Accelerating Voting by Quantum Computation

• URL: http://arxiv.org/abs/2301.02995v4
• Date: Thu, 8 Jun 2023 21:42:21 GMT
• Title: Accelerating Voting by Quantum Computation
• Authors: Ao Liu, Qishen Han, Lirong Xia, Nengkun Yu
• Abstract summary: We propose a quantum-accelerated voting algorithm that can be applied to any anonymous voting rule. Our algorithm outputs the correct winner with high probability in $Thetaleft(fracntextMOVright)$ time.
• Score: 35.03314687289671
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Studying the computational complexity and designing fast algorithms for determining winners under voting rules are classical and fundamental questions in computational social choice. In this paper, we accelerate voting by leveraging quantum computation: we propose a quantum-accelerated voting algorithm that can be applied to any anonymous voting rule. We show that our algorithm can be quadratically faster than any classical algorithm (based on sampling with replacement) under a wide range of common voting rules, including positional scoring rules, Copeland, and single transferable voting (STV). Precisely, our quantum-accelerated voting algorithm outputs the correct winner with high probability in $\Theta\left(\frac{n}{\text{MOV}}\right)$ time, where $n$ is the number of votes and $\text{MOV}$ is {\em margin of victory}, the smallest number of voters to change the winner. In contrast, any classical voting algorithm based on sampling with replacement requires $\Omega\left(\frac{n^2}{\text{MOV}^2}\right)$ time under a large class of voting rules. Our theoretical results are supported by experiments under plurality, Borda, Copeland, and STV.

Related papers

• Improving the Computational Efficiency of Adaptive Audits of IRV Elections [54.427049258408424]
  AWAIRE can audit IRV contests with any number of candidates, but the original implementation incurred memory and computation costs that grew superexponentially with the number of candidates. This paper improves the algorithmic implementation of AWAIRE in three ways that make it practical to audit IRV contests with 55 candidates, compared to the previous 6 candidates.
  arXiv  Detail & Related papers  (2024-07-23T13:28:00Z)
• Quantum-Enhanced Secure Approval Voting Protocol [0.0]
  This paper introduces a quantum voting protocol, a blend of quantum principles (entanglement and superposition), blockchain technology, and digital signatures. The protocol is tested on IBM quantum hardware, achieving impressively low error rates of just 1.17% in a four-candidate election.
  arXiv  Detail & Related papers  (2024-06-28T08:20:25Z)
• Computing Voting Rules with Elicited Incomplete Votes [11.550634521005968]
  We study voting rules that are computable by querying voters about $t m$ candidates. For scoring rules that are computable with limited-sized queries, we give parameterized upper and lower bounds on the number of such queries.
  arXiv  Detail & Related papers  (2024-02-16T22:17:01Z)
• Entanglement and coherence in Bernstein-Vazirani algorithm [58.720142291102135]
  Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle. We analyze in detail the quantum resources in the Bernstein-Vazirani algorithm. We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state.
  arXiv  Detail & Related papers  (2022-05-26T20:32:36Z)
• Obvious Manipulability of Voting Rules [105.35249497503527]
  The Gibbard-Satterthwaite theorem states that no unanimous and non-dictatorial voting rule is strategyproof. We revisit voting rules and consider a weaker notion of strategyproofness called not obvious manipulability.
  arXiv  Detail & Related papers  (2021-11-03T02:41:48Z)
• An algorithm for a fairer and better voting system [0.0]
  This article is about a novel, better ranked voting system that aims to solve the problem of finding the best candidate to represent the voters. We have the source code on GitHub, for making realistic simulations of elections, based on artificial intelligence. We have convincing evidence that our algorithm is better than Instant-Runoff Voting, Preferential Block Voting, Single Transferable Vote, and First Past The Post.
  arXiv  Detail & Related papers  (2021-10-13T22:34:49Z)
• Learning to Elect [7.893831644671976]
  Voting systems have a wide range of applications including recommender systems, web search, product design and elections. We show that set-input neural network architectures such as Set Transformers, fully-connected graph networks and DeepSets are both theoretically and empirically well-suited for learning voting rules.
  arXiv  Detail & Related papers  (2021-08-05T17:55:46Z)
• Bribery as a Measure of Candidate Success: Complexity Results for Approval-Based Multiwinner Rules [58.8640284079665]
  We study the problem of bribery in multiwinner elections, for the case where the voters cast approval ballots (i.e., sets of candidates they approve) We consider a number of approval-based multiwinner rules (AV, SAV, GAV, RAV, approval-based Chamberlin--Courant, and PAV) In general, our problems tend to be easier when we limit out bribery actions on increasing the number of approvals of the candidate that we want to be in a winning committee.
  arXiv  Detail & Related papers  (2021-04-19T08:26:40Z)
• Fine-Grained Complexity and Algorithms for the Schulze Voting Method [9.399840807973545]
  We study computational aspects of a well-known single-winner voting rule called the Schulze method. Our paper is the first to bring fine-grained complexity into the field of computational social choice.
  arXiv  Detail & Related papers  (2021-03-05T22:27:36Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.