Voting rules aggregate multiple individual preferences in order to make collective decisions. Commonly, these mechanisms are expected to respect a multitude of different fairness and reliability properties, e.g., to ensure that each voter\u27s ballot accounts for the same proportion of the elected alternatives, or that a voter cannot change the election outcome in her favor by insincerely filling out her ballot. However, no voting rule is fair in all respects, and trade-off attempts between such properties often bring out inconsistencies, which makes the construction of arguably practical and fair voting rules non-trivial and error-prone.
In this paper, we present a formal and systematic approach for the flexible and verified construction of voting rules from composable core modules to respect such properties by construction. Formal composition rules guarantee resulting properties from properties of the individual components, which are of generic nature to be reused for various voting rules. We provide a prototypical logic-based implementation with proofs for a selected set of structures and composition rules within the theorem prover Isabelle/HOL. The approach can be readily extended in order to support many voting rules from the literature by extending the set of basic modules and composition rules. We exemplarily construct the well-known voting rule sequential majority comparison (SMC) from simple generic modules, and automatically produce a formal proof that SMC satisfies the fairness property monotonicity. Monotonicity is a well-known social-choice property that is easily violated by voting rules in practice
