Unravelling Expressive Delegations: Complexity and Normative Analysis
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arXiv
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| Format: | Preprint |
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2023
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| author | Tyrovolas, Giannis Constantinescu, Andrei Elkind, Edith |
| author_facet | Tyrovolas, Giannis Constantinescu, Andrei Elkind, Edith |
| contents | We consider binary group decision-making under a rich model of liquid democracy recently proposed by Colley, Grandi, and Novaro (2022): agents submit ranked delegation options, where each option may be a function of multiple agents' votes; e.g., "I vote yes if a majority of my friends vote yes." Such ballots are unravelled into a profile of direct votes by selecting one entry from each ballot so as not to introduce cyclic dependencies. We study delegation via monotonic Boolean functions, and two unravelling procedures: MinSum, which minimises the sum of the ranks of the chosen entries, and its egalitarian counterpart, MinMax. We provide complete computational dichotomies: MinSum is hard to compute (and approximate) as soon as any non-trivial functions are permitted, and polynomial otherwise; for MinMax the easiness results extend to arbitrary-arity logical ORs and ANDs taken in isolation, but not beyond. For the classic model of delegating to individual agents, we give asymptotically near-tight algorithms for carrying out the two procedures and efficient algorithms for finding optimal unravellings with the highest vote count for a given alternative. These algorithms inspire novel tie-breaking rules for the setup of voting to change a status quo. We then introduce a new axiom, which can be viewed as a variant of the participation axiom, and use algorithmic techniques developed earlier in the paper to show that it is satisfied by MinSum and a lexicographic refinement of MinMax (but not MinMax itself). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_11932 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Unravelling Expressive Delegations: Complexity and Normative Analysis Tyrovolas, Giannis Constantinescu, Andrei Elkind, Edith Computer Science and Game Theory Computational Complexity Data Structures and Algorithms We consider binary group decision-making under a rich model of liquid democracy recently proposed by Colley, Grandi, and Novaro (2022): agents submit ranked delegation options, where each option may be a function of multiple agents' votes; e.g., "I vote yes if a majority of my friends vote yes." Such ballots are unravelled into a profile of direct votes by selecting one entry from each ballot so as not to introduce cyclic dependencies. We study delegation via monotonic Boolean functions, and two unravelling procedures: MinSum, which minimises the sum of the ranks of the chosen entries, and its egalitarian counterpart, MinMax. We provide complete computational dichotomies: MinSum is hard to compute (and approximate) as soon as any non-trivial functions are permitted, and polynomial otherwise; for MinMax the easiness results extend to arbitrary-arity logical ORs and ANDs taken in isolation, but not beyond. For the classic model of delegating to individual agents, we give asymptotically near-tight algorithms for carrying out the two procedures and efficient algorithms for finding optimal unravellings with the highest vote count for a given alternative. These algorithms inspire novel tie-breaking rules for the setup of voting to change a status quo. We then introduce a new axiom, which can be viewed as a variant of the participation axiom, and use algorithmic techniques developed earlier in the paper to show that it is satisfied by MinSum and a lexicographic refinement of MinMax (but not MinMax itself). |
| title | Unravelling Expressive Delegations: Complexity and Normative Analysis |
| topic | Computer Science and Game Theory Computational Complexity Data Structures and Algorithms |
| url | https://arxiv.org/abs/2312.11932 |