Smart contract execution -The (+-)-biased ballot problem

Lin Chen, Lei Xu, Zhimin Gao, Nolan Shah, Yang Lu, Weidong Shi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations


Transaction system build on top of blockchain, especially smart contract, is becoming an important part of world economy. However, there is a lack of formal study on the behavior of users in these systems, which leaves the correctness and security of such system without a solid foundation. Unlike mining, in which the reward for mining a block is fixed, different execution results of a smart contract may lead to significantly different payoffs of users, which gives more incentives for some user to follow a branch that contains a wrong result, even if the branch is shorter. It is thus important to understand the exact probability that a branch is being selected by the system. We formulate this problem as the (+-)-Biased Ballot Problem as follows: There are n voters one by one voting for either of the two candidates A and B. The probability of a user voting for A or B depends on whether the difference between the current votes of A and B is positive or negative. Our model takes into account the behavior of three different kinds of users when a branch occurs in the system - users having preference over a certain branch based on the history of their transactions, and users being indifferent and simply follow the longest chain. We study two important probabilities that are closely related with a blockchain based system -The probability that A wins at last, and the probability that A receives d votes first. We show how to recursively calculate the two probabilities for any fixed n and d, and also discuss their asymptotic values when n and d are sufficiently large.

Original languageEnglish
Title of host publication28th International Symposium on Algorithms and Computation, ISAAC 2017
EditorsTakeshi Tokuyama, Yoshio Okamoto
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770545
StatePublished - Dec 1 2017
Event28th International Symposium on Algorithms and Computation, ISAAC 2017 - Phuket, Thailand
Duration: Dec 9 2017Dec 22 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference28th International Symposium on Algorithms and Computation, ISAAC 2017


  • Blockchain
  • Probability
  • Random walk
  • Smart contract


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