A Lottery Model for Center-Type Problems with Outliers

In this paper, we give tight approximation algorithms for the k-center and matroid center problems with outliers. Unfairness arises naturally in this setting: certain clients could always be considered as outliers. To address this issue, we introduce a lottery model in which each client is allowed to submit a parameter indicating the lower-bound on the probability that it should be covered and we look for a random solution that satisfies all the given requests. Out techniques include a randomized rounding procedure to round a point inside a matroid intersection polytope to a basis plus at most one extra item such that all marginal probabilities are preserved and such that a certain linear function of the variables does not decrease in the process with probability one

Approximation algorithms for stochastic clustering

We consider stochastic settings for clustering, and develop provably-good approximation algorithms for a number of these notions. These algorithms yield better approximation ratios compared to the usual deterministic clustering setting. Additionally, they offer a number of advantages including clustering which is fairer and has better long-term behavior for each user. In particular, they ensure that *every user* is guaranteed to get good service (on average). We also complement some of these with impossibility results

The Relationship Between Risk Attitudes and Heuristics in Search Tasks: A Laboratory Experiment

Experimental studies of search behavior suggest that individuals stop searching earlier than predicted by the optimal, risk-neutral stopping rule. Such behavior could be generated by two different classes of decision rules: rules that are optimal conditional on utility functions departing from risk neutrality, or heuristics derived from limited cognitive processing capacities and satisfycing. To discriminate among these two possibilities, we conduct an experiment that consists of a standard search task as well as a lottery task designed to elicit utility functions. We find that search heuristics are not related to measures of risk aversion, but to measures of loss aversion

Pain-avoidance versus reward-seeking: an experimental investigation

According to fear-avoidance models, a catastrophic interpretation of a painful experience may give rise to pain-related fear and avoidance, leading to the development and maintenance of chronic pain problems in the long term. However, little is known about how exactly motivation and goal prioritization play a role in the development of pain-related fear. This study investigates these processes in healthy volunteers using an experimental context with multiple, competing goals. In a differential human fear-conditioning paradigm, 57 participants performed joystick movements. In the control condition, one movement (conditioned stimulus; CS+) was followed by a painful electrocutaneous unconditioned stimulus (pain-US) in 50% of the trials, whereas another movement (nonreinforced conditioned stimulus; CS-) was not. In the experimental condition, a reward in the form of lottery tickets (reward-US) accompanied the presentation of the pain-US. Participants were classified into 3 groups, as a function of the goal, they reported to be the most important: (1) pain-avoidance, (2) reward-seeking, and (3) both goals being equally important. Results indicated that neither the reward co-occurring with pain nor the prioritized goal modulated pain-related fear. However, during subsequent choice trials, participants selected the painful movement more often when the reward was presented compared with the context in which the reward was absent. The latter effect was dependent on goal prioritization, with more frequent selections in the reward-seeking group, and the least selections in the pain-avoidance group. Taken together, these results underscore the importance of competing goals and goal prioritization in the attenuation of avoidance behavior

Mean, Median or Mode? A Striking Conclusion From Lottery Experiments

This paper deals with estimating data from experiments determining lottery certainty equivalents. The paper presents the parametric and nonparametric results of the least squares (mean), quantile (including median) and mode estimations. The examined data are found to be positively skewed for low probabilities and negatively skewed for high probabilities. This observation leads to the striking conclusion that lottery valuations are only nonlinearly related to probability when means are considered. Such nonlinearity is not confirmed by the mode estimator in which case the most likely lottery valuations are close to their expected values. This means that the most likely behavior of a group is fully rational. This conclusion is a significant departure from one of the fundamental results concerning lottery experiments presented so far.Lottery experiments; Least Squares, Quantile, Median, and Mode Estimators; Nonparametric and Parametric Estimators; Relative Utility Function; Prospect Theory.

A Constant Approximation for Colorful k-Center

In this paper, we consider the colorful k-center problem, which is a generalization of the well-known k-center problem. Here, we are given red and blue points in a metric space, and a coverage requirement for each color. The goal is to find the smallest radius rho, such that with k balls of radius rho, the desired number of points of each color can be covered. We obtain a constant approximation for this problem in the Euclidean plane. We obtain this result by combining a "pseudo-approximation" algorithm that works in any metric space, and an approximation algorithm that works for a special class of instances in the plane. The latter algorithm uses a novel connection to a certain matching problem in graphs

Small Space Stream Summary for Matroid Center

In the matroid center problem, which generalizes the k-center problem, we need to pick a set of centers that is an independent set of a matroid with rank r. We study this problem in streaming, where elements of the ground set arrive in the stream. We first show that any randomized one-pass streaming algorithm that computes a better than Delta-approximation for partition-matroid center must use Omega(r^2) bits of space, where Delta is the aspect ratio of the metric and can be arbitrarily large. This shows a quadratic separation between matroid center and k-center, for which the Doubling algorithm [Charikar et al., 1997] gives an 8-approximation using O(k)-space and one pass. To complement this, we give a one-pass algorithm for matroid center that stores at most O(r^2 log(1/epsilon)/epsilon) points (viz., stream summary) among which a (7+epsilon)-approximate solution exists, which can be found by brute force, or a (17+epsilon)-approximation can be found with an efficient algorithm. If we are allowed a second pass, we can compute a (3+epsilon)-approximation efficiently. We also consider the problem of matroid center with z outliers and give a one-pass algorithm that outputs a set of O((r^2+rz)log(1/epsilon)/epsilon) points that contains a (15+epsilon)-approximate solution. Our techniques extend to knapsack center and knapsack center with z outliers in a straightforward way, and we get algorithms that use space linear in the size of a largest feasible set (as opposed to quadratic space for matroid center)

The Relationship Between Risk Attitudes and Heuristics in Search Tasks: A Laboratory Experiment

The existing evidence from laboratory experiments suggests that relatively simple heuristics describe observed search behavior better than the optimal stopping rule derived under risk neutrality. Such behavior could be generated by two entirely different classes of decision rules: (i) rules that are optimal conditional on utility functions that depart from risk neutrality or (ii) heuristics that derive from limited cognitive processing capacities and satisfycing. In this paper, we develop and test search models that depart from the standard assumption of risk neutrality in order to distinguish these two possibilities. In our experiment, we present subjects not only with a standard search task, but also with a series of lottery tasks that serve to elicit the shape of their utility functions. We do not find a relationship between behavior in the search task and measures of risk aversion. Our data suggest, however, that loss aversion is important for explaining search behavior.

It's the Opportunity Cost, Stupid! How Self-Employment Responds to Financial Incentives of Return, Risk and Skew

There is no robust empirical support for the effect of financial incentives on the decision to work in self-employment rather than as a wage earner. In the literature, this is seen as a puzzle. We offer a focus on the opportunity cost, i.e. the wages given up as an employee. Information on income from self-employment is of inferior quality and this is not just a problem for the outside researcher, it is an imminent problem of the individual considering self-employment. We also argue that it is not only the location of an income distribution that matters and that dispersion and (a)symmetry should not be ignored. We predict that higher mean, lower variance and higher skew in the wage distribution in a particular employment segment reduce the inclination to prefer self-employment above employee status. Using a sample of 56,000 recent graduates from a Dutch college or university, grouped in approximately 120 labor market segments, we find significant support for these propositions. The results survive various robustness checks on specifications and assumptions.entrepreneurship, self-employment, wage-employment, income distribution, income risk, income skew, income variance, occupational choice, labor market entry, labor market segments, opportunity cost

SUBJECTIVE EVALUATION OF DELAYED RISKY OUTCOMES: AN EXPERIMENTAL APPROACH

This paper uses experimental data to estimate the pure time discount rate for different lengths of times for riskless assets (bonds), and risky assets (delayed lotteries). In moving from the present time (t = 0) to the future, there is a very sharp decline (jump) in the subjective price of the assets for both buy and sell transactions. This jump corresponds to a large increase in the discount rate for the first period and a much lower discount rate for later periods (forward rate). The findings cast doubt on the relevance of the hyperbolic function approach to discounting.Willingness to accept (WTA); Willingness to pay (WTP);Intertemporal choice, Decision-making.