We propose the PeerRank method for peer assessment. This constructs a grade for an agent based on the grades proposed by the agents evaluating the agent. Since the grade of an agent is a measure of their ability to grade correctly, the PeerRank method weights grades by the grades of the grading agent. The PeerRank method also provides an incentive for agents to grade correctly. As the grades of an agent depend on the grades of the grading agents, and as these grades themselves depend on the grades of other agents, we define the PeerRank method by a fixed point equation similar to the PageRank method for ranking web-pages. We identify some formal properties of the PeerRank method (for example, it satisfies axioms of unanimity, no dummy, no discrimination and symmetry), discuss some examples, compare with related work and evaluate the performance on some synthetic data. Our results show considerable promise, reducing the error in grade predictions by a factor of 2 or more in many cases over the natural baseline of averaging peer grades.
A closely related problem is the division of cash between a group of partners @cite_11 . Each partner cares selfishly about their share but is supposed to be disinterested about the distribution of the money that he or she does not get. Partners rate the relative contributions of the other partners. With four or more partners, there exist symmetric and impartial division rules. By comparison, whilst our PeerRank rule is symmetric, it is not designed to be impartial. The grades assigned by an agent can definitely influence their final grade.
@cite_11
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This article explores how the efficiency of Internet search is changing the way Americans find romantic partners. We use a new data source, the How Couples Meet and Stay Together survey. Results show that for 60 years, family and grade school have been steadily declining in their influence over the dating market. In the past 15 years, the rise of the Internet has partly displaced not only family and school, but also neighborhood, friends, and the workplace as venues for meeting partners. The Internet increasingly allows Americans to meet and form relationships with perfect strangers, that is, people with whom they had no previous social tie. Individuals who face a thin market for potential partners, such as gays, lesbians, and middle-aged heterosexuals, are especially likely to meet partners online. One result of the increasing importance of the Internet in meeting partners is that adults with Internet access at home are substantially more likely to have partners, even after controlling for other factors.... The set of optimal matchings in the assignment matrix allows to define a reflexive and symmetric binary relation on each side of the market, the equal-partner binary relation. The number of equivalence classes of the transitive closure of the equal-partner binary relation determines the dimension of the core of the assignment game. This result provides an easy procedure to determine the dimension of the core directly from the entries of the assignment matrix and shows that the dimension of the core is not as much determined by the number of optimal matchings as by their relative position. This paper provides the first comprehensive analysis of Uber's driver-partners, based on both survey data and anonymized, aggregated administrative data. Uber has grown at an exponential rate over the last few years, and drivers who partner with Uber appear to be attracted to the platform in large part because of the flexibility it offers, the level of compensation, and the fact that earnings per hour do not vary much with hours worked, which facilitates part-time and variable hours. Uber's driver-partners are more similar in terms of their age and education to the general workforce than to taxi drivers and chauffeurs. Uber may serve as a bridge for many seeking other employment opportunities, and it may attract well-qualified individuals because, with Uber's star rating system, driver-partners' reputations are explicitly shared with potential customers. Most of Uber's driver-partners had full- or part-time employment prior to joining Uber, and many continued in those positions after starting to drive with the Uber platform, which makes the flexibility to set their own hours all the more valuable. Uber's driver-partners also often cited the desire to smooth fluctuations in their income as a reason for partnering with Uber. This paper addresses strategies for the stable marriage problem. For the Gale-Shapley algorithm with men proposing, a classical theorem states that it is impossible for every cheating man to get a better partner than the one he gets if everyone is truthful. We study how to circumvent this theorem and incite men to cheat. First we devise coalitions in which a nonempty subset of the liars get better partners and no man is worse off than before. This strategy is limited in that not everyone in the coalition has the incentive to falsify his list. In an attempt to rectify this situation we introduce the element of randomness, but the theorem shows surprising robustness: it is impossible that every liar has a chance to improve the rank of his partner while no one gets hurt. To overcome the problem that some men lack the motivation to lie, we exhibit another randomized lying strategy in which every liar can expect to get a better partner on average, though with a chance of getting a worse one. Finally, we consider a variant scenario: instead of using the Gale-Shapley algorithm, suppose the stable matching is chosen at random. We present a modified form of the coalition strategy ensuring that every man in the coalition has a new probability distribution over partners which majorizes the original one.