Related papers: The Probability Distribution for Draws Until First…
Though widely used in applications, reinforced random walk on graphs have never been the subject of a valid statistical inference. We develop in this paper a statistical framework for a general two-colored urn model. The probability to draw…
The Richardson-Lucy unfolding approach is simple and excellently performing. It efficiently suppresses artificial high frequency contributions and permits to introduce known features of the true distribution. An algorithm to fix the number…
Elections for public offices in democratic nations are large-scale examples of collective decision-making. As a complex system with a multitude of interactions among agents, we can anticipate that universal macroscopic patterns could emerge…
Researchers often face choices between multiple data sources that differ in quality, cost, and representativeness. Which sources will most improve predictive performance? We study this data prioritization problem under a random distribution…
As observers of the universe we are physical systems within it. If the universe is very large in space and/or time, the probability becomes significant that the data on which we base predictions is replicated at other locations in…
There are $n$ independent Bernoulli random variables with parameters $p_i$ that are observed sequentially. Two players, A and B, act in turns starting with player A. Each player has the possibility on his turn, when $I_k=1$, to choose…
Predicting the winner of an election is of importance to multiple stakeholders. To formulate the problem, we consider an independent sequence of categorical data with a finite number of possible outcomes in each. The data is assumed to be…
The study of "random segments" is a classic issue in geometrical probability, whose complexity depends on how it is defined. But in apparently simple models, the random behavior is not immediate. In the present manuscript the following…
How can we probabilistically predict the winner in a ranked-choice election without all ballots being counted? In this study, we introduce a novel algorithm designed to predict outcomes in Instant Runoff Voting (IRV) elections. The…
The election is a classical problem in distributed algorithmic. It aims to design and to analyze a distributed algorithm choosing a node in a graph, here, in a tree. In this paper, a class of randomized algorithms for the election is…
We study a resource allocation setting where $m$ discrete items are to be divided among $n$ agents with additive utilities, and the agents' utilities for individual items are drawn at random from a probability distribution. Since common…
We study a mathematical model of voting contest with $m$ voters and $n$ candidates, with each voter ranking the candidates in order of preference, without ties. A Condorcet winner is a candidate who gets more than $m/2$ votes in pairwise…
In the game of cricket, the result of coin toss is assumed to be one of the determinants of match outcome. The decision to bat first after winning the toss is often taken to make the best use of superior pitch conditions and set a big…
We study coverage processes in which each draw reveals a subset of $[n]$, and the goal is to determine the expected number of draws until all items are seen at least once. A classical example is the Coupon Collector's Problem, where each…
We consider the unbalanced allocation of $m$ balls into $n$ bins by a randomized algorithm using the "power of two choices". For each ball, we select a set of bins at random, then place the ball in the fullest bin within the set.…
We find a remarkable agreement between the statistics of a randomly divided interval and the observed statistical patterns and distributions found in horse racing betting markets. We compare the distribution of implied winning odds, the…
We propose results of the investigation of properties of the random sums of random variables. We consider the case, where the number of summands is the first moment of an event occurrence. An integral equation is presented that determines…
We model the joint distribution of choice probabilities and decision times in binary choice tasks as the solution to a problem of optimal sequential sampling, where the agent is uncertain of the utility of each action and pays a constant…
We examine rules for predicting whether a point in $\mathbb{R}$ generated from a 50-50 mixture of two different probability distributions came from one distribution or the other, given limited (or no) information on the two distributions,…
This paper proposes normative criteria for voting rules under uncertainty about individual preferences. The criteria emphasize the importance of responsiveness, i.e., the probability that the social outcome coincides with the realized…