Related papers: The James Function
A dataset has been classified by some unknown classifier into two types of points. What were the most important factors in determining the classification outcome? In this work, we employ an axiomatic approach in order to uniquely…
We present an extensive statistical analysis of the results of all sports competitions in five major sports leagues in England and the United States. We characterize the parity among teams by the variance in the winning fraction from…
In previous work cite{Ha98:Towards} we presented a case-based approach to eliciting and reasoning with preferences. A key issue in this approach is the definition of similarity between user preferences. We introduced the probabilistic…
Batting average is one of the principle performance measures for an individual baseball player. It is natural to statistically model this as a binomial-variable proportion, with a given (observed) number of qualifying attempts (called…
Several performance metrics for quantifying the in-game performances of individual football players have been proposed in recent years. Although the majority of the on-the-ball actions during games constitutes of passes, many of the…
Predicting the outcome of sports events is a hard task. We quantify this difficulty with a coefficient that measures the distance between the observed final results of sports leagues and idealized perfectly balanced competitions in terms of…
We explain why numbers occurring in the classification of polygon spaces coincide with numbers of self-dual equivalence classes of threshold functions, or of regular Boolean functions, or of decisive weighted majority games.
Uncertainty associated with statistical problems arises due to what has not been seen as opposed to what has been seen. Using probability to quantify the uncertainty the task is to construct a probability model for what has not been seen…
In this paper, we study a game with positive or plus infinite expectation and determine the optimal proportion of investment for maximizing the limit expectation of growth rate per attempt. With this objective, we introduce a new pricing…
The research on coalitional games has focused on how to share the reward among a coalition such that players are incentivised to collaborate together. It assumes that the (deterministic or stochastic) characteristic function is known in…
Agents often have individual goals which depend on a group's actions. If agents trust a forecast of collective action and adapt strategically, such prediction can influence outcomes non-trivially, resulting in a form of performative…
This paper studies the correlations of the average winnings of agents and the volatilities of systems based on mix-game model which is an extension of minority game (MG). In mix-game, there are two groups of agents; group1 plays the…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
We consider a simple and altruistic multiagent system in which the agents are eager to perform a collective task but where their real engagement depends on the willingness to perform the task of other influential agents. We model this…
This paper introduces a new model and methodology for estimating the ability of NBA players. The main idea is to directly measure how good a player is by comparing how their team performs when they are on the court as opposed to when they…
We investigate further several properties of the minority game we have recently introduced. We explain the origin of the phase transition and give an analytical expression of $\sigma^2/N$ in the $N\ll2^M$ region. The ability of the players…
Algorithms are often used to produce decision-making rules that classify or evaluate individuals. When these individuals have incentives to be classified a certain way, they may behave strategically to influence their outcomes. We develop a…
It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
Standard probability theory has been extremely successful but there are some conceptually possible scenarios, such as fair infinite lotteries, that it does not model well. For this reason alternative probability theories have been…