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This paper introduces Voting with Random Proposers (VRP) procedure to address the challenges of agenda manipulation in voting. In each round of VRP, a randomly selected proposer suggests an alternative that is voted on against the previous round's winner. In a framework with single-peaked preferences, we show that the VRP procedure guarantees that the Condorcet winner is implemented in a few rounds with truthful voting, and in just two rounds under sufficiently symmetric preference distributions or if status quo positions are not extreme. The results have applications for committee decisions, legislative decision-making, and the organization of citizens' assemblies and decentralized autonomous organizations.

This paper investigates which alternative benefits from vote delegation in binary collective decisions within blockchains. We begin by examining two extreme cases of voting weight distributions: Equal-Weight (EW), where each voter has equal voting weight, and Dominant-Weight (DW), where a single voter holds a majority of the voting weights before any delegation occurs. We show that vote delegation tends to benefit the ex-ante minority under EW, i.e., the alternative with a lower initial probability of winning. The converse holds under DW distribution. Through numerical simulations, we extend our findings to arbitrary voting weight distributions, showing that vote delegation benefits the ex-ante majority when it leads to a more balanced distribution of voting weights. Finally, in large communities where all agents have equal voting weight, vote delegation has a negligible impact on the outcome. These insights provide practical guidance for governance decisions in blockchains.

Bug bounty programs, where external agents are invited to search and report vulnerabilities (bugs) in exchange for rewards (bounty), have become a major tool for companies to improve their systems. We suggest augmenting such programs by inserting artificial bugs to increase the incentives to search for real (organic) bugs. Using a model of crowdsearch, we identify the efficiency gains by artificial bugs, and we show that for this, it is sufficient to insert only one artificial bug. Artificial bugs are particularly beneficial, for instance, if the designer places high valuations on finding organic bugs or if the budget for bounty is not sufficiently high. We discuss how to implement artificial bugs and outline their further benefits.

A common economic process is crowdsearch, wherein a group of agents is invited to search for a valuable physical or virtual object, e.g. creating and patenting an invention, solving an open scientific problem, or identifying vulnerabilities in software. We study a binary model of crowdsearch in which agents have different abilities to find the object. We characterize the types of equilibria and identify which type of crowd maximizes the likelihood of finding the object. Sometimes, however, an unlimited crowd is not sufficient to guarantee that the object is found. It even can happen that inviting more agents lowers the probability of finding the object. We characterize the optimal prize and show that offering only one prize (winner-takes-all) maximizes the probability of finding the object but is not necessarily optimal for the crowdsearch designer., Comment: arXiv admin note: substantial text overlap with arXiv:2304.00077

Systems and blockchains often have security vulnerabilities and can be attacked by adversaries, with potentially significant negative consequences. Therefore, infrastructure providers increasingly rely on bug bounty programs, where external individuals probe the system and report any vulnerabilities (bugs) in exchange for rewards (bounty). We develop a simple contest model of bug bounty. A group of individuals of arbitrary size is invited to undertake a costly search for bugs. The individuals differ with regard to their abilities, which we capture by different costs to achieve a certain probability to find bugs if any exist. Costs are private information. We study equilibria of the contest and characterize the optimal design of bug bounty schemes. In particular, the designer can vary the size of the group of individuals invited to search, add a paid expert, insert an artificial bug with some probability, and pay multiple prizes.

On several proof-of-stake blockchains, agents engaged in validating transactions can open a pool to which others can delegate their stake in order to earn higher returns. We develop a model of staking pool formation in the presence of malicious agents and establish existence and uniqueness of equilibria. We then identify potential and risk of staking pools. First, allowing for staking pools lowers blockchain security. Yet, honest stake holders obtain higher returns. Second, by choosing welfare optimal distribution rewards, staking pools prevent that malicious agents receive large rewards. Third, when pool owners can freely distribute the returns from validation to delegators, staking pools disrupt blockchain operations, since malicious agents attract most delegators by offering generous returns.

We examine vote delegation when preferences of agents are private information. One group of agents (delegators) does not want to participate in voting and abstains under conventional voting or can delegate its votes to the other group (voters) who decide between two alternatives. We show that free delegation favors minorities, that is, alternatives that have a lower chance of winning ex-ante. The same occurs if the number of voting rights that actual voters can have is capped. When the number of delegators increases, the probability that the ex-ante minority wins under free and capped delegation converges to the one under conventional voting--albeit non-monotonically. Our results are obtained in a private value setting but can be readily translated into an information aggregation setting when voters receive a signal about the ''correct" alternative with some probability.

We study vote delegation with "well-behaving" and "misbehaving" agents and compare it with conventional voting. Typical examples for vote delegation are validation or governance tasks on blockchains. There is a majority of well-behaving agents, but they may abstain or delegate their vote to other agents since voting is costly. Misbehaving agents always vote. We compare conventional voting allowing for abstention with vote delegation. Preferences of voters are private information and a positive outcome is achieved if well-behaving agents win. We illustrate that vote delegation leads to quite different outcomes than conventional voting with abstention. In particular, we obtain three insights: First, if the number of misbehaving voters, denoted by f , is high, both voting methods fail to deliver a positive outcome. Second, if f takes an intermediate value, conventional voting delivers a positive outcome, while vote delegation fails with probability one. Third, if f is low, delegation delivers a positive outcome with higher probability than conventional voting. Finally, our results characterize worst-case outcomes that can happen in a liquid democracy.

The rapid rise of antibiotic resistance is a serious threat to global public health. Without further incentives, pharmaceutical companies have little interest in developing antibiotics, since the success probability is low and development costs are huge. The situation is exacerbated by the "antibiotics dilemma": Developing narrow-spectrum antibiotics against resistant bacteria is most beneficial for society, but least attractive for companies since their usage is more limited than for broad-spectrum drugs and thus sales are low. Starting from a general mathematical framework for the study of antibiotic-resistance dynamics with an arbitrary number of antibiotics, we identify efficient treatment protocols and introduce a market-based refunding scheme that incentivizes pharmaceutical companies to develop narrow-spectrum antibiotics: Successful companies can claim a refund from a newly established antibiotics fund that partially covers their development costs. The proposed refund involves a fixed and variable part. The latter (i) increases with the use of the new antibiotic for currently resistant strains in comparison with other newly developed antibiotics for this purpose---the resistance premium---and (ii) decreases with the use of this antibiotic for non-resistant bacteria. We outline how such a refunding scheme can solve the antibiotics dilemma and cope with various sources of uncertainty inherent in antibiotic R\&D. Finally, connecting our refunding approach to the recently established antimicrobial resistance (AMR) action fund, we discuss how the antibiotics fund can be financed., Comment: 21 pages and 10 figures

Many democratic societies have become more politically polarized, with the U.S. as the main example. The origins of this phenomenon are still not well-understood and subject to debate. To better understand the mechanisms underlying political polarization, we develop a mathematical framework and employ information-theoretic concepts to analyze empirical data on political polarization that has been collected by Pew Research Center from 1994 to 2017. Our framework can capture the evolution of polarization in the Democratic- and Republican-leaning segments of the U.S. public and allows us to identify its drivers. Our findings provide empirical and quantitative evidence that political polarization in the U.S. is mainly driven by strong and more left-leaning policy/cultural innovations in the Democratic party., Comment: 23 pages, 10 figures

Recent empirical findings suggest that societies have become more polarized in various countries. That is, the median voter of today represents a smaller fraction of society compared to two decades ago and yet, the mechanisms underlying this phenomenon are not fully understood. Since interactions between influential actors ("activists") and voters play a major role in opinion formation, e.g. through social media, we develop a macroscopic opinion model in which competing activists spread their political ideas in specific groups of society. These ideas spread further to other groups in declining strength. While unilateral spreading shifts the opinion distribution, competition of activists leads to additional phenomena: Small heterogeneities among competing activists cause them to target different groups in society, which amplifies polarization. For moderate heterogeneities, we obtain target cycles and further amplification of polarization. In such cycles, the stronger activist differentiates himself from the weaker one, while the latter aims to imitate the stronger activist., Comment: 21 pages, 11 figures

Recent political campaigns have demonstrated how technologies are used to boost election outcomes by microtargeting voters. We propose and analyze a framework which analyzes how political activists use technologies to target voters. Voters are represented as nodes of a network. Political activists reach out locally to voters and try to convince them. Depending on their technological advantage and budget, political activists target certain regions in the network where their activities are able to generate the largest vote-share gains. Analytically and numerically, we quantify vote-share gains and savings in terms of budget and number of activists from employing superior targeting technologies compared to traditional campaigns. Moreover, we demonstrate that the technological precision must surpass a certain threshold in order to lead to a vote-share gain or budget advantage. Finally, by calibrating the technology parameters to the recent U.S. presidential election, we show that a pure targeting technology advantage is consistent with Trump winning against Clinton., Comment: 25 pages, 7 figures

Political campaigns involve, in the simplest case, two competing campaign groups which try to obtain a majority of votes. We propose a novel mathematical framework to study political campaign dynamics on social networks whose constituents are either political activists or persuadable individuals. Activists are convinced and do not change their opinion and they are able to move around in the social network to motivate persuadable individuals to vote according to their opinion. We describe the influence of the complex interplay between the number of activists, political clout, budgets, and campaign costs on the campaign result. We also identify situations where the choice of one campaign group to send a certain number of activists already pre-determines their victory. Moreover, we show that a candidate's advantage in terms of political clout can overcome a substantial budget disadvantage or a lower number of activists, as illustrated by the US presidential election 2016., Comment: 23 pages, 10 figures

Decoy ballots do not count in election outcomes, but otherwise they are indistinguishable from real ballots. By means of a game-theoretical model, we show that decoy ballots may not provide effective protection against a malevolent adversary trying to buy real ballots. If the citizenry is divided into subgroups (or districts), the adversary can construct a so-called "Devil's Menu" consisting of several prices. In equilibrium, the adversary can buy the real ballots of any strict subset of districts at a price corresponding to the willingness to sell on the part of the citizens holding such ballots. By contrast, decoy voters are trapped into selling their ballots at a low, or even negligible, price. Blowing up the adversary's budget by introducing decoy ballots may thus turn out to be futile. The Devil's Menu can also be applied to the well-known "Lemons Problem".

We analyze Assessment Voting, a new two-round voting procedure that can be applied to binary decisions in democratic societies. In the first round, a randomly-selected number of citizens cast their vote on one of the two alternatives at hand, thereby irrevocably exercising their right to vote. In the second round, after the results of the first round have been published, the remaining citizens decide whether to vote for one alternative or to ab- stain. The votes from both rounds are aggregated, and the final outcome is obtained by applying the majority rule, with ties being broken by fair randomization. Within a costly voting framework, we show that large elec- torates will choose the preferred alternative of the majority with high prob- ability, and that average costs will be low. This result is in contrast with the literature on one-round voting, which predicts either higher voting costs (when voting is compulsory) or decisions that often do not represent the preferences of the majority (when voting is voluntary).