A current trend in social choice theory is to study new models that have the flavor of both collective decision-making and fair division. Examples include multi-winner elections (which are concerned with the composition of committees of a fixed size), participatory budgeting (which deals with the allocation of a public budget among various projects), and probabilistic social choice (which studies voting rules that allow for lotteries as outcomes).

The unifying theme of these settings is that a society of agents aims at collectively deciding on the allocation of some—divisible or indivisible—public resource such as money, time, seats, or probability to various possible entities such as candidates, projects, activities, or parties. The basis for these collective decisions are the preferences of the individual agents, and a common obstacle in the design of attractive allocation rules is the pervasive conflict between efficiency, strategyproofness, and fairness.

Some of the settings described above are especially well-studied in the computational social choice community. However, we solicited submissions from all backgrounds, and no computational studies were required. All submissions went through Social Choice and Welfare’s rigorous peer-reviewing process, and we are happy to present ten high-quality articles in a double special issue.

A General Framework for Participatory Budgeting with Additional Constraints:

Simon Rey, Ulle Endriss, and Ronald de Haan propose a computationally tractable method of embedding participatory budgeting into judgment aggregation. This enables them to capture settings where there are additional constraints, such as dependencies between projects and quotas over categories of projects. The paper then reinterprets popular judgment aggregation rules in the context of participatory budgeting and checks whether they satisfy common participatory budgeting axioms.

Quadratic Funding with Incomplete Information:

Luis Mota Freitas and Wilfredo Leiva Maldonado show how the inefficiency of quadratic funding can be measured in settings of incomplete information. It turns out that quadratic funding can only guarantee efficiency in degenerate cases, that is, for a rather narrow class of utility functions.

Individual Representation in Approval-Based Committee Voting:

Markus Brill, Jonas Israel, Evi Micha, and Jannik Peters introduce and investigate a new criterion to measure the individual representation of outcomes in approval-based committee elections. While it is generally NP-hard to decide whether a committee satisfies this condition, the authors identify restricted domains of preferences that allow checking the condition in polynomial time.

Approval-Based Shortlisting:

Martin Lackner and Jan Maly study an important but so far neglected problem: shortlisting, that is, selecting from a long set of alternatives a small list whose size is not fixed in advance. They analyze, axiomatically and experimentally, a number of shortlisting methods with approval ballots as input, and end up giving a short list of recommendations.

Optimal Algorithms for Multiwinner Elections and the Chamberlin-Courant Rule:

Kamesh Munagala, Zeyu Shen, and Kangning Wang study greedy algorithms for popular multiwinner voting rules with ranked ballots, such as the Chamberlin-Courant rule and the s-Borda rule. They show that the greedy approach, which is computationally efficient, offers excellent approximation for the satisfaction versions of these problems. For the dissatisfaction version, they formulate an optimal benchmark score and show that it is satisfied by the Banzhaf rule.

Proportional Representation in Matching Markets: Selecting Multiple Matchings under Dichotomous Preferences:

Niclas Böhmer, Markus Brill, and Ulrike Schmidt-Kraepelin consider a problem at the interface of matching theory and multi-winner voting. Given a set of agents who have dichotomous preferences over each other, the goal is to select a set of matchings of the agents that fairly represent the agents’ preferences. The authors apply ideas from proportional representation in multi-winner voting to the problem of selecting a set of matchings.

Dynamic Proportional Rankings:

Jonas Israel and Markus Brill study the problem of dynamically or sequentially selecting alternatives with the goal of ensuring “proportional representativeness.” The problem is motivated by the application of live Question and Answer platforms, where posted questions are ranked based on the interests of the audience. The authors leverage ideas from approval-based multi-winner voting.

Flexible Representative Democracy: An Introduction with Binary Issues:

Ben Abramovitz and Nicholas Mattei introduce flexible representative democracy, which takes the best of both worlds from direct democracy and representative democracy. As in representative democracy, voters elect a set of representatives, but they have great flexibility in determining how they are represented. As a result, representatives are weighted, and their weights can differ over time and across issues. The main finding is that assigning representatives issue-specific weights based on voter delegations can yield significant improvements in the quality of decision outcomes.

Truthful Cake Sharing:

Xiaohui Bei, Xinhang Lu, and Warut Suksompong consider a new problem: fair cake sharing. Here, the cake is the unit interval. A set of agents must choose collectively a subset of the cake, subject to a length constraint. Assuming that agents have piecewise uniform preferences (they express the parts of the cake they like, and their utility is the length of the part of the selected subset that they like), the authors show that the leximin mechanism is excludable truthful (agents have no incentive to lie if they will be able to access only parts of the cake that they declared to like), and that the maximum Nash welfare mechanism is excludable truthful only for two agents.

Fair group decisions via non-deterministic proportional consensus:

Jobst Heitzig, Forest W. Simmons, and Sara M. Constantino propose a new voting rule called Maximum Partial Consensus (MaxParC). The aim of this rule is to incentivize voters to seek consensus options while sharing the voting power consensually among groups of voters and using as little randomness as possible. The main technical tool is the use of conditional commitments, which enable the voters to coordinate on plausible alternatives. The theoretical analysis is complemented by an online MTurk experiment as well as by agent-based simulations.

***

We are confident that this fine collection of articles in the emerging area of fair public decision-making will resonate well with the readers of Social Choice and Welfare.