DeepAI AI Chat
Log In Sign Up

Iterative Local Voting for Collective Decision-making in Continuous Spaces

02/26/2017
by   Nikhil Garg, et al.
Duke University
berkeley college
Stanford University
University of Illinois at Chicago
0

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 meta-algorithm called Iterative Local Voting for collective decision-making in this setting, in which 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. In general, such schemes do not converge, or, when they do, the resulting solution does not have a natural description. We first prove the convergence of this algorithm under appropriate choices of neighborhoods to plausible solutions 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 4,000 workers, employing neighborhoods defined by L^1, L^2 and L^∞ balls. We make several observations that inform future implementations of such a procedure.

READ FULL TEXT

page 11

page 13

page 15

page 16

page 18

03/04/2013

Restricted Manipulation in Iterative Voting: Convergence and Condorcet Efficiency

In collective decision making, where a voting rule is used to take a col...
07/31/2021

Iterative Deliberation via Metric Aggregation

We investigate an iterative deliberation process for an agent community ...
10/02/2017

Sequential Deliberation for Social Choice

In large scale collective decision making, social choice is a normative ...
07/04/2010

A Fast Decision Technique for Hierarchical Hough Transform for Line Detection

Many techniques have been proposed to speedup the performance of classic...
08/09/2018

Hunting for Tractable Languages for Judgment Aggregation

Judgment aggregation is a general framework for collective decision maki...
02/13/2011

Guaranteeing Convergence of Iterative Skewed Voting Algorithms for Image Segmentation

In this paper we provide rigorous proof for the convergence of an iterat...