text: 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.
  @cite_3: We consider the special case of approval voting when the set of agents and the set of alternatives coincide. This captures situations in which the members of an organization want to elect a president or a committee from their ranks, as well as a variety of problems in networked environments, for example in internet search, social networks like Twitter, or reputation systems like Epinions. More precisely, we look at a setting where each member of a set of n agents approves or disapproves of any other member of the set and we want to select a subset of k agents, for a given value of k, in a strategyproof and approximately efficient way. Here, strategyproofness means that no agent can improve its own chances of being selected by changing the set of other agents it approves. A mechanism is said to provide an approximation ratio of α for some α ≥ 1 if the ratio between the sum of approval scores of any set of size k and that of the set selected by the mechanism is always at most α. We show that for k ∈ 1, 2,..., n − 1 , no deterministic strategyproof mechanism can provide a finite approximation ratio. We then present a randomized strategyproof mechanism that provides an approximation ratio that is bounded from above by four for any value of k, and approaches one as k grows.
summary: Another related problem is selection from the selectors'' @cite_3 . The goal here is to select a subset of @math agents from a group (e.g. to select a subcommittee). The problem of awarding a prize from a group of peers can be seen as the special case of @math . As approval voting is not impartial, Alon, Fischer, Procaccia and Tennenholtz look for impartial rules that approximate approval voting (that is, guarantee that the total approval scores of the @math winners are within a fixed fraction of the optimal answer). Again, a difference with this work is that we are not trying to achieve or approximate impartiality.