Elliot Anshelevich

We provide mechanisms and new metric distortion bounds for line-up elections. In such elections, a set of n voters, k candidates, and ell positions are all located in a metric space. The goal is to choose a set of candidates and assign them to different positions, so as to minimize the total cost of the voters. The cost of each voter consists of the distances from itself to the chosen candidates (measuring how much the voter likes the chosen candidates, or how similar it is to them), as well as the distances from the candidates to the positions they are assigned to (measuring the fitness of the candidates for their positions). Our mechanisms, however, do not know the exact distances, and instead produce good outcomes while only using a smaller amount of information, resulting in small distortion. We consider several different types of information: ordinal voter preferences, ordinal position preferences, and knowing the exact locations of candidates and positions, but not those of voters. In each of these cases, we provide constant distortion bounds, thus showing that only a small amount of information is enough to form outcomes close to optimum in line-up elections.

We consider a social choice setting in which agents and alternatives are represented by points in a metric space, and the cost of an agent for an alternative is the distance between the corresponding points in the space. The goal is to choose a single alternative to (approximately) minimize the social cost (cost of all agents) or the maximum cost of any agent, when only limited information about the preferences of the agents is given. Previous work has shown that the best possible distortion one can hope to achieve is 3 when access to the ordinal preferences of the agents is given, even when the distances between alternatives in the metric space are known. We improve upon this bound of 3 by designing deterministic mechanisms that exploit a bit of cardinal information. We show that it is possible to achieve distortion 1+sqrt(2) by using the ordinal preferences of the agents, the distances between alternatives, and a threshold approval set per agent that contains all alternatives for whom her cost is within an appropriately chosen factor of her cost for her most-preferred alternative. We show that this bound is the best possible for any deterministic mechanism in general metric spaces, and also provide improved bounds for the fundamental case of a line metric.

We analyze traffic exchange between Internet Service Providers (ISPs) at an Internet Exchange Point (IXP) as a non-cooperative game with ISPs as self-interested agents. Each ISP has the choice of exchanging traffic either using the shared IXP facilities, or outside the IXP – through their transit providers or private peering. We analyze the efficiency (social cost optimality) of the traffic exchange equilibrium at the IXP taking into consideration the congestion cost experienced by the ISPs at the IXP. To model both non-profit and for profit IXPs, we consider several cases, i) where the IXP does not charge any price to ISPs for the traffic exchanged (zero pricing), ii) when it charges a price that is proportional to the aggregate level of congestion at the IXP (proportional pricing), and iii) when it charges a constant price per unit traffic (constant pricing). Further, we also analyze the profit earned by the IXP under these pricing policies, under two different models of the congestion cost (delay) functions. Simulations conducted using data for actual IXPs obtained from PeeringDB demonstrate that the theoretical bounds derived for social cost and profit optimality at equilibrium (measured as the Price of Anarchy) are fairly tight, and correctly capture the performance trends against the variation of key model parameters. Further, the results show that for proportional pricing, there is an operating price range that attains near-optimal social cost and near-optimal IXP profit simultaneously . We also demonstrate -through both theoretical analysis and simulations -that as compared to zero and constant pricing policies, proportional pricing attains better tradeoff between social cost and IXP profit, and also results in a performance that is more robust to price variations.

We study the classic facility location setting, where we are given n clients and m possible facility locations in some arbitrary metric space, and want to choose a location to build a facility. The exact same setting also arises in spatial social choice, where voters are the clients and the goal is to choose a candidate or outcome, with the distance from a voter to an outcome representing the cost of this outcome for the voter (e.g., based on their ideological differences). Unlike most previous work, we do not focus on a single objective to optimize (e.g., the total distance from clients to the facility, or the maximum distance, etc.), but instead attempt to optimize several different objectives simultaneously. More specifically, we consider the l-centrum family of objectives, which includes the total distance, max distance, and many others. We present tight bounds on how well any pair of such objectives (e.g., max and sum) can be simultaneously approximated compared to their optimum outcomes. In particular, we show that for any such pair of objectives, it is always possible to choose an outcome which simultaneously approximates both objectives within a factor of 1 plus square root of 2, and give a precise characterization of how this factor improves as the two objectives being optimized become more similar. For q>2 different centrum objectives, we show that it is always possible to approximate all q of these objectives within a small constant, and that this constant approaches 3 as q increases. Our results show that when optimizing only a few simultaneous objectives, it is always possible to form an outcome which is a significantly better than 3 approximation for all of these objectives.