Learning Real-Life Approval Elections

TL;DR

The paper addresses learning probabilistic models for approval elections by introducing IAMs and mixtures, learned via MLE and Bayesian methods, and applying them to the Pabulib dataset. It shows that single IAMs are often insufficient and that mixtures (learned with EM or Bayesian inference) better capture real-world elections, generating realistic synthetic data. The work provides both algorithmic results (partition-based learning, polynomial-time procedures for 2- and t-parameter IAMs) and empirical evidence that mixtures outperform single components, with practical implications for simulating elections and understanding electoral cultures. This advances the modeling of real-life approval elections and offers a flexible framework for analyzing and generating election data with controllable complexity.

Abstract

We study the independent approval model (IAM) for approval elections, where each candidate has its own approval probability and is approved independently of the other ones. This model generalizes, e.g., the impartial culture, the Hamming noise model, and the resampling model. We propose algorithms for learning IAMs and their mixtures from data, using either maximum likelihood estimation or Bayesian learning. We then apply these algorithms to a large set of elections from the Pabulib database. In particular, we find that single-component models are rarely sufficient to capture the complexity of real-life data, whereas their mixtures perform well.

Figures (6)

• Figure 1: Absolute distance between the Amsterdam 289 election (38 candidates, left) or Warszawa 2020 Ochota election (51 candidates, right) and single-component $t$-parameter IAMs, as a function of $t$, from $1$ to the number of candidates.
• Figure 2: The relation between the average vote length and baseline distance (left plot), and absolute distances from the best learned model (right plot). Each dot depicts a single Pabulib instance. The color gives the profile's saturation (i.e., the average vote length divided by the number of candidates).
• Figure 3: The relation between the (negative) log-likelihood and the absolute distance (left plot), and relative distance (right plot). Each dot depicts a single Pabulib instance. The color corresponds to the average vote length.
• Figure 4: The comparison of the absolute and relative distances. The left plot shows from which city each instance originates (for Lodz and Warszawa we use different shades of green and blue, respectively, for different years). The right plot compares the single- and multi-component approaches. Each dot depicts a single Pabulib instance (the number of dots doubles in the right plot due to two approaches used).
• Figure 5: Comparison of Bayes and EM learning methods. The upper plots show the absolute distances for both methods, and the lower ones show the relative distances. By red (green) color we mark the cases where Bayes (EM) achieved smaller distance. Each dot depicts a single Pabulib instance.

Theorems & Definitions (22)

• Remark 2.1
• Remark 3.1
• Proposition 4.1
• proof
• Proposition 4.2
• proof
• Corollary 4.3
• Proposition 4.4
• Theorem 4.5
• proof : Proof of \ref{['thm:2-iam']}