Size versus truthfulness in the house allocation problem

We study the House Allocation problem (also known as the Assignment problem), i.e., the problem of allocating a set of objects among a set of agents, where each agent has ordinal preferences (possibly involving ties) over a subset of the objects. We focus on truthful mechanisms without monetary transfers for finding large Pareto optimal matchings. It is straightforward to show that no deterministic truthful mechanism can approximate a maximum cardinality Pareto optimal matching with ratio better than 2. We thus consider randomized mechanisms. We give a natural and explicit extension of the classical Random Serial Dictatorship Mechanism (RSDM) specifically for the House Allocation problem where preference lists can include ties. We thus obtain a universally truthful randomized mechanism for finding a Pareto optimal matching and show that it achieves an approximation ratio of eovere-1. The same bound holds even when agents have priorities (weights) and our goal is to find a maximum weight (as opposed to maximum cardinality) Pareto optimal matching. On the other hand we give a lower bound of 18 over 13 on the approximation ratio of any universally truthful Pareto optimal mechanism in settings with strict preferences. In the case that the mechanism must additionally be non-bossy, an improved lower bound of eovere-1 holds. This lower bound is tight given that RSDM for strict preference lists is non-bossy. We moreover interpret our problem in terms of the classical secretary problem and prove that our mechanism provides the best randomized strategy of the administrator who interviews the applicants

Size versus truthfulness in the House Allocation problem

We study the House Allocation problem (also known as the Assignment problem), i.e., the problem of allocating a set of objects among a set of agents, where each agent has ordinal preferences (possibly involving ties) over a subset of the objects. We focus on truthful mechanisms without monetary transfers for finding large Pareto optimal matchings. It is straightforward to show that no deterministic truthful mechanism can approximate a maximum cardinality Pareto optimal matching with ratio better than 2. We thus consider randomised mechanisms. We give a natural and explicit extension of the classical Random Serial Dictatorship Mechanism (RSDM) specifically for the House Allocation problem where preference lists can include ties. We thus obtain a universally truthful randomised mechanism for finding a Pareto optimal matching and show that it achieves an approximation ratio of $\frac{e}{e-1}$. The same bound holds even when agents have priorities (weights) and our goal is to find a maximum weight (as opposed to maximum cardinality) Pareto optimal matching. On the other hand we give a lower bound of $\frac{18}{13}$ on the approximation ratio of any universally truthful Pareto optimal mechanism in settings with strict preferences. In the case that the mechanism must additionally be non-bossy with an additional technical assumption, we show by utilising a result of Bade that an improved lower bound of $\frac{e}{e-1}$ holds. This lower bound is tight since RSDM for strict preference lists is non-bossy. We moreover interpret our problem in terms of the classical secretary problem and prove that our mechanism provides the best randomised strategy of the administrator who interviews the applicants.Comment: To appear in Algorithmica (preliminary version appeared in the Proceedings of EC 2014

What Do Our Choices Say About Our Preferences?

Taking online decisions is a part of everyday life. Think of buying a house, parking a car or taking part in an auction. We often take those decisions publicly, which may breach our privacy - a party observing our choices may learn a lot about our preferences. In this paper we investigate the online stopping algorithms from the privacy preserving perspective, using a mathematically rigorous differential privacy notion. In differentially private algorithms there is usually an issue of balancing the privacy and utility. In this regime, in most cases, having both optimality and high level of privacy at the same time is impossible. We propose a natural mechanism to achieve a controllable trade-off, quantified by a parameter, between the accuracy of the online algorithm and its privacy. Depending on the parameter, our mechanism can be optimal with weaker differential privacy or suboptimal, yet more privacy-preserving. We conduct a detailed accuracy and privacy analysis of our mechanism applied to the optimal algorithm for the classical secretary problem. Thereby the classical notions from two distinct areas - optimal stopping and differential privacy - meet for the first time.Comment: 22 pages, 6 figure

Harnessing Markets for Water Quality

This issue of IMPACT is devoted to exploring and understanding the opportunities and challenges of harnessing markets to improve water quality. It looks at how markets could be implemented to address the growing concern of nonpoint source pollution as well as point sources. Recently, the EPA proposed a water quality trading proposal, which is summarized, reviewed, and critiqued

Cinderella Sovereignty

The Blocher-Gulati critique of the barriers to secession under public international law is insightful and thought provoking, an important contribution in its own right. I wish it had not been eclipsed by the authors\u27 clever and provocative fix: turning sovereignty into a tradable commodity. I suspect that this fix would bring about more suffering than the status quo for two reasons. First, a market for sovereign control is unlikely to be a market in any meaningful sense. Therefore, trading sovereignty would not discipline oppressors. Second, should something like a real market materialize, it could diminish the incentives for states to treat their populations better just as plausibly as it could improve them. Distant empires could find it easier to traffic in oppressed people and territories, which would pass from state to state as their masters lose interest. A class of marginal client statelets would grow, endowed with a poor stepchild of sovereignty, which would leave their people defenseless and voiceless

The Development of British Commercial and Political Networks in the Straits Settlements 1800 to 1868: The Rise of a Colonial and Regional Economic Identity?

This paper examines the growth of the British commercial communities in the Straits Settlements in the first half of the nineteenth century. It describes how they emerged as a coherent commercial and political interest group, separate from the Indian empire, with their own network of allies and commercial partners in Britain. As such, the Straits merchants emerged as a significant political lobby in their own right. It contends that in the process, they revived earlier notions of Southeast Asia as a discrete geographical region, in which political and ethnic diversity was bridged by the flourishing of maritime commercial networks

Cinderella Sovereignty

The Blocher-Gulati critique of the barriers to secession under public international law is insightful and thought provoking, an important contribution in its own right. I wish it had not been eclipsed by the authors\u27 clever and provocative fix: turning sovereignty into a tradable commodity. I suspect that this fix would bring about more suffering than the status quo for two reasons. First, a market for sovereign control is unlikely to be a market in any meaningful sense. Therefore, trading sovereignty would not discipline oppressors. Second, should something like a real market materialize, it could diminish the incentives for states to treat their populations better just as plausibly as it could improve them. Distant empires could find it easier to traffic in oppressed people and territories, which would pass from state to state as their masters lose interest. A class of marginal client statelets would grow, endowed with a poor stepchild of sovereignty, which would leave their people defenseless and voiceless

Preparatory study for the revaluation of the EQ-5D tariff: methodology report.

BACKGROUND: EQ-5D is a widely used generic measure of health with a 'tariff', or preference weights, obtained from the general population, using time trade-off (TTO). PRET (Preparatory study for the Re-valuation of the EQ-5D Tariff project) contributes towards the methodology for its revaluation. METHODS: Stage 1 examined key assumptions typically involved in health-state valuations through a series of binary choice exercises, namely that health-state preferences are independent of (1) duration of the state; (2) whose health it is (i.e. perspective); (3) length of 'lead time' (a mechanism to value all states on the same scale, including those who are worse than being dead); (4) when health events take place (time preference); and (5) satisfaction associated with the state. Further topics addressed were (6) exhaustion of lead time in the worst state; (7) health-state valuation using discrete choice experiments (DCEs) with a duration attribute; and (8) binary choice administration of lead time - time trade-off (LT-TTO). Stage 1 consisted of an online survey with 6000 respondents. Stage 2 compared the results above to those of an identical survey conducted in 200 face-to-face computer-assisted personal interviews (CAPIs), covering topics (1) to (7). Stages 3 and 4 examined - in more detail and depth - issues taken from stage 1. Stage 3 consisted of CAPI surveys of a representative UK sample of 300, using examples of TTO, LT-TTO, and DCE with duration, each followed by extensive feedback questions. Stage 4 was a more intensive exercise involving a qualitative analysis of people's thought processes during both binary choice and iterative health-state valuation exercises. Data were collected through 'think-aloud' methods in 30 interviews of a convenience sample. RESULTS: Stage 1 found that health-state values are not independent of (1) duration of the state but there is no clear pattern; (2) whose health it is; (3) the duration of 'lead time' but there was no clear pattern; (4) when health events take place; or (5) satisfaction associated with the state. Furthermore, (6) exhaustion of lead time in the worst state was subject to substantial framing effects; (7) the five-level version of the EQ-5D (EQ-5D-5L) can be valued using DCE with duration as an attribute; and (8) binary choice LT-TTO can be administered in an online environment. Stage 2 found that although online surveys and CAPI surveys resulted in different compositions of respondents, at the aggregate, their responses to the experimental questions covering (1) to (7) above were not statistically significantly different from each other. Stages 3 and 4 found that TTO and LT-TTO were easier than DCE with duration; respondents did not necessarily trade across all attributes of EQ-5D; some respondents found it difficult to distinguish between the two worst levels of EQ-5D-5L, and some respondents may be thinking about the impact of their ill health on their family. CONCLUSIONS: In order for the National Institute for Health and Care Excellence to make the most appropriate decisions, the EQ-5D tariff needs to incorporate the latest understanding of health-state preferences. PRET contributed to the knowledge base on the conduct of health-state valuation studies. FUNDING: The Medical Research Council (MRC)-National Institute for Health Research (NIHR) Methodology Research Programme funded the PRET project (MRC ref. G0901500), and the EuroQol Group funded the PRET-AS project (Preparatory study for the Re-valuation of the EQ-5D Tariff project - Additional Sample) as an extension to the PRET project with formal agreement from the MRC