Creating closed lists for proportional elections: Mechanism design for inner-coalition elections

Abstract:   During parliamentary elections, it is common in many countries to use the D'Hondt method known to promote coalitions with closed lists. It follows that a game exists between parties of the same coalition to determine the list that they submit to represent the coalition in the election. It is common for list makers to impose criteria on the lists (e.g., female/male equality) unrelated to the parties for promotional or legal purposes. These criteria can impact the preferences parties/players have for the positions on the list.   In this paper, we define how to create a default list that maintains the stability of the coalition. We then consider how the criterion impacts the preferences of the parties/players. We show that no mechanism provides a list that verifies the three axioms: Pareto-efficiency (there is no list that is better for at least one player without being worse for another), d'Hondt Fairness (at least as good as the default list for all players), and Strategy-proofness. However, we can find non-trivial, intuitive, and practical solutions for any two axioms inspired by well-known algorithms.