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1. Statement Voting

   https://doi.org/10.1007/978-3-030-32101-7_38  

   Zhang, Bingsheng ; Zhou, Hong-Sheng ( September 2019 , Lecture notes in computer science)

   The conventional (election) voting systems, e.g., representative democracy, have many limitations and often fail to serve the best interest of the people in a collective decision-making process. To address this issue, the concept of liquid democracy has been emerging as an alternative decision-making model to make better use of “the wisdom of crowds”. However, there is no known cryptographically secure e-voting implementation that supports liquid democracy. In this work, we propose a new voting concept called statement voting, which can be viewed as a natural extension of the conventional voting approaches. In the statement voting, instead of defining a concrete elec- tion candidate, each voter can define a statement in his/her ballot but leave the vote “undefined” during the voting phase. During the tally phase, the (conditional) actions expressed in the statement will be carried out to determine the final vote. We initiate the study of statement voting under the Universal Composability (UC) framework, and propose several construction frameworks together with their instantiations. As an application, we show how statement voting can be used to realize a UC-secure liquid democracy voting system. We remark that our statement voting can be extended to enable more complex voting and generic ledger-based non-interactive multi-party computation. We believe that the statement voting concept opens a door for constructing a new class of e-voting schemes. 

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2. Explainable Voting

   Peters, Dominik ; Procaccia, Ariel D. ( January 2020 , NeurIPS)
3. Phrase-Verified Voting: Verifiable low-tech remote boardroom voting

   Blanchard, Enka ; Robucci, Ryan ; Selker, Ted ; Sherman, Alan T. ( January 2021 , 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. 

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4. Voting Against Autocracy

   https://doi.org/10.1353/wp.2023.a908772  

   Svolik, Milan W. ( October 2023 , World Politics)

   When and how do voters punish politicians for subverting democracy? To investigate the role of the public in democratic backsliding, I develop a conceptual framework that differentiates among three mechanisms: vote switching, backlash, and disengagement. The first mechanism entails defection by voters from a candidate who undermines democracy to one who does not; the latter two mechanisms entail transitions between voting and abstention. I estimate the magnitude of each mechanism by combining evidence from a series of original survey experiments, traditional surveys, and a quasi-experiment afforded by the rerun of the 2019 Istanbul mayoral election, in which the governing party, akp, attempted to overturn the result of an election that it had lost. I find that although vote switching and backlash contributed to the akp's eventual defeat the most, each of the three mechanisms served as a democratic check in some subset of the Istanbul electorate. Persuasion, mobilization, and even demobilization are all viable tools for curbing the authoritarian tendencies of elected politicians. 

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5. Polynomial Voting Rules

   https://doi.org/10.1287/moor.2023.0080  

   Tang, Wenpin ; Yao, David D. ( February 2024 , Mathematics of Operations Research)

   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.

    

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