Approval-Based Voting with Mixed Goods

Authors: Xinhang Lu, Jannik Peters, Haris Aziz, Xiaohui Bei, Warut Suksompong

AAAI 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We introduce two variants of EJR suitable for the mixed-goods setting... We then extend three multiwinner voting rules to our setting... In Section 4, we turn our attention to the concept of proportionality degree... An overview of our results can be found in Table 1.
Researcher Affiliation Academia 1School of Computer Science and Engineering, University of New South Wales 2Efficient Algorithms Research Group, Technische Universit at Berlin 3School of Physical and Mathematical Sciences, Nanyang Technological University 4School of Computing, National University of Singapore
Pseudocode Yes Greedy EJR-M Step 1: Initialize N = N and R = . Step 2: Let t be the largest nonnegative real number for which there exist = N N and R R such that N is a t -cohesive group, R Ri for all i N , and s(R ) = t . Consider any such pair (N , R ). Remove N from N and add the part of R that is not already in R to R . Step 3: If N = , return R . Else, go back to Step 2. Generalized MES Step 1: Initialize R = (C , G ) = ( , ) and bi = α/n for each i N. Step 2: Divide the remaining cake C into intervals I1, . . . , Ik so that each agent approves each interval either entirely or not at all. For each interval Ij = [x0, x1], x (x0, x1], and ρ 0, we say that Ij is (x, ρ)-affordable if X i NIj min(bi, (x x0) ρ) = x x0, where NIj N denotes the set of remaining agents who approve Ij. Similarly, for each remaining good g G and ρ 0, we say that g is ρ-affordable if X i Ng min(bi, ρ) = 1, where Ng N denotes the set of remaining agents who approve g. Step 3: If for every ρ, no ρ-affordable good or (x, ρ)affordable piece of cake exists, return R . Else, take either an interval Ij with the smallest ρ along with the largest x such that Ij is (x, ρ)-affordable, or a good g with the smallest ρ such that g is ρaffordable, depending on which ρ is smaller. In the former case, deduct min(bi, (x x0) ρ) from bi for each i NIj, and set C = C \[x0, x] and C = C [x0, x]. In the latter case, deduct min(bi, ρ) from bi for each i Ng, and set G = G \ {g} and G = G {g}. Remove all agents who have run out of budget from N, and go back to Step 2.
Open Source Code No The paper does not provide a link to source code or explicitly state that the code for the described methodology is publicly available.
Open Datasets No The paper is theoretical and does not involve empirical experiments with datasets, thus no information about public dataset availability is provided.
Dataset Splits No The paper is theoretical and does not involve empirical experiments with datasets, thus no information about dataset splits for training, validation, or testing is provided.
Hardware Specification No The paper is theoretical and does not report on computational experiments that would require hardware specifications.
Software Dependencies No The paper is theoretical and does not report on computational experiments, thus no specific software dependencies with version numbers are listed.
Experiment Setup No The paper is theoretical and does not describe computational experiments, thus no specific experimental setup details like hyperparameters or training configurations are provided.