Topic
Majority problem
About: Majority problem is a research topic. Over the lifetime, 42 publications have been published within this topic receiving 682 citations.
Papers
TL;DR: Binary voting automata as well as solutions to the multiple voting problem, where agents can vote for one candidate among |C| ≥ 2 candidates and need to determine the majority vote, are presented.
Abstract: A networked set of agents holding binary opinions does not seem to be able to compute its majority opinion by means of local binary interactions only. However, the majority problem can be solved using two or more bits, instead of one (F. Benezit , “Interval consensus: From quantized gossip to voting”, Apr. 2009, pp. 3661-3664). Pairs of agents asynchronously exchange their states and update them according to a voting automaton. This paper presents binary voting automata as well as solutions to the multiple voting problem, where agents can vote for one candidate among |C| ≥ 2 candidates and need to determine the majority vote. The voting automata are derived from the pairwise gossip algorithm, which computes averages. In the binary case (|C|=2), we focus on averages in dimension 1, but in the multiple case (|C| ≥ 2) we quantize gossip in dimension |C| - 1 , which is larger than or equal to 1. We show in particular that a consensus on majority can be reached using 15 possible states (4 bits) for the ternary voting problem, and using 100 possible states (7 bits) for the quaternary voting problem.
60 citations
16 Aug 2005
TL;DR: Given that the oblivious strategies are oblivious, a linear upper bound is established for the Majority problem with arbitrarily many different colors and it is shown that the Plurality problem is significantly more difficult by establishing quadratic lower and upper bounds.
Abstract: In the well-studied Majority problem, we are given a set of n balls colored with two or more colors, and the goal is to use the minimum number of color comparisons to find a ball of the majority color (i.e., a color that occurs for more than ⌈ n/2 ⌉ times). The Plurality problem has exactly the same setting while the goal is to find a ball of the dominant color (i.e., a color that occurs most often). Previous literature regarding this topic dealt mainly with adaptive strategies, whereas in this paper we focus more on the oblivious (i.e., non-adaptive) strategies. Given that our strategies are oblivious, we establish a linear upper bound for the Majority problem with arbitrarily many different colors. We then show that the Plurality problem is significantly more difficult by establishing quadratic lower and upper bounds. In the end, we also discuss some generalized upper bounds for adaptive strategies in the k-color Plurality problem.
22 citations
27 Nov 1995
TL;DR: The max-min propagation neural network model is considered as a hierarchical mixture of experts by replacing the max (min) units with softmax functions, and a gradient ascent algorithm and an expectation-maximization algorithm are presented.
Abstract: The max-min propagation neural network model is considered as a hierarchical mixture of experts by replacing the max (min) units with softmax functions. The resulting mixture is different from the model of Jordan and Jacobs, but we exploit the similarities between both models to derive a probability model. Learning is treated as a maximum-likelihood problem, in particular we present a gradient ascent algorithm and an expectation-maximization algorithm. Simulation results on the parity problem and the majority problem are reported.
18 citations
TL;DR: It is proved that (c − 1)(n2) color comparisons are necessary in the worst case to determine the plurality color and given an algorithm requiring (0.775) + 5.9) + 0.9 to determine an element of the plurality (most frequently occurring) color.
Abstract: Given a set of n elements, each of which is colored one of c colors, we must determine an element of the plurality (most frequently occurring) color by pairwise equal/unequal color comparisons of elements. We prove that (c − 1)(n − c)/2 color comparisons are necessary in the worst case to determine the plurality color and give an algorithm requiring (0.775c + 5.9)n + O(c2) color comparisons for c ≥ 9.
17 citations
TL;DR: A novel representation based on the ternary representation used for Learning Classifier Systems is designed and found able to produce superior performance to the bit string traditionally used for representing Cellular automata.
Abstract: The Density Classification Task is a well known test problem for two-state discrete dynamical systems. For many years researchers have used a variety of evolutionary computation approaches to evolve solutions to this problem. In this paper, we investigate the evolvability of solutions when the underlying Cellular Automaton is augmented with a type of memory based on the Least Mean Square algorithm. To obtain high performance solutions using a simple non-hybrid genetic algorithm, we design a novel representation based on the ternary representation used for Learning Classifier Systems. The new representation is found able to produce superior performance to the bit string traditionally used for representing Cellular automata. Moreover, memory is shown to improve evolvability of solutions and appropriate memory settings are able to be evolved as a component part of these solutions.
16 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 3 |
| 2020 | 3 |
| 2019 | 2 |
| 2018 | 2 |
| 2017 | 3 |
| 2016 | 4 |