Choosing the best among peers

AbstractA group of n peers, e.g., computer scientists, has to choose the best, i.e., the most competent among them. Each member of the group may vote for one other member, or abstain. Self-voting is not allowed. A voting graph is a directed graph in which an arc (u,v) means that u votes for v. While opinions may be subjective, resulting in various voting graphs, it is natural to assume that more competent peers are also, in general, more competent in evaluating competence of others. We capture this by proposing a voting system in which each member is assigned a positive integer value satisfying the following strict support monotonicity property: the value of x is larger than the value of y if and only if the sum of values of members voting for x is larger than the sum of values of members voting for y. Then we choose the member with the highest value, or if there are several such members, another election mechanism, e.g., using randomness, chooses one of them.We show that for every voting graph there is a value function satisfying the strict support monotonicity property and that such a function can be computed in linear time. However, it turns out that this method of choosing the best among peers is vulnerable to vote manipulation: even one voter of very low value may change his/her vote so as to get the highest value. This is due to the possibility of loops (directed cycles) in the voting graph. Hence we slightly modify voting graphs by erasing all arcs that belong to some cycle. This modification results in a pruned voting graph which is always a rooted forest. We show that for all pruned voting graphs there are value functions giving a guarantee against manipulation. More precisely, we show a value function guaranteeing that no coalition of k members all of whose values are lower than those of (1−1/(k+1))n other members can manipulate their votes so that one of them gets the largest value. In particular, no single member from the lower half of the group is able to manipulate his/her vote to become elected. We also show that no better guarantee can be given for any value function satisfying the strict support monotonicity property

High School Choice in New York City: A Report on the School Choices and Placements of Low-Achieving Students

School choice policies, a fixture of efforts to improve public education in many cities. aim to enable families to choose a school that they believe will best meet their child's needs. In New York City, choice and the development of a diverse portfolio of options have played central roles in the Department of Education's high school reform efforts. This report examines the choices and placements of New York City's lowest-achieving students: those scoring among the bottom 20 percent on standardized state tests in middle school. Focusing on data from 2007 to 2011, the report looks at who these low-achieving students are, including how their demographics compare to other students in NYC, the educational challenges they face, and where they live. The bulk of the report reviews low-achieving students' most preferred schools and the ones to which they were ultimately assigned, assessing how these schools compare to those of their higher-achieving peers. The findings show that low-achieving students attended schools that were lower performing, on average, than those of all other students. This was driven by differences in students' initial choices: low-achieving students' first-choice schools were less selective, lower-performing, and more disadvantaged. Overall, lower-achievingand higher-achieving students were matched to their top choices at the same rate. Importantly, both low- and higher-achieving students appear to prefer schools that are close to home, suggesting that differences in students' choices likely reflect, at least in part, the fact that lower-achieving students are highly concentrated in poor neighborhoods, where options may be more limited

Mode-Suppression: A Simple, Stable and Scalable Chunk-Sharing Algorithm for P2P Networks

The ability of a P2P network to scale its throughput up in proportion to the arrival rate of peers has recently been shown to be crucially dependent on the chunk sharing policy employed. Some policies can result in low frequencies of a particular chunk, known as the missing chunk syndrome, which can dramatically reduce throughput and lead to instability of the system. For instance, commonly used policies that nominally "boost" the sharing of infrequent chunks such as the well known rarest-first algorithm have been shown to be unstable. Recent efforts have largely focused on the careful design of boosting policies to mitigate this issue. We take a complementary viewpoint, and instead consider a policy that simply prevents the sharing of the most frequent chunk(s). Following terminology from statistics wherein the most frequent value in a data set is called the mode, we refer to this policy as mode-suppression. We also consider a more general version that suppresses the mode only if the mode frequency is larger than the lowest frequency by a fixed threshold. We prove the stability of mode-suppression using Lyapunov techniques, and use a Kingman bound argument to show that the total download time does not increase with peer arrival rate. We then design versions of mode-suppression that sample a small number of peers at each time, and construct noisy mode estimates by aggregating these samples over time. We show numerically that the variants of mode-suppression yield near-optimal download times, and outperform all other recently proposed chunk sharing algorithms

Keeping Up with CEO Jones: Benchmarking and Executive Compensation

This paper seeks to understand the role that peer comparisons play in the determination of executive compensation. I exploit a recent change in the Securities and Exchange Commission’s regulations that requires firms to disclose the peer companies used for determining the compensation of their top executives. Using a new dataset of S&P 900 companies’ choice of benchmarking firms during two fiscal periods (2007 and 2008), I investigate what determines the choice of comparison firms. I find that companies have a preference for choosing larger and higher-CEO-compensation firms as their benchmark. Though I find that companies prefer to choose as their benchmark peers with similar firm characteristics, for CEO compensation, this effect is countered by a preference for firms with higher-than-own CEO compensation. Using the complete map of firms’ choices, I implement an instrumental variable strategy that uses the characteristics of peers-of-peers to estimate the effect of others’ compensation on own compensation. For Fiscal Year 2007, I find an elasticity of 0.5

Use of a controlled experiment and computational models to measure the impact of sequential peer exposures on decision making

It is widely believed that one's peers influence product adoption behaviors. This relationship has been linked to the number of signals a decision-maker receives in a social network. But it is unclear if these same principles hold when the pattern by which it receives these signals vary and when peer influence is directed towards choices which are not optimal. To investigate that, we manipulate social signal exposure in an online controlled experiment using a game with human participants. Each participant in the game makes a decision among choices with differing utilities. We observe the following: (1) even in the presence of monetary risks and previously acquired knowledge of the choices, decision-makers tend to deviate from the obvious optimal decision when their peers make similar decision which we call the influence decision, (2) when the quantity of social signals vary over time, the forwarding probability of the influence decision and therefore being responsive to social influence does not necessarily correlate proportionally to the absolute quantity of signals. To better understand how these rules of peer influence could be used in modeling applications of real world diffusion and in networked environments, we use our behavioral findings to simulate spreading dynamics in real world case studies. We specifically try to see how cumulative influence plays out in the presence of user uncertainty and measure its outcome on rumor diffusion, which we model as an example of sub-optimal choice diffusion. Together, our simulation results indicate that sequential peer effects from the influence decision overcomes individual uncertainty to guide faster rumor diffusion over time. However, when the rate of diffusion is slow in the beginning, user uncertainty can have a substantial role compared to peer influence in deciding the adoption trajectory of a piece of questionable information

Small Is Not Always Beautiful

Peer-to-peer content distribution systems have been enjoying great popularity, and are now gaining momentum as a means of disseminating video streams over the Internet. In many of these protocols, including the popular BitTorrent, content is split into mostly fixed-size pieces, allowing a client to download data from many peers simultaneously. This makes piece size potentially critical for performance. However, previous research efforts have largely overlooked this parameter, opting to focus on others instead. This paper presents the results of real experiments with varying piece sizes on a controlled BitTorrent testbed. We demonstrate that this parameter is indeed critical, as it determines the degree of parallelism in the system, and we investigate optimal piece sizes for distributing small and large content. We also pinpoint a related design trade-off, and explain how BitTorrent's choice of dividing pieces into subpieces attempts to address it

Towards a quantitative evaluation of the relationship between the domain knowledge and the ability to assess peer work

In this work we present the preliminary results provided by the statistical modeling of the cognitive relationship between the knowledge about a topic a the ability to assess peer achievements on the same topic. Our starting point is Bloom's taxonomy of educational objectives in the cognitive domain, and our outcomes confirm the hypothesized ranking. A further consideration that can be derived is that meta-cognitive abilities (e.g., assessment) require deeper domain knowledge

'A boy would be friends with boys... and a girl... with girls' : gender norms in early adolescent friendships in Egypt and Belgium

Purpose: A gender analysis was conducted to illuminate the key elements of friendships highlighted by early adolescent girls and boys in two sites for the purpose of better understanding the impact of gender norms on adolescent friendships in different contexts. Methods: Narrative interviews with early adolescents were conducted in two sites: Assiut, Egypt (n = 37) and Ghent, Belgium (n = 30). The interviews were recorded, transcribed, translated into English, and coded using Atlas.ti for analysis. Results: In both Assiut and Ghent, early adolescents reported some similarities in defining key characteristics of their same-sex friends as well as in the activities they share. However, differences were noticed among boys and girls within each site. In addition, the scope of shared activity was broader in Ghent than in Assiut. In both sites, few opposite-sex friendships were reported. Gender norms influenced choice of friends as well as the type and place of shared activities. Conclusions: Building on knowledge that adolescent friendships guide and reinforce attitudes, beliefs, and behaviors that impact immediate and long-term health, our findings indicate that gender norms inform early adolescent friendships, which may impact healthy development

Being a non-drinking student: an interpretative phenomenological analysis

Recent research suggests that safer student alcohol consumption might be assisted by understanding how social occasions are managed by non-drinkers. In-depth, semi-structured interviews with five 19-22 year old non-drinking English undergraduates were subjected to interpretative phenomenological analysis (IPA). We present five inter-linked themes: ‘living with challenges to non drinking’; ‘seeing what goes on in drinking environments’; ‘dealing with conversations about non-drinking (‘making excuses vs. coming out’)’; ‘knowing which friends care about you’; and ‘the importance of withholding “legroom” for peer pressure’. Participants felt under persistent peer scrutiny (as a form of peer pressure) and could feel alienated in drinking environments. Talking about non-drinking was characterised by whether to ‘come out’ (as a non-drinker) or ‘fake it’ (e.g., ‘I’m on antibiotics’). Loyal friendships were reported as particularly important in this context. The decision not to drink was experienced as providing a successful buffer to peer pressure for former drinkers. Our findings unsettle traditional health promotion campaigns which advocate moderate drinking among students without always suggesting how it might be most successfully accomplished, and offer tentative guidance on how non-drinking during specific social occasions might be managed more successfully. Findings are discussed in relation to extant literature and future research directions are suggested