Discrete Incremental Voting on Expanders
Colin Cooper, Tomasz Radzik, Takeharu Shiraga

TL;DR
This paper introduces discrete incremental voting on expanders, analyzing how opinions evolve in a graph where vertices update opinions gradually towards neighbors, and shows that under certain conditions the final opinion approximates a weighted average of initial opinions.
Contribution
It models a new form of pull voting with discrete opinion changes and proves that on expanders, the final consensus closely matches the initial weighted average under specific spectral and size conditions.
Findings
Final opinion approximates initial weighted average c.
Convergence occurs with high probability on expanders.
Results depend on spectral gap and number of opinions.
Abstract
Pull voting is a random process in which vertices of a connected graph have initial opinions chosen from a set of distinct opinions, and at each step a random vertex alters its opinion to that of a randomly chosen neighbour. If the system reaches a state where each vertex holds the same opinion, then this opinion will persist forthwith. In general the opinions are regarded as incommensurate, whereas in this paper we consider a type of pull voting suitable for integer opinions such as which can be compared on a linear scale; for example, 1 ('disagree strongly'), 2 ('disagree'), 5 ('agree strongly'). On observing the opinion of a random neighbour, a vertex updates its opinion by a discrete change towards the value of the neighbour's opinion, if different. Discrete incremental voting is a pull voting process which mimics this behaviour. At each step a…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsInternet Traffic Analysis and Secure E-voting · Game Theory and Voting Systems · Auction Theory and Applications
