Abstract
We consider approval-based committee voting, i.e. the setting where each voter approves a subset of candidates, and these votes are then used to select a fixed-size set of winners (committee). We propose a natural axiom for this setting, which we call justified representation (JR). This axiom requires that if a large enough group of voters exhibits agreement by supporting the same candidate, then at least one voter in this group has an approved candidate in the winning committee. We show that for every list of ballots it is possible to select a committee that provides JR. However, it turns out that several prominent approval-based voting rules may fail to output such a committee. In particular, while Proportional Approval Voting (PAV) always outputs a committee that provides JR , Sequential Proportional Approval Voting (SeqPAV), which is a tractable approximation to PAV , does not have this property. We then introduce a stronger version of the JR axiom, which we call extended justified representation (EJR), and show that PAV satisfies EJR , while other rules we consider do not; indeed, EJR can be used to characterize PAV within the class of weighted PAV rules. We also consider several other questions related to JR and EJR , including the relationship between JR /EJR and core stability, and the complexity of the associated computational problems.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 461-485 |
| Number of pages | 25 |
| Journal | Social Choice and Welfare |
| Volume | 48 |
| Issue number | 2 |
| DOIs | |
| State | Published - Feb 1 2017 |
Funding
The authors thank the anonymous reviewers of the Multidisciplinary Workshop on Advances in Preference Handling (MPREF 2014), and the Twenty-ninth AAAI Conference (AAAI 2015) for their helpful feedback on earlier versions of the paper. We further thank Svante Janson, Martin Lackner, Xavier Mora, and Piotr Skowron for valuable discussions. Brill, Conitzer, and Freeman were supported by NSF and ARO under Grants CCF-1101659, IIS-0953756, IIS-1527434, CCF-1337215, W911NF-12-1-0550, and W911NF-11-1-0332, by a Feodor Lynen research fellowship of the Alexander von Humboldt Foundation, and by COST Action IC1205 on Computational Social Choice. Aziz is supported by a Julius Career Award. Brill and Elkind were partially supported by ERC-StG 639945. Conitzer is supported by a Guggenheim Fellowship. Walsh also receives support from the Asian Office of Aerospace Research and Development (AOARD 124056) and the German Federal Ministry for Education and Research through the Alexander von Humboldt Foundation.
ASJC Scopus subject areas
- Social Sciences (miscellaneous)
- Economics and Econometrics