Distortion in Social Choice Problems: The First 15 Years and beyond

The notion of distortion in social choice problems has been defined to measure the loss in efficiency-typically measured by the utilitarian social welfare, the sum of utilities of the participating agents-due to having access only to limited information about the preferences of the agents. We survey the most significant results of the literature on distortion from the past 15 years, and highlight important open problems and the most promising avenues of ongoing and future work

A note on the efficiency of position mechanisms with budget constraints

We study the social efficiency of several well-known mechanisms for the allocation of a set of available (advertising) positions to a set of competing budget-constrained users (advertisers). Specifically, we focus on the Generalized Second Price auction (GSP), the Vickrey–Clarke–Groves mechanism (VCG) and the Expressive Generalized First Price auction (EGFP). Using liquid welfare as our efficiency benchmark, we prove a tight bound of 2 on the liquid price of anarchy and stability of these mechanisms for pure Nash equilibria

Optimizing positional scoring rules for rank aggregation

Nowadays, several crowdsourcing projects exploit social choice methods for computing an aggregate ranking of alternatives given individual rankings provided by workers. Motivated by such systems, we consider a setting where each worker is asked to rank a fixed (small) number of alternatives and, then, a positional scoring rule is used to compute the aggregate ranking. Among the apparently infinite such rules, what is the best one to use? To answer this question, we assume that we have partial access to an underlying true ranking. Then, the important optimization problem to be solved is to compute the positional scoring rule whose outcome, when applied to the profile of individual rankings, is as close as possible to the part of the underlying true ranking we know. We study this fundamental problem from a theoretical viewpoint and present positive and negative complexity results and, furthermore, complement our theoretical findings with experiments on real-world and synthetic data

Optimally deceiving a learning leader in Stackelberg games

Recent results have shown that algorithms for learning the optimal commitment in a Stackelberg game are susceptible to manipulation by the follower. These learning algorithms operate by querying the best responses of the follower, who consequently can deceive the algorithm by using fake best responses, typically by responding according to fake payoffs that are different from the actual ones. For this strategic behavior to be successful, the main challenge faced by the follower is to pinpoint the fake payoffs that would make the learning algorithm output a commitment that benefits them the most. While this problem has been considered before, the related literature has only focused on a simple setting where the follower can only choose from a finite set of payoff matrices, thus leaving the general version of the problem unanswered. In this paper, we fill this gap by showing that it is always possible for the follower to efficiently compute (near-)optimal fake payoffs, for various scenarios of learning interaction between the leader and the follower. Our results also establish an interesting connection between the follower’s deception and the leader’s maximin utility: through deception, the follower can induce almost any (fake) Stackelberg equilibrium if and only if the leader obtains at least their maximin utility in this equilibrium

Groundwater hydrogeochemistry of Trikala municipality, central Greece

Sixty-four samples from the groundwater resources of Trikala municipality, central Greece, were collected during two periods (2006 and 2007) and analyzed for physico-chemical parameters (temperature, pH, specific electrical conductivity, and total dissolved solids), major ions (Ca2+, Cl-, HCO (3) (-) , K+, Mg2+, Na+, NO (3) (-) , SO (4) (2-) ), and several potentially toxic elements (Al, B, Ba, Br, Ca, Ce, Cl, Cr, Cu, Fe, K, La, Li, Mg, Mn, Mo, Na, Nd, Ni, P, Pb, Rb, S, Sc, Si, Sn, Sr, U, V, Y, Zn). European Council directives and USEPA guidelines were used to assess the water quality. The results indicate that all samples are fresh water, suitable for human consumption. All basic ions and physico-chemical parameters have average concentrations below their recommended optimum limits with the exception of electrical conductivity, for January 2007, and nitrate for October 2006 and January 2007 sampling periods. This exceedance is the result of dissolution of minerals such as calcite and dolomite that are present in the surrounding rocks and the application of fertilizers, respectively. Lead is the only element with an average value that exceeds the recommended EC guideline, while special attention should be paid to one borehole (T9) which has elevated NO (3) (-) values which may pose a risk to human health