Title
Anonymity in predicting the future
Contributors
Creator: Velleman, Daniel J. (Amherst College. Department of Mathematics and Statistics)
Creator: Bajpai, Dvij (Amherst College. Department of Mathematics and Statistics)
Creator: Bajpai, Dvij (Amherst College. Department of Mathematics and Statistics)
Genre
Publication Information
Published Version
Date Issued
2016-10
Note
Copyright 2016 Mathematical Association of America. All Rights Reserved.
Note
Final published version appeared in American Mathematical Monthly.
Abstract
Consider an arbitrary set S and an arbitrary function f : ℝ → S. We think of the domain of f as representing time, and for each x ∈ ℝ, we think of f(x) as the state of some system at time x. Imagine that, at each time x, there is an agent who can see the values of f on (−∞, x) and is trying to guess f(x)—in other words, the agent is trying to guess the present state of the system from its past history. In a 2008 paper, Christopher Hardin and Alan Taylor use the axiom of choice to construct a strategy that the agents can use to guarantee that, for every function f, all but countably many of them will guess correctly. In a 2013 monograph, they introduce the idea of anonymous guessing strategies, in which the agents can see the past but don't know where they are located in time. In this paper, we consider a number of variations on anonymity. For instance, what if, in addition to not knowing where they are located in time, agents also do not know the rate at which time is progressing? What if they have no sense of how much time elapses between any two events? We show that in some cases agents can still guess successfully, while in others they perform very poorly.
Subjects
Identifier (DOI)
10.4169/amer.math.monthly.123.08.777
Language
English
Files referenced in this Digital Object
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