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Many societal decision problems lie in high-dimensional continuous spaces not amenable to the voting techniques common for their discrete or single-dimensional counterparts. These problems are typically discretized before running an election or decided upon through negotiation by representatives. We propose a algorithm called Iterative Local Voting for collective decision-making in this setting. In this algorithm, voters are sequentially sampled and asked to modify a candidate solution within some local neighborhood of its current value, as defined by a ball in some chosen norm, with the size of the ball shrinking at a specified rate. We first prove the convergence of this algorithm under appropriate choices of neighborhoods to Pareto optimal solutions with desirable fairness properties in certain natural settings: when the voters' utilities can be expressed in terms of some form of distance from their ideal solution, and when these utilities are additively decomposable across dimensions. In many of these cases, we obtain convergence to the societal welfare maximizing solution.We then describe an experiment in which we test our algorithm for the decision of the U.S. Federal Budget on Mechanical Turk with over 2,000 workers, employing neighborhoods defined by various L-Norm balls. We make several observations that inform future implementations of such a procedure.
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Pairwise Distances and the Problem of Multiple Optima
Discrete optimization problems arise in many biological contexts and, in many cases, we seek to make inferences from the optimal solutions. However, the number of optimal solutions is frequently very large and making inferences from any single solution may result in conclusions that are not supported by other optimal solutions. We describe a general approach for efficiently (polynomial time) and exactly (without sampling) computing statistics on the space of optimal solutions. These statistics provide insights into the space of optimal solutions that can be used to support the use of a single optimum (e.g., when the optimal solutions are similar) or justify the need for selecting multiple optima (e.g., when the solution space is large and diverse) from which to make inferences. We demonstrate this approach on two well-known problems and identify the properties of these problems that make them amenable to this method.
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- Award ID(s):
- 2231150
- PAR ID:
- 10539014
- Editor(s):
- Singh, M
- Publisher / Repository:
- Mary Ann Liebert
- Date Published:
- Journal Name:
- Journal of Computational Biology
- Volume:
- 31
- Issue:
- 7
- ISSN:
- 1557-8666
- Page Range / eLocation ID:
- 638 to 650
- Format(s):
- Medium: X Other: pdf
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1089/cmb.2023.0382
