widely used in the social and health
sciences to estimate causal effects using observational data. Often the
objective is to find comparable groups with similar covariate distributions in
a dataset, with the aim to reduce bias in a random experiment. We aim to
develop a foundation for deterministic methods which provide results with low
bias, while retaining interpretability. The proposed method matches on the
covariates and calculates all possible maximal exact matchesfor a given dataset
without adding numerical errors. Notable advantages of our method over existing
matching algorithms are that all available information for exact matches is
used, no additional bias is introduced, it can be combined with other matching
methods for inexact matching to reduce pruning and that the result is
calculated in a fast and deterministic way. For a given dataset the result is
therefore provably unique for exact matches in the mathematical sense. We
provide proofs, instructions for implementation as well as a numerical example
calculated for comparison on a complete survey.
