Abstract
Solving the collective action problem is to understand how people decide to act together for the common good when individual rationality would lead to non-cooperative selfish behaviour. Two important features that can foster collective action are achieving common knowledge about the problem faced and the existence of a shared cooperative ethos. Based on the work of Ober, who argued that the success of classical Athens was the result of its shared commitments, social values and specific procedural rules, we define a probabilistic model in Markov Logic of a specific prosecution against an Athenian trader who neglected to contribute to the city when it was in a crisis. In order to join together for a common good, our model focuses on a decision-making approach based on reasoning about common knowledge. For example, knowledge about the ethos of the court towards convicting traitors can be seen as common knowledge gained from public monuments recording these verdicts. We expect that our computational model of this case study can be generalised to other problems of reasoning about collective action based on common knowledge in future work.
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- 1.
We do not attempt to model any reasoning about whether a citizen prosecuted for treachery really is guilty. Instead we focus on the argument for conviction (assuming guilt) based on the upholding of social order. In fact, in the real scenario, Leocrates was not convicted, as evidence of his guilt was not convincing to the court.
- 2.
- 3.
MLN inference does not scale well [23], so explicitly modelling a large number of citizens is not feasible.
- 4.
According to Toumela [24] there is a mutual belief that, if a group has set of ethoses, all its members are collectively committed and accepted to that ethoses. Essentially this is common knowledge.
- 5.
Due to difficulties in expressing conditional probabilities in MLN clauses [6], this knowledge is expressed in terms of joint probabilities of cooperation and holding a certain ethos.
- 6.
ProbCog provides an “exist” operator but not a “for all” one.
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Acknowledgements
This work was supported by the Marsden Fund Council from New Zealand Government funding, managed by Royal Society Te Apārangi.
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Srivathsan, S., Cranefield, S., Pitt, J. (2022). Reasoning About Collective Action in Markov Logic: A Case Study from Classical Athens. In: Ajmeri, N., Morris Martin, A., Savarimuthu, B.T.R. (eds) Coordination, Organizations, Institutions, Norms, and Ethics for Governance of Multi-Agent Systems XV. COINE 2022. Lecture Notes in Computer Science(), vol 13549. Springer, Cham. https://doi.org/10.1007/978-3-031-20845-4_13
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