Related papers: Approximating power by weights
It is well known that the Penrose-Banzhaf index of a weighted game can differ starkly from corresponding weights. Limit results are quite the opposite, i.e., under certain conditions the power distribution approaches the weight…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
We investigate the distribution of the well-studied Shapley--Shubik values in weighted voting games where the agents are stochastically determined. The Shapley--Shubik value measures the voting power of an agent, in typical collective…
In this paper, we consider lightweight decentralised algorithms for achieving consensus in distributed systems. Each member of a distributed group has a private value from a fixed set consisting of, say, two elements, and the goal is for…
Polarization-adjusted convolutional (PAC) codes combine the polar and convolutional transformations to enhance the distance properties of polar codes. They offer a performance very close to the finite length information-theoretic bounds for…
Covariate balance is crucial for unconfounded descriptive or causal comparisons. However, lack of balance is common in observational studies. This article considers weighting strategies for balancing covariates. We define a general class of…
Covariate balance is crucial for unconfounded descriptive or causal comparisons. However, lack of balance is common in observational studies. This article considers weighting strategies for balancing covariates. We define a general class of…
We derive new approximations for the Value at Risk and the Expected Shortfall at high levels of loss distributions with positive skewness and excess kurtosis, and we describe their precisions for notable ones such as for exponential, Pareto…
While proportionality is frequently named as a desirable property of voting rules, its interpretation in multiwinner voting differs significantly from that in apportionment. We aim to bridge these two distinct notions of proportionality by…
Balancing numbers possess, as Fibonacci numbers, a Binet formula. Using this, partial sums of arbitrary powers of balancing numbers can be summed explicitly. For this, as a first step, a power $B_n^l$ is expressed as a linear combination of…
Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…
Behavioural economics provides labels for patterns in human economic behaviour. Probability weighting is one such label. It expresses a mismatch between probabilities used in a formal model of a decision (i.e. model parameters) and…
The determination of weight distribution of cyclic codes involves evaluation of Gauss sums and exponential sums. Despite of some cases where a neat expression is available, the computation is generally rather complicated. In this note, we…
Power-law distributions occur in wide variety of physical, biological, and social phenomena. In this paper, we propose a statistical hypothesis test based on the log-likelihood ratio to assess whether two samples of discrete data are drawn…
This paper deals with interactions between committee members as they rank a large list of applicants for a given position and eventually reach consensus. We will see that for a natural deterministic model the ranking can be described by…
Power-law distributions are common, particularly in social physics. Here, we explore whether power-laws might arise as a consequence of a general variational principle for stochastic processes. We describe communities of 'social particles',…
We consider a social choice problem where only a small number of people out of a large population are sufficiently available or motivated to vote. A common solution to increase participation is to allow voters use a proxy, that is, transfer…
Following Zhang and Grossi~(AAAI 2021), we study in more depth a variant of weighted voting games in which agents' weights are induced by a transitive support structure. This class of simple games is notably well suited to study the…
The ideas of model averaging are used to find weights in peak-over-threshold problems using a possible range of thresholds. A range of the largest observations are chosen and considered as possible thresholds, each time performing…
We analyze properties of apportionment functions in context of the problem of allocating seats in the European Parliament. Necessary and sufficient conditions for apportionment functions are investigated. Some exemplary families of…