Related papers: Should you believe that this coin is fair?
Two possibly unfair $n$-sided dice, both labelled $1, 2, \ldots, n$, are rolled, and the sum is recorded. How should the dice's sides be weighted so that the resulting sum is closest to the uniform distribution on $2, 3, \ldots, 2n$? We…
Modern NLP systems exhibit a range of biases, which a growing literature on model debiasing attempts to correct. However current progress is hampered by a plurality of definitions of bias, means of quantification, and oftentimes vague…
Coin flipping is a fundamental cryptographic primitive that enables two distrustful and far apart parties to create a uniformly random bit [Blu81]. Quantum information allows for protocols in the information theoretic setting where no…
Machine learning algorithms can produce biased outcome/prediction, typically, against minorities and under-represented sub-populations. Therefore, fairness is emerging as an important requirement for the large scale application of machine…
Many popular algorithmic fairness measures depend on the joint distribution of predictions, outcomes, and a sensitive feature like race or gender. These measures are sensitive to distribution shift: a predictor which is trained to satisfy…
Negative probabilities emerged at intermediate steps in various attempts to predict the distributions of quantum interference. There is no consensus on their meaning yet. It has been suggested (Khrennikov, 1998) that negative probabilities…
We explore the following question: Is a decision-making program fair, for some useful definition of fairness? First, we describe how several algorithmic fairness questions can be phrased as program verification problems. Second, we discuss…
Developing a better understanding of surprising or counterintuitive phenomena has constituted a significant portion of deep learning research in recent years. These include double descent, grokking, and the lottery ticket hypothesis --…
Inspired by the theory of desirable gambles that is used to model uncertainty in the field of imprecise probabilities, I present a theory of desirable things. Its aim is to model a subject's beliefs about which things are desirable. What…
A set of objects is to be divided fairly among agents with different tastes, modeled by additive utility-functions. If we consider the objects as indivisible, many instances of the decision problem: ``Is there a fair division of the objects…
Preferences for mixing can reveal ambiguity perception and attitude on a single event. The validity of the approach is discussed for multiple preference classes including maxmin, maxmax, variational, and smooth second-order preferences. An…
Getting an unbiased result is a remarkably long standing problem of collective observation/measurement. It is pointed out that quantum coin tossing can generate unbiased result defeating dishonesty.
In this short note we show that the Bitcoin network can allow remote parties to gamble with their bitcoins by tossing a fair or biased coin, with no need for a trusted party, and without the possibility of extortion by dishonest parties who…
A signed probability distribution may extend a given traditional probability from observable events to all events. We formalize and illustrate this approach. We also illustrate its limitation. We argue that the right question is not what…
In this paper, we consider the problem of fair statistical inference involving outcome variables. Examples include classification and regression problems, and estimating treatment effects in randomized trials or observational data. The…
In this article we show for the first time that quantum coin flipping with security guarantees that are strictly better than any classical protocol is possible to implement with current technology. Our protocol takes into account all…
In this note we give an example of a nonmeasurable set in the probability space for an infinite sequence of coin flips. The example arises naturally from the notion of an equivariant function, and serves as a pedagogical illustration of the…
The definition and implementation of fairness in automated decisions has been extensively studied by the research community. Yet, there hides fallacious reasoning, misleading assertions, and questionable practices at the foundations of the…
The laws of chance are often subtle and deceptive. This is why games of chance work. People are convinced that they obey seemingly intuitive laws, while the underlying mathematical structure reveals a different and more complex reality.…
Even though classic theories and models of discrete choice pose man as a rational being, it has been shown extensively that people persistently violate rationality in their actual choices. Recent models of decision-making take these…