Size approval voting

We propose a new class of voting rules, called Size Approval Voting. According to this rule, the effective weight of a vote from a given individual depends on how many other alternatives the very same individual votes for. In particular, weights are assumed to be non-negative and weakly decreasing in the number of approved alternatives. Then, for a given profile of individual votes, all those alternatives with the maximal sum of weighted votes are elected. We show in our axiomatic analysis that the family of all Size Approval Voting is characterized by a set of natural properties

Satisfaction approval voting

We propose a new voting system, satisfaction approval voting (SAV), for multiwinner elections, in which voters can approve of as many candidates or as many parties as they like. However, the winners are not those who receive the most votes, as under approval voting (AV), but those who maximize the sum of the satisfaction scores of all voters, where a voter’s satisfaction score is the fraction of his or her approved candidates who are elected. SAV may give a different outcome from A--in fact, SAV and AV outcomes may be disjoint—but SAV generally chooses candidates representing more diverse interests than does AV (this is demonstrated empirically in the case of a recent election of the Game Theory Society). A decision-theoretic analysis shows that all strategies except approving of a least-preferred candidate are undominated, so voters will often find it optimal to approve of more than one candidate. In party-list systems, SAV apportions seats to parties according to the Jefferson/d’Hondt method with a quota constraint, which favors large parties and gives an incentive to smaller parties to coordinate their policies and forge alliances, even before an election, that reflect their supporters’ coalitional preferences.multiwinner election; voting system; approval ballot; proportional representation; apportonment

The measurement of the value of a language

We address the problem of assessing the value of a language. We consider a stylized model of multilingual societies in which we introduce axioms formalizing the principles of impartiality, monotonicity, invariance and consistency. We show that the combination of these axioms characterizes a family of communicative benefit functions which assign a value to each language in the society. The functions within the family involve a two-step procedure. First, they identify the groups of agents that can communicate in each language. Second, each group is assigned an aggregate (size-dependent) value, which is evenly divided among the languages in which the group can communicate. Our novel approach could be useful in a wide range of empirical applications and policy decisions.The first author acknowledges the financial support from the Spanish Government through grant PGC2018-093542-B-I00 funded by MCIN/AEI/10.13039/501100011033 and by 'ERDF A way of making Europe'. The second author acknowledges the Spanish Government through grant PID2020-115011GB-I00, funded by MCIN/AEI/10.13039/501100011033. Funding for publishing: Universidad Pablo de Olavide/CBUA

Qualified voting mechanisms

We study voting mechanisms, which consist of two elements: a profile of sets of votes (this profile describes the votes that voters are allowed to cast) and a voting scheme (which explains how to aggregate those votes). To investigate how these two elements interact, we impose some properties on the sets of votes (i.e., regularity ) and on the voting scheme (i.e., candidate monotonicity, candidate anonymity, and weak neutrality ). We characterize the family of voting schemes that satisfy some of those properties and analyze the role played by the structure of the sets of votes in these characterizations. Voting, approval voting rule, plurality rule, monotonicity, anonymity, neutrality, qualified votin

Decentralized revenue sharing from broadcasting sports

We study the problem of sharing the revenues from broadcasting sports leagues among participating clubs. First, we characterize the set of rules satisfying two basic axioms: anonymity and additivity. Then, we decentralize the problem by letting clubs vote for rules. No majority equilibrium exists when they are allowed to vote for any rule within the characterized set. However, if the set is restricted in a meaningful and plausible way (just replacing anonymity by equal treatment of equals), majority equilibrium does exist.Universidad Pablo de Olavide. Departamento de Economía, Métodos Cuantitativos e Historia Económic

Non-anonymous ballot aggregation: an axiomatic generalization of Approval Voting

We study axiomatically situations in which the society agrees to treat voters with different characteristics distinctly. In this setting, we propose a set of intuitive axioms and show that they jointly characterize a new class of voting procedures, called Type-weighted Approval Voting. According to this family, each voter has a strictly positive and finite weight (the weight is necessarily the same for all voters with the same characteristics) and the alternative with the highest number of weighted votes is elected. The implemented voting procedure reduces to Approval Voting in case all voters are identical or the procedure assigns the same weight to all types. Using this idea, we also obtain a new characterization of Approval Voting.The first author’s financial support from the Spanish Ministry of Education and Science, through the project ECO2012–34202, and Fundación Ramón Areces is gratefully acknowledged. The second author’s financial support from the Spanish Ministry of Education and Science, through the project ECO2012–31985, and Fundación Ramón Areces is gratefully acknowledged