307 research outputs found
How Bad is Forming Your Own Opinion?
The question of how people form their opinion has fascinated economists and
sociologists for quite some time. In many of the models, a group of people in a
social network, each holding a numerical opinion, arrive at a shared opinion
through repeated averaging with their neighbors in the network. Motivated by
the observation that consensus is rarely reached in real opinion dynamics, we
study a related sociological model in which individuals' intrinsic beliefs
counterbalance the averaging process and yield a diversity of opinions.
By interpreting the repeated averaging as best-response dynamics in an
underlying game with natural payoffs, and the limit of the process as an
equilibrium, we are able to study the cost of disagreement in these models
relative to a social optimum. We provide a tight bound on the cost at
equilibrium relative to the optimum; our analysis draws a connection between
these agreement models and extremal problems that lead to generalized
eigenvalues. We also consider a natural network design problem in this setting:
which links can we add to the underlying network to reduce the cost of
disagreement at equilibrium
Improving Christofides' Algorithm for the s-t Path TSP
We present a deterministic (1+sqrt(5))/2-approximation algorithm for the s-t
path TSP for an arbitrary metric. Given a symmetric metric cost on n vertices
including two prespecified endpoints, the problem is to find a shortest
Hamiltonian path between the two endpoints; Hoogeveen showed that the natural
variant of Christofides' algorithm is a 5/3-approximation algorithm for this
problem, and this asymptotically tight bound in fact has been the best
approximation ratio known until now. We modify this algorithm so that it
chooses the initial spanning tree based on an optimal solution to the Held-Karp
relaxation rather than a minimum spanning tree; we prove this simple but
crucial modification leads to an improved approximation ratio, surpassing the
20-year-old barrier set by the natural Christofides' algorithm variant. Our
algorithm also proves an upper bound of (1+sqrt(5))/2 on the integrality gap of
the path-variant Held-Karp relaxation. The techniques devised in this paper can
be applied to other optimization problems as well: these applications include
improved approximation algorithms and improved LP integrality gap upper bounds
for the prize-collecting s-t path problem and the unit-weight graphical metric
s-t path TSP.Comment: 31 pages, 5 figure
Sequential item pricing for unlimited supply
We investigate the extent to which price updates can increase the revenue of
a seller with little prior information on demand. We study prior-free revenue
maximization for a seller with unlimited supply of n item types facing m myopic
buyers present for k < log n days. For the static (k = 1) case, Balcan et al.
[2] show that one random item price (the same on each item) yields revenue
within a \Theta(log m + log n) factor of optimum and this factor is tight. We
define the hereditary maximizers property of buyer valuations (satisfied by any
multi-unit or gross substitutes valuation) that is sufficient for a significant
improvement of the approximation factor in the dynamic (k > 1) setting. Our
main result is a non-increasing, randomized, schedule of k equal item prices
with expected revenue within a O((log m + log n) / k) factor of optimum for
private valuations with hereditary maximizers. This factor is almost tight: we
show that any pricing scheme over k days has a revenue approximation factor of
at least (log m + log n) / (3k). We obtain analogous matching lower and upper
bounds of \Theta((log n) / k) if all valuations have the same maximum. We
expect our upper bound technique to be of broader interest; for example, it can
significantly improve the result of Akhlaghpour et al. [1]. We also initiate
the study of revenue maximization given allocative externalities (i.e.
influences) between buyers with combinatorial valuations. We provide a rather
general model of positive influence of others' ownership of items on a buyer's
valuation. For affine, submodular externalities and valuations with hereditary
maximizers we present an influence-and-exploit (Hartline et al. [13]) marketing
strategy based on our algorithm for private valuations. This strategy preserves
our approximation factor, despite an affine increase (due to externalities) in
the optimum revenue.Comment: 18 pages, 1 figur
Algorithmic Fairness from a Non-ideal Perspective
Inspired by recent breakthroughs in predictive modeling, practitioners in both industry and government have turned to machine learning with hopes of operationalizing predictions to drive automated decisions. Unfortunately, many social desiderata concerning consequential decisions, such as justice or fairness, have no natural formulation within a purely predictive framework. In efforts to mitigate these problems, researchers have proposed a variety of metrics for quantifying deviations from various statistical parities that we might expect to observe in a fair world and offered a variety of algorithms in attempts to satisfy subsets of these parities or to trade o the degree to which they are satised against utility. In this paper, we connect this approach to fair machine learning to the literature on ideal and non-ideal methodological approaches in political philosophy. The ideal approach requires positing the principles according to which a just world would operate. In the most straightforward application of ideal theory, one supports a proposed policy by arguing that it closes a discrepancy between the real and the perfectly just world. However, by failing to account for the mechanisms by which our non-ideal world arose, the responsibilities of various decision-makers, and the impacts of proposed policies, naive applications of ideal thinking can lead to misguided interventions. In this paper, we demonstrate a connection between the fair machine learning literature and the ideal approach in political philosophy, and argue that the increasingly apparent shortcomings of proposed fair machine learning algorithms reflect broader troubles
faced by the ideal approach. We conclude with a critical discussion of the harms of misguided solutions, a
reinterpretation of impossibility results, and directions for future researc
Improved Bounds on Information Dissemination by Manhattan Random Waypoint Model
With the popularity of portable wireless devices it is important to model and
predict how information or contagions spread by natural human mobility -- for
understanding the spreading of deadly infectious diseases and for improving
delay tolerant communication schemes. Formally, we model this problem by
considering moving agents, where each agent initially carries a
\emph{distinct} bit of information. When two agents are at the same location or
in close proximity to one another, they share all their information with each
other. We would like to know the time it takes until all bits of information
reach all agents, called the \textit{flood time}, and how it depends on the way
agents move, the size and shape of the network and the number of agents moving
in the network.
We provide rigorous analysis for the \MRWP model (which takes paths with
minimum number of turns), a convenient model used previously to analyze mobile
agents, and find that with high probability the flood time is bounded by
, where agents move on an
grid. In addition to extensive simulations, we use a data set of
taxi trajectories to show that our method can successfully predict flood times
in both experimental settings and the real world.Comment: 10 pages, ACM SIGSPATIAL 2018, Seattle, U
Do Diffusion Protocols Govern Cascade Growth?
Large cascades can develop in online social networks as people share
information with one another. Though simple reshare cascades have been studied
extensively, the full range of cascading behaviors on social media is much more
diverse. Here we study how diffusion protocols, or the social exchanges that
enable information transmission, affect cascade growth, analogous to the way
communication protocols define how information is transmitted from one point to
another. Studying 98 of the largest information cascades on Facebook, we find a
wide range of diffusion protocols - from cascading reshares of images, which
use a simple protocol of tapping a single button for propagation, to the ALS
Ice Bucket Challenge, whose diffusion protocol involved individuals creating
and posting a video, and then nominating specific others to do the same. We
find recurring classes of diffusion protocols, and identify two key
counterbalancing factors in the construction of these protocols, with
implications for a cascade's growth: the effort required to participate in the
cascade, and the social cost of staying on the sidelines. Protocols requiring
greater individual effort slow down a cascade's propagation, while those
imposing a greater social cost of not participating increase the cascade's
adoption likelihood. The predictability of transmission also varies with
protocol. But regardless of mechanism, the cascades in our analysis all have a
similar reproduction number ( 1.8), meaning that lower rates of
exposure can be offset with higher per-exposure rates of adoption. Last, we
show how a cascade's structure can not only differentiate these protocols, but
also be modeled through branching processes. Together, these findings provide a
framework for understanding how a wide variety of information cascades can
achieve substantial adoption across a network.Comment: ICWSM 201
How negative ads from diverse right-wing media makes conservative voters dislike Democratic candidates even more
Recent years have seen growing hostility between those who support different political parties in America. But what is the media’s role in creating this increasing dislike? In new research, Richard Lau, David Andersen, Tessa Ditonto, Mona Kleinberg and David Redlawsk investigate this “affective polarization” by exposing participants to different news sources and positive and negative political advertising. They find that hostility towards the opposite party is at its highest when conservative subjects are exposed to negative ads and can customize their news environment
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Adaptive Limited-Supply Online Auctions
We study a limited-supply online auction problem, in which an auctioneer has k goods to sell and bidders arrive and depart dynamically. We suppose that agent valuations are drawn independently from some unknown distribution and construct an adaptive auction that is nevertheless value- andtime-strategy proof. For the k=1 problem we have a strategyproof variant on the classic secretary problem. We present a 4-competitive (e-competitive) strategyproof online algorithm with respect to offline Vickrey for revenue (efficiency). We also show (in a model that slightly generalizes the assumption of independent valuations) that no mechanism can be better than 3/2-competitive (2-competitive) for revenue (efficiency). Our general approach considers a learning phase followed by an accepting phase, and is careful to handle incentive issues for agents that span the two phases. We extend to the k›1 case, by deriving strategyproof mechanisms which are constant-competitive for revenue and efficiency. Finally, we present some strategyproof competitive algorithms for the case in which adversary uses a distribution known to the mechanism.Engineering and Applied Science
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