There are no known efficient algorithms to calculate distance in the one-skeleta of associahedra, a problem that is equivalent to finding rotation distance between rooted binary trees or the flip distance between polygonal triangulations. One measure of the difference between trees is the number of conflicting edge pairs, and a natural way of trying to find short paths is to minimize successively this number of conflicting edge pairs using flip operations in the corresponding triangulations. We describe examples that show that the number of such conflicts does not always decrease along geodesics. Thus, a greedy algorithm that always chooses a transformation that reduces conflicts will not produce a geodesic in all cases. Further, for any specified amount, there are examples of pairs of all large sizes showing that the number of conflicts can increase by that amount along any geodesic between the pairs.
Decision-making systems increasingly orchestrate our world: how to intervene on the algorithmic components to build fair and equitable systems is therefore a question of utmost importance; one that is substantially complicated by the context-dependent nature of fairness and discrimination. Modern systems incorporate machinelearned predictions in broader decision-making pipelines, implicating concerns like constrained allocation and strategic behavior that are typically thought of as mechanism design problems. Although both machine learning and mechanism design have individually developed frameworks for addressing issues of fairness and equity, in some complex decision-making systems, neither framework is individually sufficient. In this paper, we develop the position that building fair decision-making systems requires overcoming these limitations which, we argue, are inherent to the individual frameworks of machine learning and mechanism design. Our ultimate objective is to build an encompassing framework that cohesively bridges the individual frameworks. We begin to lay the ground work towards achieving this goal by comparing the perspective each individual discipline takes on fair decision-making, teasing out the lessons each field has taught and can teach the other, and highlighting application domains that require a strong collaboration between these disciplines.
It is an open question whether there exists a polynomial-time algorithm for computing the rotation distances between pairs of extended ordered binary trees.The problem of computing the rotation distance between an arbitrary pair of trees, (S, T), can be efficiently reduced to the problem of computing the rotation distance between a difficult pair of trees (S', T'), where there is no known first step which is guaranteed to be the beginning of a minimal length path. Of interest, therefore, is how to sample such difficult pairs of trees of a fixed size. We show that it is possible to do so efficiently, and present such an algorithm that runs in time O(n4).
The United Nations Consumer Protection Guidelines lists "access ... to adequate information ... to make informed choices" as a core consumer protection right. However, problematic online reviews and imperfections in algorithms that detect those reviews pose obstacles to the fulfillment of this right. Research on reviews and review platforms often derives insights from a single web crawl, but the decisions those crawls observe may not be static. A platform may feature a review one day and filter it from view the next day. An appreciation for these dynamics is necessary to understand how a platform chooses which reviews consumers encounter and which reviews may be unhelpful or suspicious. We introduce a novel longitudinal angle to the study of reviews. We focus on "reclassification," wherein a platform changes its filtering decision for a review. To that end, we perform repeated web crawls of Yelp to create three longitudinal datasets. These datasets highlight the platform's dynamic treatment of reviews. We compile over 12.5M reviews-more than 2M unique-across over 10k businesses. Our datasets are available for researchers to use.Our longitudinal approach gives us a unique perspective on Yelp's classifier and allows us to explore reclassification. We find that reviews routinely move between Yelp's two main classifier classes ("Recommended" and "Not Recommended") -up to 8% over eight years -raising concerns about prior works' use of Yelp's classes as ground truth. These changes have impacts on small scales; for example, a business going from a 3.5 to 4.5 star rating despite no new reviews. Some reviews move multiple times: we observed up to five reclassifications in eleven months. Our data suggests demographic disparities in reclassifications, with more changes in lower density and low-middle income areas. Because our web crawls coincided with the COVID-19 pandemic, our data also allowed limited exploration of the impact of mask policies and discussions on reviews.
It is an open question whether there exists a polynomial-time algorithm for computing the rotation distances between pairs of extended ordered binary trees. The problem of computing the rotation distance between an arbitrary pair of trees, (S, T ), can be efficiently reduced to the problem of computing the rotation distance between a difficult pair of trees (S , T ), where there is no known first step which is guarranteed to be the beginning of a minimal length path. Of interest, therefore, is how to sample such difficult pairs of trees of a fixed size. We show that it is possible to do so efficiently, and present such an algorithm that runs in time O(n 4 ).
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