Abstract
Voting methods are widely used in collective decision making, not only among people but also for the purposes of artificial agents. Computing the winners of voting for some voting methods like Borda count is computationally easy, while for others, like Kemeny and Dodgson, this is a computationally hard problem. The question we explore here is can winners of Kemeny and Dodgson elections be predicted using supervised machine learning methods? We explore this question empirically using common machine learning methods like XGBoost, Linear Support Vector Machines, Multilayer Perceptron and regularized linear classifiers with stochastic gradient descent. We analyze elections of 20 alternatives and 25 voters and build models that predict the winners of the Borda, Kemeny and Dodgson methods. We find that, as expected, Borda winners are predictable with high accuracy (99%), while for Kemeny and Dodgson the best accuracy we could obtain is 85% for Kemeny and 89% for Dodgson.
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Notes
- 1.
To be fair, the value of the properties that Dodgson satisfies has been disputed [3].
- 2.
The satisfiability problem sat is the problem of deciding whether a given a Boolean formula is admits a truth assignment to each of its variables such that the formula evaluates true.
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- 4.
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- 6.
- 7.
The seed for the random number generator during the split is equal to 42.
- 8.
Algorithms that learn from a training dataset incrementally.
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Acknowledgements
The research was partly supported by the project “Better Video workflows via Real-Time Collaboration and AI-Techniques in TV and New Media”, funded by the Research Council of Norway under Grant No.: 269790.
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Appendix -Figures
Appendix -Figures
Train and validation learning curves for Borda models learned in Repres. 2.
Train and validation learning curves for Kemeny using Repres. 3., SDG classifier.
Train and validation learning curves for Kemeny using Repres. 3., SDG classifier top, 2Random Forest classifier bottom.
Learning curve for Dodgson using Representation 1
Learning curve for Dodgson using Representation 2
Learning curve for Dodgson using Repres. 3
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Kujawska, H., Slavkovik, M., Rückmann, JJ. (2020). Predicting the Winners of Borda, Kemeny and Dodgson Elections with Supervised Machine Learning. In: Bassiliades, N., Chalkiadakis, G., de Jonge, D. (eds) Multi-Agent Systems and Agreement Technologies. EUMAS AT 2020 2020. Lecture Notes in Computer Science(), vol 12520. Springer, Cham. https://doi.org/10.1007/978-3-030-66412-1_28
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