Monotonicity criterion

Abstract: We show that the Ranked Pairs Rule is equivalent to selecting the maximal linear orders with respect to a DiscriMin relation, which is a natural refinement of the Min relation used to define Arrow and Raynaud’s prudent orders. We provide an axiomatic characterization of the Ranked Pairs Rule by building on an earlier characterization of the prudent order ranking rule. We conclude that a monotonicity criterion is the main distinction between the two ranking rules.

Abstract: The correctness of ballot counting in electronically held elections is a cornerstone for establishing trust in the final result. Vote counting protocols in particular can be formally specified by as systems of rules, where each rule application represents the effect of a single action in the tallying process that progresses the count. We show that this way of formalising vote counting protocols is also particularly suitable for (formally) establishing properties of tallying schemes. The key notion is that of an invariant: properties that transfer from premiss to conclusion of all vote counting rules. We show that the rule-based formulation of tallying schemes allows us to give transparent formal proofs of properties of the respective scheme with relative ease. As our proofs are based on the specification of vote counting protocols, rather than a program that implements them, we are guaranteed that the property holds for every possible specification-confirming implementation of the respective protocol. This in particular includes the vote counting programs that are automatically extracted from the specification. We demonstrate this point by means of two examples: the monotonicity criterion for majority (first-past-the-post) voting, and the majority criterion for a simple version of single transferable vote.

Abstract: We show how modern interactive verification tools can be used to prove complex properties of vote-counting software. Specifically, we give an ML implementation of a votecounting program for plurality voting; we give an encoding of this program into the higher-order logic of the HOL4 theorem prover; we give an encoding of the monotonicity property in the same higher-order logic; we then show how we proved that the encoding of the program satisfies the encoding of the monotonicity property using the interactive theorem prover HOL4. As an aside, we also show how to prove the correctness of the vote-counting program. We then discuss the robustness of our approach.