How to choose a non-controversial list with k names

Barberà and Coelho (2006) documented six screening rules associated with the rule of k names that are used by different institutions around the world. Here, we study whether these screening rules satisfy stability. A set is said to be a weak Condorcet set la Gehrlein (1985) if no candidate in this set can be defeated by any candidate from outside the set on the basis of simple majority rule. We say that a screening rule is stable if it always selects a weak Condorcet set whenever such set exists. We show that all of the six procedures which are used in reality do violate stability if the voters act not strategically. We then show that there are screening rules which satisfy stability. Finally, we provide two results that can explain the widespread use of unstable screening rules.NULL

Proportional justified representation

Proceedings of: 31st AAAI Conference on Artificial Intelligence (AAAI-17), San Francisco, California, USA, February 4-9, 2017.The goal of multi-winner elections is to choose a fixed-size committee based on voters’ preferences. An important concern in this setting is representation: large groups of voters with cohesive preferences should be adequately represented by the election winners. Recently, Aziz et al. proposed two axioms that aim to capture this idea: justified representation (JR) and its strengthening extended justified representation (EJR). In this paper, we extend the work of Aziz et al. in several directions. First, we answer an open question of Aziz et al., by showing that Reweighted Approval Voting satisfies JR for k = 3; 4; 5, but fails it for k >= 6. Second, we observe that EJR is incompatible with the Perfect Representation criterion, which is important for many applications of multi-winner voting, and propose a relaxation of EJR, which we call Proportional Justified Representation (PJR). PJR is more demanding than JR, but, unlike EJR, it is compatible with perfect representation, and a committee that provides PJR can be computed in polynomial time if the committee size divides the number of voters. Moreover, just like EJR, PJR can be used to characterize the classic PAV rule in the class of weighted PAV rules. On the other hand, we show that EJR provides stronger guarantees with respect to average voter satisfaction than PJR does.This research was supported in part by the Spanish Ministerio de Economía y Competitividad (project HERMES-SMARTDRIVER TIN2013-46801-C4-2-R), by the Autonomous Community of Madrid (project e-Madrid S2013/ICE-2715), and by ERC Starting Grant 639945

Compromising on compromise rules

We propose three mechanisms to reach compromise between two opposing parties. They are based on the use of Rules of k Names, whereby one of the parties proposes a shortlist and the other chooses from it. Methods of this class are used in practice to appoint Supreme Court justices and have been recently proposed for arbitration selection processes. Those we suggest are flexible and allow the parties to participate in the endogenous determination of the role of proposer and the shortlist size. They involve few stages, implement the Unanimity Compromise Set, and are robust to the strategic inclusion of candidates