skip to main content

Attention:

The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 11:00 PM ET on Thursday, October 10 until 2:00 AM ET on Friday, October 11 due to maintenance. We apologize for the inconvenience.

Explore Research Products in the NSF-PAR

This content will become publicly available on February 7, 2025

Title: Polynomial Voting Rules

We propose and study a new class of polynomial voting rules for a general decentralized decision/consensus system, and more specifically for the proof-of-stake protocol. The main idea, inspired by the Penrose square-root law and the more recent quadratic voting rule, is to differentiate a voter’s voting power and the voter’s share (fraction of the total in the system). We show that, whereas voter shares form a martingale process that converges to a Dirichlet distribution, their voting powers follow a supermartingale process that decays to zero over time. This prevents any voter from controlling the voting process and, thus, enhances security. For both limiting results, we also provide explicit rates of convergence. When the initial total volume of votes (or stakes) is large, we show a phase transition in share stability (or the lack thereof), corresponding to the voter’s initial share relative to the total. We also study the scenario in which trading (of votes/stakes) among the voters is allowed and quantify the level of risk sensitivity (or risk aversion) in three categories, corresponding to the voter’s utility being a supermartingale, a submartingale, and a martingale. For each category, we identify the voter’s best strategy in terms of participation and trading.

Funding: W. Tang gratefully acknowledges financial support through the National Science Foundation [Grants DMS-2113779 and DMS-2206038] and through a start-up grant at Columbia University. D. D. Yao’s work is part of a Columbia–City University/Hong Kong collaborative project that is supported by InnoHK Initiative, the Government of Hong Kong Special Administrative Region, and the Laboratory for AI-Powered Financial Technologies.

  more » « less
Award ID(s):
2206038 2113779
NSF-PAR ID:
10490341
Author(s) / Creator(s):
;
Publisher / Repository:
Institute for Operations Research and the Management Sciences
Date Published:
Journal Name:
Mathematics of Operations Research
ISSN:
0364-765X
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; ( , Management Science)

    Although leveraged exchange-traded funds (ETFs) are popular products for retail investors, how to hedge them poses a great challenge to financial institutions. We develop an optimal rebalancing (hedging) model for leveraged ETFs in a comprehensive setting, including overnight market closure and market frictions. The model allows for an analytical optimal rebalancing strategy. The result extends the principle of “aiming in front of target” introduced by Gârleanu and Pedersen (2013) from a constant weight between current and future positions to a time-varying weight because the rebalancing performance is monitored only at discrete time points, but the rebalancing takes place continuously. Empirical findings and implications for the weekend effect and the intraday trading volume are also presented.

    This paper was accepted by Agostino Capponi, finance.

    Funding: M. Dai acknowledges support from the National Natural Science Foundation of China [Grant 12071333], the Hong Kong Polytechnic University [Grant P0039114], and the Singapore Ministry of Education [Grants R-146-000-243/306/311-114 and R-703-000-032-112]. H. M. Soner acknowledges partial support from the National Science Foundation [Grant DMS 2106462]. C. Yang acknowledges support from the Chinese University of Hong Kong [Grant 4055132 and a University Startup Grant].

    Supplemental Material: Data and the online supplement are available at https://doi.org/10.1287/mnsc.2022.4407 .

     
    more » « less
  2. ; ( , Mathematical Finance)
    Abstract

    We develop a continuous‐time control approach to optimal trading in a Proof‐of‐Stake (PoS) blockchain, formulated as a consumption‐investment problem that aims to strike the optimal balance between a participant's (or agent's) utility from holding/trading stakes and utility from consumption. We present solutions via dynamic programming and the Hamilton–Jacobi–Bellman (HJB) equations. When the utility functions are linear or convex, we derive close‐form solutions and show that the bang‐bang strategy is optimal (i.e., always buy or sell at full capacity). Furthermore, we bring out the explicit connection between the rate of return in trading/holding stakes and the participant's risk‐adjusted valuation of the stakes. In particular, we show when a participant is risk‐neutral or risk‐seeking, corresponding to the risk‐adjusted valuation being a martingale or a sub‐martingale, the optimal strategy must be to either buy all the time, sell all the time, or first buy then sell, and with both buying and selling executed at full capacity. We also propose a risk‐control version of the consumption‐investment problem; and for a special case, the “stake‐parity” problem, we show a mean‐reverting strategy is optimal.

     
    more » « less
  3. ; ; ; ( , Cryptologia)
    null (Ed.)
    We present Phrase-Verified Voting, a voter-verifiable remote voting system easily assembled from commercial off-the-shelf software for small private elections. The system is transparent and enables each voter to verify that the tally includes their ballot selection without requiring any understanding of cryptography. This system is an example of making voter verification usable. The paper describes the system and an experience with it in fall 2020, to vote remotely in promotion committees in a university. Each voter fills out a form in the cloud with their selection $V$ for each race and a two-word passphrase $P$. The system generates a verification prompt of the $(V,P)$ pairs and a tally of the votes, organized to help visualize how the votes add up. After the polls close, each voter verifies that this table lists their $(V,P)$ pair and that the tally is computed correctly. The system is especially appropriate for any small group making sensitive decisions. Because the system would not prevent a coercer from demanding that their victim use a specified passphrase, it is not designed for applications where such malfeasance would be likely or go undetected. Results from 43 voters show that the system performed effectively for its intended purpose, and introduced users to the concept of voter-verified elections. Compared to the commonly-used alternatives of paper ballots or voting by email, voters found the system easier to use, and that it provided greater privacy and outcome integrity. 
    more » « less
  4. ; ; ; ; ; ; ; ; ; ( , E-VOTE-ID 2022)
    We solve a long-standing challenge to the integrity of votes cast without the supervision of a voting booth: ``{\it improper influence},'' which typically refers to any combination of vote buying and voter coercion. Our approach allows each voter, or their trusted agents (which we call ``{\it hedgehogs}''), to {\it ``nullify''} (effectively cancel) their vote in a way that is unstoppable, irrevocable, and forever unattributable to the voter. In particular, our approach enhances security of online, remote, public-sector elections, for which there is a growing need and the threat of improper influence is most acute. We introduce the new approach, give detailed cryptographic protocols, show how it can be applied to several voting settings, and describe our implementation. The protocols compose a full voting system, which we call {\it {\votexx}}, including registration, voting, nullification, and tallying---using an anonymous communication system for registration, vote casting, and other communication in the system. We demonstrate how the technique can be applied to known systems, including where ballots can be mailed to voters and voters use codes on the ballot to cast their votes online. In comparison with previous proposals, our system makes fewer assumptions and protects against a strong adversary who learns all of the voter's keys. In {\votexx}, each voter has two public-private key pairs. Without revealing their private keys, each voter registers their public keys with the election authority. Each voter may share their keys with one or more hedgehogs. During nullification, the voter, or one or more of their hedgehogs, can interact through the anonymous communication system to nullify a vote by proving knowledge of one of the voter's private keys via a zero-knowledge proof without revealing the private key. We describe a fully decentralizable implementation of {\votexx}, including its public bulletin board, which could be implemented on a blockchain. 
    more » « less
  5. ; ; ( , Operations Research)
    We study systemic risk in a supply chain network where firms are connected through purchase orders. Firms can be hit by cost or demand shocks, which can cause defaults. These shocks propagate through the supply chain network via input-output linkages between buyers and suppliers. Firms endogenously take contingency plans to mitigate the impact generated from disruptions. We show that, as long as firms have large initial equity buffers, network fragility is low if both buyer diversification and supplier diversification are low. We find that a single-sourcing strategy is beneficial for a firm only if the default probability of the firm’s supplier is low. Otherwise, a multiple-sourcing strategy is ex post more cost effective for a firm. Funding: J.R. Birge acknowledges financial support from the University of Chicago Booth School of Business. The research of A. Capponi has been supported by the NSF/CMMI CAREER-1752326 award. P.-C. Chen acknowledges financial support from the Research Grant Council of Hong Kong [Early Career Scheme Grant 27210118]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2022.2409 . 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email