Abstract
Most research on influence maximization considers asimple diffusion model, in which binary information is being diffused (i.e., vertices – corresponding to agents – are either active or passive). Here we consider a more involved model of opinion diffusion: In our model, each vertex in the network has either approval-based or ordinal-based preferences and we consider diffusion processes in which each vertex is influenced by its neighborhood following a local election, according to certain “local” voting rules. We are interested in externally changing the preferences of certain vertices (i.e., campaigning) in order to influence the resulting election, whose winner is decided according to some “global” voting rule, operating after the diffusion converges. As the corresponding combinatorial problem is computationally intractable in general, and as we wish to incorporate probabilistic diffusion processes, we consider classic heuristics adapted to our setting: A greedy heuristic and a local search heuristic. We study their properties for plurality elections, approval elections, and ordinal elections, and evaluate their quality experimentally. The bottom line of our experiments is that the heuristics we propose perform reasonably well on both the real world and synthetic instances. Moreover, examining our results in detail also shows how the different parameters (ballot type, bribery type, graph structure, number of voters and candidates, etc.) influence the run time and quality of solutions. This knowledge can guide further research and applications.
Partially supported by Ministry of Science, Technology and Space Binational Israel-Taiwan grant, number 3-16542.
Partially supported by Charles University project UNCE/SCI/004 and by the project 22-22997S of GA ČR. Computational resources were supplied by the project “e-Infrastruktura CZ" (e-INFRA CZ LM2018140) supported by the Ministry of Education, Youth and Sports of the Czech Republic, and by the ELIXIR-CZ project (LM2018131), part of the international ELIXIR infrastructure.
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Notes
- 1.
For simplicity, we assume bribery operations always succeed. A relaxation of this assumption is left for future work.
- 2.
To avoid division by zero, we define the Borda score of a candidate ranked as jth to be \(|A|-j+1\) instead of \(|A|-j\), although the latter is more common. These definitions are mathematically equivalent.
- 3.
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Gonen, R., Koutecký, M., Menashof, R., Talmon, N. (2023). Heuristics for Opinion Diffusion via Local Elections. In: Gąsieniec, L. (eds) SOFSEM 2023: Theory and Practice of Computer Science. SOFSEM 2023. Lecture Notes in Computer Science, vol 13878. Springer, Cham. https://doi.org/10.1007/978-3-031-23101-8_10
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