Order Symmetry: A New Fairness Criterion for Assignment Mechanisms

We introduce a new fairness criterion, order symmetry, for assignment mechanisms that match n objects to n agents with ordinal preferences over the objects. An assignment mechanism is order symmetric with respect to some probability measure over preference profiles if every agent is equally likely to receive their favorite object, every agent is equally likely to receive their second favorite, and so on. When associated with a sufficiently symmetric probability measure, order symmetry is a relaxation of anonymity that, crucially, can be satisfied by discrete assignment mechanisms. Furthermore, it can be achieved without sacrificing other desirable axiomatic properties satisfied by existing mechanisms. In particular, we show that it can be achieved in conjunction with strategyproofness and ex post efficiency via the top trading cycles mechanism (but not serial dictatorship). We additionally design a novel mechanism that is both order symmetric and ordinally efficient. The practical utility of order symmetry is substantiated by simulations on Impartial Culture and Mallows-distributed preferences for four common assignment mechanisms.

Algorithms for Average Regret Minimization

In this paper, we study a problem from the realm of multicriteria decision making in which the goal is to select from a given set S of d-dimensional objects a minimum sized subset S0 with bounded regret. Thereby, regret measures the unhappiness of users which would like to select their favorite object from set S but now can only select their favorite object from the subset S0. Previous work focused on bounding the maximum regret which is determined by the most unhappy user. We propose to consider the average regret instead which is determined by the sum of (un)happiness of all possible users. We show that this regret measure comes with desirable properties as supermodularity which allows to construct approximation algorithms. Furthermore, we introduce the regret minimizing permutation problem and discuss extensions of our algorithms to the recently proposed k-regret measure. Our theoretical results are accompanied with experiments on a variety of inputs with d up to 7.

Is There Anybody Out There?

Prior research shows that there are stable personality differences in the tendency to attribute human-like mental states to (i.e., anthropomorphize) non-human targets. A separate line of research has explored the extent to which individuals turn to non-human targets as a source of the support and security people often derive from close relationships. The current paper offers a first integration of these lines of research by testing whether trait differences in the tendency to anthropomorphize non-human targets predicts the extent to which individuals derive feelings of security from a favorite belonging. An experimental study finds that individuals who tend to anthropomorphize feel greater security after a reminder of a favorite object (vs. close other) and that these feelings of security subsequently enhance motivations for personal growth, an established benefit of interpersonal relationships.

The distribution and reactions of the land snails in the vicinity of Columbia Missouri

Text from page 3: "Introduction: The following study was undertaken at the suggestion of Dr.G .S .Dodds, ,with the intent of discovering the factors which determine the distribution of a group of our local fauna, the land gastropods. This group has been a favorite object of study with naturalists for the past century, and a great mass of literature exists on isolated collections made the country over. In Missouri a certain amount of collecting has been done, probably exhausting largely the possibilities so far as species are concerned. However, some interesting additions to our knowle[d]ge of the regional distribution have been ad1ed in the course of the present study, as will be noted later. Greger (1905) has made extensive collections in Callaway County, Pilsbfy and Ferris (1S06) in the Ozark Region, and Sampson (1913) over most of the State. There are besides, more general collections, as those of Binney (1885), in which mention is made of Missouri shells. Heretofore no attempt has been made to correlate the information scattered. Thru these papers, or to study the distribution from an ecological standpoint, and there has not been an intensive study of a single region in Missouri."