Related papers: Generalized roll-call model for the Shapley-Shubik…
We present a model for quantitatively identifying swing voters in congressional elections. This is achieved by predicting an individual voter's likelihood to vote and an individual voter's likelihood to vote for a given party, if he votes.…
In a country with many elections, it may prove economically expedient to hold multiple elections simultaneously on a common polling date. We show that in a polarized society, in which each voter has a preferred party, an increase in the…
Generalized probability distributions for Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics, with unequal source probabilities $q_i$ for each level $i$, are obtained by combinatorial reasoning. For equiprobable degenerate…
In global sensitivity analysis, the well known Sobol' sensitivity indices aim to quantify how the variance in the output of a mathematical model can be apportioned to the different variances of its input random variables. These indices are…
The Shapley-Shubik index is a specialization of the Shapley value and is widely applied to evaluate the power distribution in committees drawing binary decisions. It was generalized to decisions with more than two levels of approval both in…
We propose a probabilistic model to aggregate the answers of respondents answering multiple-choice questions. The model does not assume that everyone has access to the same information, and so does not assume that the consensus answer is…
The voter model is a toy model of consensus formation based on nearest-neighbor interactions. A voter sits at each vertex in a hypercubic lattice (of dimension $d$) and is in one of two possible opinion states. The opinion state of each…
The global sensitivity analysis of a numerical model aims to quantify, by means of sensitivity indices estimate, the contributions of each uncertain input variable to the model output uncertainty. The so-called Sobol' indices, which are…
Consider an election between k candidates in which each voter votes randomly (but not necessarily independently) and suppose that there is a single candidate that every voter prefers (in the sense that each voter is more likely to vote for…
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…
Consider an urn filled with balls, each labeled with one of several possible collective decisions. Now, let a random voter draw two balls from the urn and pick her more preferred as the collective decision. Relabel the losing ball with the…
Elections, the cornerstone of democratic societies, are usually regarded as unpredictable due to the complex interactions that shape them at different levels. In this work, we show that voter turnouts contain crucial information that can be…
Variable selection, also known as feature selection in machine learning, plays an important role in modeling high dimensional data and is key to data-driven scientific discoveries. We consider here the problem of detecting influential…
The Council of the European Union (EU) is one of the main decision-making bodies of the EU. A number of decisions require a qualified majority, the support of 55% of the member states (currently 15) that represent at least 65% of the total…
The voter model is a classical interacting particle system, modelling how global consensus is formed by local imitation. We analyse the time to consensus for a particular family of voter models when the underlying structure is a scale-free…
The Shapley value provides a principled framework for fairly distributing rewards among participants according to their individual contributions. While prior work has applied this concept to data valuation in machine learning, existing…
We consider a model where a subset of candidates must be selected based on voter preferences, subject to general constraints that specify which subsets are feasible. This model generalizes committee elections with diversity constraints,…
Consider informative selection of a sample from a finite population. Responses are realized as independent and identically distributed (i.i.d.) random variables with a probability density function (p.d.f.) f, referred to as the…
We define the pivotal set of a Boolean function and we prove a fundamental inequality on its expected size, when the inputs are independent random coins of parameter~$p$. We give two complete proofs of this inequality. Along the way, we…
We generalize the original majority-vote model by incorporating an inertia into the microscopic dynamics of the spin flipping, where the spin-flip probability of any individual depends not only on the states of its neighbors, but also on…