Truthful aggregation of budget proposals

We consider a participatory budgeting problem in which each voter submits a proposal for how to divide a single divisible resource (such as money or time) among several possible alternatives (such as public projects or activities) and these proposals must be aggregated into a single aggregate division. Under l1 preferences—for which a voter’s disutility is given by the l1 distance between the aggregate division and the division he or she most prefers—the social welfare-maximizing mechanism, which minimizes the average l1 distance between the outcome and each voter’s proposal, is incentive compatible [Goel et al. 2019]. However, it fails to satisfy a natural fairness notion of proportionality, placing too much weight on majority preferences. Leveraging a connection between market prices and the generalized median rules of Moulin [1980], we introduce the independent markets mechanism, which is both incentive compatible and proportional. We unify the social welfare-maximizing mechanism and the independent markets mechanism by defining a broad class of moving phantom mechanisms that includes both. We show that every moving phantom mechanism is incentive compatible. Finally, we characterize the social welfare-maximizing mechanism as the unique Pareto-optimal mechanism in this class, suggesting an inherent tradeoff between Pareto optimality and proportionality.

[1]  E. Yanovskaya.  A probabilistic model of social choice , 2006 .

[2]  Y. Cabannes.  Participatory budgeting: a significant contribution to participatory democracy , 2004 .

[3]  Fred W. Roush,et al.  Nonmanipulability in two dimensions , 1984 .

[4]  E. Eisenberg,et al.  CONSENSUS OF SUBJECTIVE PROBABILITIES: THE PARI-MUTUEL METHOD, , 1959 .

[5]  Dominik Peters,et al.  Fair division of the commons , 2019 .

[6]  Aaron Schneider,et al.  Budgets and ballots in Brazil : participatory budgeting from the city to the state , 2002 .

[7]  Kamesh Munagala,et al.  Iterative Local Voting for Collective Decision-making in Continuous Spaces , 2017, J. Artif. Intell. Res..

[8]  Nimrod Talmon,et al.  Proportionally Representative Participatory Budgeting: Axioms and Algorithms , 2017, AAMAS.

[9]  Ariel D. Procaccia,et al.  Preference Elicitation For Participatory Budgeting , 2017, AAAI.

[10]  S. Barberà,et al.  Voting under Constraints , 1997 .

[11]  Ariel D. Procaccia,et al.  Truthful Univariate Estimators , 2016, ICML.

[12]  Ioannis Caragiannis,et al.  Portioning Using Ordinal Preferences: Fairness and Efficiency , 2019, IJCAI.

[13]  R. Clemen.  Combining forecasts: A review and annotated bibliography , 1989 .

[14]  Klaus Nehring,et al.  Resource allocation by frugal majority rule , 2019 .

[15]  Faruk Gul,et al.  Generalized Median Voter Schemes and Committees , 1993 .

[16]  H. Peters,et al.  Pareto optimality, anonymity, and strategy-proofness in location problems , 1992 .

[17]  Jordi Massó,et al.  On strategy-proofness and symmetric single-peakedness , 2011, Games Econ. Behav..

[18]  Craig Boutilier,et al.  Social Choice : From Consensus to Personalized Decision Making , 2011 .

[19]  Haris Aziz,et al.  Fair Mixing: the Case of Dichotomous Preferences , 2017, EC.

[20]  M. Jackson,et al.  A characterization of strategy-proof social choice functions for economies with pure public goods , 1994 .

[21]  Haris Aziz,et al.  Participatory Budgeting: Models and Approaches , 2020, Pathways Between Social Science and Computational Social Science.

[22]  Kamesh Munagala,et al.  The Core of the Participatory Budgeting Problem , 2016, WINE.

[23]  Kim C. Border,et al.  Straightforward Elections, Unanimity, and Phantom Voters , 1983 .

[24]  Vincent Conitzer,et al.  Crowdsourcing Societal Tradeoffs , 2015, AAMAS.

[25]  D. J. Roberts,et al.  THE INCENTIVES FOR PRICE-TAKING BEHAVIOR IN LARGE EXCHANGE ECONOMIES , 1976 .

[26]  Christian Genest,et al.  Combining Probability Distributions: A Critique and an Annotated Bibliography , 1986 .

[27]  Ashish Goel,et al.  Knapsack Voting for Participatory Budgeting , 2019, ACM Trans. Economics and Comput..

[28]  Michael D. Intriligator,et al.  A Probabilistic Model of Social Choice , 1973 .

[29]  H. Moulin.  On strategy-proofness and single peakedness , 1980 .

[30]  Peter J. Varman,et al.  Demand Based Hierarchical QoS Using Storage Resource Pools , 2012, USENIX Annual Technical Conference.

[31]  Alexander Schrijver,et al.  Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.

[32]  Vincent Conitzer,et al.  Rules for Choosing Societal Tradeoffs , 2016, ISAIM.

[33]  Richard Stong,et al.  Collective choice under dichotomous preferences , 2005, J. Econ. Theory.

[34]  Conal Duddy,et al.  Fair sharing under dichotomous preferences , 2015, Math. Soc. Sci..

[35]  Gilbert Laffond,et al.  Euclidean preferences, option sets and strategyproofness , 2011 .