MoL-2025-28: de Jong, Otto (2025) Structured Justifications for Binary Aggregation. [Report]
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Abstract
In binary aggregation (with integrity constraints), a group of voters votes on a set of issues. Each person votes by submitting a ballot in the form of a binary vector, stating for each issue whether they accept or reject it. An integrity constraint is a propositional formula over the different issues that states which ballots the voters are allowed to submit. A (consistent) aggregation rule then decides on a set of possible outcomes. Like the ballots submitted, each possible outcome is a binary vector, accepting or rejecting every issue while also taking into account the integrity constraint, i.e. not violating it.
Suppose we are in such a setting, where every voter has submitted a ballot and the aggregation rule decided on one or more possible outcomes. Given a set of normative principles that we call axioms, one can try to justify the chosen outcome(s). This can be done by showing that collectively accepting this set of axioms forces the outputted outcome under the inputted ballots, no matter the specific aggregation rule.
In an unstructured justification, we provide an explanation in the form of a set of specific instances of these axioms that together justify the outcome. In a structured justification, we also provide a structured way to read this explanation.
In the first part of this thesis, we will define unstructured and structured justifications for binary aggregation. First, we propose a new definition of outcome statements that are used to describe aggregation rules. Thereafter, we define a tableau-based calculus in which we can structure the justifications. In the second part, we encode the framework of binary aggregation in Python, and we develop an algorithm that allows us to generate justifications with the help of a SAT solver and an MUS extraction tool.
| Item Type: | Report |
|---|---|
| Report Nr: | MoL-2025-28 |
| Series Name: | Master of Logic Thesis (MoL) Series |
| Year: | 2025 |
| Subjects: | Logic Mathematics |
| Depositing User: | Dr Marco Vervoort |
| Date Deposited: | 02 Dec 2025 22:20 |
| Last Modified: | 02 Dec 2025 22:20 |
| URI: | https://eprints.illc.uva.nl/id/eprint/2401 |
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