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Iterative Goal-Based Approval Voting

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Multi-Agent Systems (EUMAS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13442))

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Abstract

In iterative voting, a group of agents who has to take a collective decision has the possibility to individually and sequentially alter their vote, to improve the outcome for themselves. In this paper, we extend with an iterative component the recent framework of goal-based voting, where agents submit compactly expressed individual goals. For the aggregation, we focus on an adaptation of the classical Approval rule to this setting, and we model agents having optimistic or pessimistic satisfaction functions based on the Hamming distance. The results of our analysis are twofold: first, we provide conditions under which the application of the Approval rule is guaranteed to converge to a stable outcome; second, we study the quality of the social welfare yielded by the iteration process.

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Notes

  1. 1.

    Observe that, as mentioned in the introduction, while the choice of representation of the agents’ input—i.e., goals expressed compactly as propositional formulas, or explicitly as the set of their models—has immediate consequences on the computational complexity of some related problems [26], since these fall outside of the scope of this paper we will often represent the corresponding set of models for ease of illustration.

  2. 2.

    In the case of strategy-proofness this action is called a manipulation; we prefer to avoid this negative connotation for iterative voting and we simply say that agents alter their vote.

  3. 3.

    Note that this does not hold for arbitrary weak preferences over sets of interpretations \(w_j\). Let the best outcomes for agent 1 be \(\mathcal {P}(\{w_1,w_3,w_5\}) \cup \mathcal {P}(\{w_2,w_4\})\); those of agent 2 be \(\mathcal {P}(\{w_2,w_4,w_5\}) \cup \mathcal {P}(\{w_1,w_3\}\); and that of agent 3 be \(\{w_5\}\). Initially, agent 1 submits \(\{w_2,w_4\}\), agent 2 sends \(\{w_1,w_3\}\) and agent 3 sends \(\{w_5\}\). Then, agent 1 alters to \(\{w_1,w_2,w_5\}\), while agent 2 alters to \(\{w_2,w_3\}\) next. Not only we have \(k_1 = k_2\), but we can construct a circular iteration following a similar structure to that of the example in Table 2.

  4. 4.

    A truth-biased agent has an incentive to alter to her truthful goal when the corresponding outcome which will be obtained by this alteration is at least as satisfying as the current outcome.

  5. 5.

    Alterations (i) and (ii) from Definition 3 correspond to dilatation and erosion manipulation, respectively, in the literature on strategic goal-based voting [27] and belief merging [12].

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Acknowledgements

We would like to thank the reviewers for their detailed and valuable comments. We also thank the actions transversales du Centre d’Economie de la Sorbonne for funding Leyla Ade’s research visit to work on the results presented here.

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Authors and Affiliations

  1. Institut für Philosphie, Universität Bayreuth, Bayreuth, Germany

    Leyla Ade

  2. Centre d’Economie de la Sorbonne, Université Paris 1 Panthéon-Sorbonne, Paris, France

    Arianna Novaro

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  1. Leyla Ade
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  2. Arianna Novaro
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Correspondence to Arianna Novaro .

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  1. University of Düsseldorf, Düsseldorf, Germany

    Dorothea Baumeister

  2. University of Düsseldorf, Düsseldorf, Germany

    Jörg Rothe

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Ade, L., Novaro, A. (2022). Iterative Goal-Based Approval Voting. In: Baumeister, D., Rothe, J. (eds) Multi-Agent Systems. EUMAS 2022. Lecture Notes in Computer Science(), vol 13442. Springer, Cham. https://doi.org/10.1007/978-3-031-20614-6_1

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  • DOI: https://doi.org/10.1007/978-3-031-20614-6_1

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