Pref.Tools: Voting

For more information, see the prefsampling package.

• Impartial Culture (IC)
• Impartial Anonymous Culture (IAC)
• Urn
  alpha : float in [0, ∞) - After sampling a ranking, alpha * m! copies are added to the urn, where m is the number of candidates. A value of 0 corresponds to Impartial Culture. A value of 1.0 means that in the second iteration, there is a chance of 0.5 that the ballot of the first iteration is chosen and a chance of 0.5 that a new ballot is drawn according to Impartial Culture.
• Mallows
  phi : float in [0, 1] - dispersion parameter of the Mallows model where phi = 1 leads to Impartial Culture and phi = 0 leads to every voter having the same ranking.
  False True normalise_phi : bool - whether to normalize the phi parameter as as discussed in Boehmer, Faliszewski and Kraiczy (2023).
• Single-peaked (uniformly distributed, "Walsh")
• Single-peaked (peaks uniformly distributed, "Conitzer")
• Single-peaked on a circle
• Single-crossing
• Euclidean
  dimension : int - dimension of the Euclidean space
  Uniform cube Uniform ball Uniform sphere Gaussian cube Gaussian ball Unbounded Gaussian space : str - probability distribution of the voter and candidate points
• Plackett-Luce
  alphas : list of floats - Comma-separated list indicating for each alternative how many "balls" to place in the urn - rankings will be produced by sequentially drawing balls from the urn without replacement.
• Direct Dirichlet
  alphas : list of floats - The Direct Dirichlet model is very similar to the Plackett-Luce model, but the quality of the candidates is drawn from a Dirichlet distribution. The key difference is that the higher the sum of the alphas, the more correlated the votes are (the more concentrated the Dirichlet distribution is).

• Load PAV compared to Phragmén-style rules (shown at startup) Peters and Skowron, 2020, "Proportionality and the Limits of Welfarism", Introduction
• Load Running example used by Lackner and Skowron (2023) Lackner and Skowron, 2023, "Multi-Winner Voting with Approval Preferences", Springer, Example 2.1
• Load PAV fails core Aziz et al, 2016, "Justified Representation in Approval-Based Committee Voting", Example 6
• Load Seq-PAV fails JR (minimal example, k = 6, 108 voters) Sánchez-Fernández et al, 2016, "Proportional Justified Representation", Table 2
• Load Seq-Phragmén fails EJR Brill et al, 2021, "Phragmen's Voting Methods and Justified Representation", Example 6
• Load leximax- and var-phragmen fail EJR Brill et al, 2021, "Phragmen's Voting Methods and Justified Representation", Example 5
• Load Rev-Seq-PAV fails JR Aziz, 2017, "A Note on Justified Representation Under the Reverse Sequential PAV rule", Proposition 2 for k = 5
• Load Seq-Phragmén/seq-PAV/Equal Shares fail Pareto optimality Lackner and Skowron, 2020, "Utilitarian welfare and representation guarantees of approval-based multiwinner rules", Example 2