Smart Contract Execution - the (+-)-Biased Ballot Problem

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

Short proofs in extrema of spectrally one sided Lévy processes

We provide short and simple proofs of the continuous time ballot theorem for processes with cyclically interchangeable increments and Kendall's identity for spectrally positive Lévy processes. We obtain the later result as a direct consequence of the former. The ballot theorem is extended to processes having possible negative jumps. Then we prove through straightforward arguments based on the law of bridges and Kendall's identity, Theorem 2.4 in [19] which gives an expression for the law of the supremum of spectrally positive Lévy processes. An analogous formula is obtained for the supremum of spectrally negative Lévy processes

Popular Sovereignty during the COVID-19 Pandemic: Lessons from the Visegrád Countries. National and Local Elections in the Shadow of the Coronavirus

The coronavirus crisis led to severe restrictions of numerous fundamental rights almost globally, amongst which the right to vote was also concerned. Our research article aims to integrate the experience of the Visegrád region into the emerging strand of international legal scholarship from the long-term impact of the public health emergency on electoral frameworks. Based on a research collaboration funded by the International Visegrád Fund, the study presents the adaptative measures implemented by the four Visegrád countries to hold national or municipal elections in the shadow of the global pandemic, and contextualizes these interventions in the light of the global electoral tendencies. Finally, based on our research, the expected features of post-COVID electoral frameworks in the Visegrád region were also provided. Alternative electoral regimes are discussed for the promotion of flexibility and resilience, which are grounded on the combined elements of the traditional voting system, on additional public health requirements, and also on the extensive application of postal- and electronic voting

The Intelligibility of Referendum Issues and the Opportunities to Inform Voters. Comparative Observations with Special Regard to Hungary

The intelligibility of initiative proposals is of utmost importance in case of direct democratic decisions. This study sums up the tools by means of which voters are informed about referendum issues in countries or states with well developed direct democratic traditions, like Switzerland, Oregon and California. A special attention is paid to ballot pamphlets and requirements regarding the wording of the proposal. The second part of the study focuses on Hungary. Ballot pamphlets are not in use here, the practice of the authorities is centred on the “requirement of the unambiguity of the question”. Based on an analysis of the resolutions of the National Election Committee, the decisions of the Constitutional Court and the Curia (Supreme Court) of Hungary, the authors demonstrate that the requirement of unambiguity has become an obligation of initiators which is very difficult to comply with. The study finally recommends possible solutions in order to make the tool of bottom-up initiative a more practicable instrument of direct democracy in Hungary

Consolidated proposal for encoding the Old Hungarian script in the UCS

This is a proposal to encode the Old Hungarian script in the international character encoding standard Unicode. The script was published in Unicode Standard version 8.0 in June 2015. The script was used to write the Hungarian language, and continues in limited use today. It is also known by the name Rovásírás as well as other names

Maximal displacement of a branching random walk in time-inhomogeneous environment

Consider a branching random walk evolving in a macroscopic time-inhomogeneous environment, that scales with the length $n$ of the process under study. We compute the first two terms of the asymptotic of the maximal displacement at time $n$. The coefficient of the first (ballistic) order is obtained as the solution of an optimization problem, while the second term, of order $n^{1/3}$, comes from time-inhomogeneous random walk estimates, that may be of independent interest. This result partially answers a conjecture of Fang and Zeitouni. Same techniques are used to obtain the asymptotic of other quantities, such as the consistent maximal displacement.Comment: 51 pages, to appear in SP