在本文中，我們提出了一種新的平均模型用於模擬在選舉過程中當有n個選民和K個候選人的競爭影響。對於這種影響傳播模型，我們解決了候選人需要在未決定選民中投放多少種子選民才能贏得選舉的問題。我們表明，對於從隨機區塊模型(stochastic block model)生成的隨機網絡，如果候選人所放置的種子選民的數量超過閾值，則存在逾滲閾值(percolation threshold)讓候選人贏得選舉。通過進行大量的實驗，我們證明了我們的理論滲透閾值非常接近於隨機網絡模擬得到的那些實驗值，並且在真實網絡的實驗誤差在10％以內。

In this thesis, we propose a new averaging model for modeling the competitive influence of K candidates among n voters in an election process. For such an influence propagation
model, we address the question of how many seeded voters a candidate needs to place among undecided voters in order to win an election. We show that for a random network generated from the stochastic block model, there exists a percolation threshold for a
candidate to win the election if the number of seeded voters placed by the candidate exceeds the threshold. By conducting extensive experiments, we show that our theoretical
percolation thresholds are very close to those obtained from simulations for random networks and the errors are within 10% for a real-world network.

摘要
目錄
Introduction---------4
The model for competitive influence propagation---------8
Competitive influence propagation in stochastic block models-----14
Experiments---------20
Conclusion and future work---------31
Appendix---------32
Bibliography-------37

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