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on Collective Decision-Making |
| By: | Kazuya Kikuchi; Yukio Koriyama |
| Abstract: | We consider collective decision making when the society consists of groups endowed with voting weights. Each group chooses an internal rule that specifies the allocation of its weight to the alternatives as a function of its members' preferences. Under fairly general conditions, we show that the winner-take-all rule is a dominant strategy, while the equilibrium is Pareto dominated, highlighting the dilemma structure between optimality for each group and for the whole society. We also develop a technique for asymptotic analysis and show Pareto dominance of the proportional rule. Our numerical computation for the US Electoral College verifies its sensibility. |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2206.09574&r= |
| By: | Kiran Tomlinson; Johan Ugander; Jon Kleinberg |
| Abstract: | Instant runoff voting (IRV) is an increasingly-popular alternative to traditional plurality voting in which voters submit rankings over the candidates rather than individual votes. In practice, municipalities often restrict the ballot length, the number of candidates a voter is allowed to rank on their ballot. We theoretically and empirically analyze how ballot length can influence the outcome of an election, given fixed voter preferences. We show that there exist preference profiles over $k$ candidates such that up to $k-1$ different candidates win at different ballot lengths. We derive exact lower bounds on the number of voters required for such profiles and provide constructions matching these bounds. Additionally, we fully characterize which sequences of winners are possible over ballot lengths and provide explicit profile constructions achieving any feasible winner sequence. Finally, we analyze a collection of 168 real-world elections, where we truncate rankings to simulate shorter ballots. We find that shorter ballots could have changed the outcome in one quarter of these elections and that longer ballots can favor particular candidates. Our results highlight ballot length as a consequential degree of freedom in the design of IRV elections. |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2207.08958&r= |
| By: | Gogulapati Sreedurga; Soumyarup Sadhukhan; Souvik Roy; Yadati Narahari |
| Abstract: | We study fairness in social choice settings under single-peaked preferences. Construction and characterization of social choice rules in the single-peaked domain has been extensively studied in prior works. In fact, in the single-peaked domain, it is known that unanimous and strategy-proof deterministic rules have to be min-max rules and those that also satisfy anonymity have to be median rules. Further, random social choice rules satisfying these properties have been shown to be convex combinations of respective deterministic rules. We non-trivially add to this body of results by including fairness considerations in social choice. Our study directly addresses fairness for groups of agents. To study group-fairness, we consider an existing partition of the agents into logical groups, based on natural attributes such as gender, race, and location. To capture fairness within each group, we introduce the notion of group-wise anonymity. To capture fairness across the groups, we propose a weak notion as well as a strong notion of fairness. The proposed fairness notions turn out to be natural generalizations of existing individual-fairness notions and moreover provide non-trivial outcomes for strict ordinal preferences, unlike the existing group-fairness notions. We provide two separate characterizations of random social choice rules that satisfy group-fairness: (i) direct characterization (ii) extreme point characterization (as convex combinations of fair deterministic social choice rules). We also explore the special case where there are no groups and provide sharper characterizations of rules that achieve individual-fairness. |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2207.07984&r= |
| By: | Terrence Iverson |
| Abstract: | A two-tier climate club exploits the comparative advantage of large countries to mete out punishments through trade, while taking their capacity to resist punishment as a constraint. Countries outside the coalition price carbon at a fixed fraction of the average carbon price adopted within the coalition, or face tariffs. Coalition countries abate more since doing so induces matching abatement elsewhere. If the rate at which noncoalition countries match coalition abatement goes to one, equilibrium abatement approximates the globally efficient outcome even though the coalition only internalizes damages within its borders. Even with a low match rate, the arrangement drastically reduces aggregate abatement costs. In contrast to a single-tier climate club in which many stable coalitions are possible, the stable coalition in the calibrated model is unique and consists of the US and the EU. Global abatement achieved by the stable agreement is about 40 percent of the efficient level. |
| Keywords: | international environmental agreement, climate club, trade sanctions, retaliation, incomplete participation costs, country-size heterogeneity |
| JEL: | Q54 Q56 Q58 F18 F53 H23 H41 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9831&r= |