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A new concept of the available force in long-range interaction complex systems is proposed. The relationship between the available force in different time intervals and the interaction parameters of complex systems is described. It is found…
We estimate the performance of Feynman's ratchet at given values of the ratio of cold to hot reservoir temperatures ($\theta$) and the figure of merit (efficiency in the case of engine and coefficienct of performance in the case of…
We address the question of aggregating the preferences of voters in the context of participatory budgeting. We scrutinize the voting method currently used in practice, underline its drawbacks, and introduce a novel scheme tailored to this…
Selective regression allows abstention from prediction if the confidence to make an accurate prediction is not sufficient. In general, by allowing a reject option, one expects the performance of a regression model to increase at the cost of…
Electoral control refers to attempts by an election's organizer ("the chair") to influence the outcome by adding/deleting/partitioning voters or candidates. The groundbreaking work of Bartholdi, Tovey, and Trick [BTT92] on (constructive)…
Why not have a computer just draw a map? This is something you hear a lot when people talk about gerrymandering, and it's easy to think at first that this could solve redistricting altogether. But there are more than a couple problems with…
The integrity of elections is central to democratic systems. However, a myriad of malicious actors aspire to influence election outcomes for financial or political benefit. A common means to such ends is by manipulating perceptions of the…
Performance measurement in competitive domains is frequently confounded by shared environmental factors that obscure true performance differences. For instance, absolute metrics can be heavily influenced by factors as varied as weather…
This thesis develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…
In an attempt to provide an answer to the increasing criticism against p-values and to bridge the gap between statistical inference and prediction modelling, we introduce the probability of improved prediction (PIP). In general, the PIP is…
Fractional cumulative residual inaccuracy (FCRI) measure allows to determine regions of discrepancy between systems, depending on their respective fractional and chaotic map parameters. Most of the theoretical results and applications…
Unlike their conventional use as estimators of probability density functions in reinforcement learning (RL), this paper introduces a novel function-approximation role for Gaussian mixture models (GMMs) as direct surrogates for Q-function…
In this paper, we address a longstanding puzzle over the functional form that better approximates voter's political utility. Though it has become the norm in the literature to represent the voters' political utility with concave loss…
We study the complexity of (approximate) winner determination under the Monroe and Chamberlin--Courant multiwinner voting rules, which determine the set of representatives by optimizing the total (dis)satisfaction of the voters with their…
We consider a classical problem in choice theory -- vote aggregation -- using novel distance measures between permutations that arise in several practical applications. The distance measures are derived through an axiomatic approach, taking…
A method is given for quantitatively rating the social acceptance of different options which are the matter of a preferential vote. In contrast to a previous article, here the individual votes are allowed to be incomplete, that is, they…
A local bootstrap method is proposed for the analysis of electoral vote-count first-digit frequencies, complementing the Benford's Law limit. The method is calibrated on five presidential-election first rounds (2002--2006) and applied to…
What is a fair performance metric? We consider the choice of fairness metrics through the lens of metric elicitation -- a principled framework for selecting performance metrics that best reflect implicit preferences. The use of metric…
The problem of how to allocate to states the seats in the US House of Representatives is the most studied instance of what is termed the `apportionment problem'. We propose a new method of apportionment which is stochastic, which meets the…
Measure of the weighted cumulative entropy about the predictability of failure time of a system have been introduced in [3]. Referring properties of doubly truncated (interval) cumulative residual and past entropy, several bounds and…