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Register a new userA Partial Order on Preference Profiles
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Wayne Yuan Gao
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We propose a theoretical framework under which preference profiles can be meaningfully compared. Specifically, given a finite set of feasible allocations and a preference profile, we first define a ranking vector of an allocation as the vector of all individuals rankings of this allocation. We then define a partial order on preference profiles and write $P geq P^{}$, if there exists an onto mapping $psi$ from the Pareto frontier of $P^{}$ onto the Pareto frontier of $P$, such that the ranking vector of any Pareto efficient allocation $x$ under $P^{}$ is weakly dominated by the ranking vector of the image allocation $psi(x)$ under $P$. We provide a characterization of the maximal and minimal elements under the partial order. In particular, we illustrate how an emph{individualistic} form of social preferences can be $trianglerighteqslant$-maximal in a specific setting. We also discuss how the framework can be further generalized to incorporate additional economic ingredients.
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We provide two characterizations, one axiomatic and the other neuro-computational, of the dependence of choice probabilities on deadlines, within the widely used softmax representation [ p_{t}left( a,Aright) =dfrac{e^{frac{uleft( aright) }{lambda left( tright) }+alpha left( aright) }}{sum_{bin A}e^{frac{uleft( bright) }{lambda left( tright) }+alpha left( bright) }}% ] where $p_{t}left( a,Aright) $ is the probability that alternative $a$ is selected from the set $A$ of feasible alternatives if $t$ is the time available to decide, $lambda$ is a time dependent noise parameter measuring the unit cost of information, $u$ is a time independent utility function, and $alpha$ is an alternative-specific bias that determines the initial choice probabilities reflecting prior information and memory anchoring. Our axiomatic analysis provides a behavioral foundation of softmax (also known as Multinomial Logit Model when $alpha$ is constant). Our neuro-computational derivation provides a biologically inspired algorithm that may explain the emergence of softmax in choice behavior. Jointly, the two approaches provide a thorough understanding of soft-maximization in terms of internal causes (neurophysiological mechanisms) and external effects (testable implications).
Let m and n be any integers with n>m>=2. Using just the entropy function it is possible to define a partial order on S_mn (the symmetric group on mn letters) modulo a subgroup isomorphic to S_m x S_n. We explore this partial order in the case m=2, n=3, where thanks to the outer automorphism the quotient space is actually isomorphic to a parabolic quotient of S_6. Furthermore we show that in this case it has a fairly simple algebraic description in terms of elements of the group ring.
We investigate a 4-state ferromagnetic Potts model with a special type of geometrical frustration on a three dimensional diamond lattice by means of Wang-Landau Monte Carlo simulation motivated by a peculiar structural phase transition found in $beta$-pyrochlore oxide KOs$_2$O$_6$. We find that this model undergoes unconventional first-order phase transition; half of the spins in the system order in a two dimensional hexagonal-sheet-like structure, while the remaining half stay disordered. The ordered sheets and the disordered sheets stack one after another. We obtain a fairly large residual entropy at $T = 0$ which originates from the disordered sheets.
We analyze statistical discrimination in hiring markets using a multi-armed bandit model. Myopic firms face workers arriving with heterogeneous observable characteristics. The association between the workers skill and characteristics is unknown ex ante; thus, firms need to learn it. Laissez-faire causes perpetual underestimation: minority workers are rarely hired, and therefore, underestimation towards them tends to persist. Even a slight population-ratio imbalance frequently produces perpetual underestimation. We propose two policy solutions: a novel subsidy rule (the hybrid mechanism) and the Rooney Rule. Our results indicate that temporary affirmative actions effectively mitigate discrimination caused by insufficient data.
Recently there has been much interest in performing search queries over encrypted data to enable functionality while protecting sensitive data. One particularly efficient mechanism for executing such queries is order-preserving encryption/encoding (OPE) which results in ciphertexts that preserve the relative order of the underlying plaintexts thus allowing range and comparison queries to be performed directly on ciphertexts. In this paper, we propose an alternative approach to range queries over encrypted data that is optimized to support insert-heavy workloads as are common in big data applications while still maintaining search functionality and achieving stronger security. Specifically, we propose a new primitive called partial order preserving encoding (POPE) that achieves ideal OPE security with frequency hiding and also leaves a sizable fraction of the data pairwise incomparable. Using only O(1) persistent and $O(n^epsilon)$ non-persistent client storage for $0<epsilon<1$, our POPE scheme provides extremely fast batch insertion consisting of a single round, and efficient search with O(1) amortized cost for up to $O(n^{1-epsilon})$ search queries. This improved security and performance makes our scheme better suited for todays insert-heavy databases.
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