Related papers: On the Construction of High Dimensional Simple Gam…
In this communication, we propose a tentative to set the fundamental problem of measuring process done by a large structure on a microsopic one. We consider the example of voting when an entire society tries to measure globally opinions of…
For $S \subseteq \{0,1\}^n$ a Boolean function $f \colon S \to \{-1,1\}$ is a polynomial threshold function (PTF) of degree $d$ and weight $W$ if there is a polynomial $p$ with integer coefficients of degree $d$ and with sum of absolute…
In multiagent settings where the agents have different preferences, preference aggregation is a central issue. Voting is a general method for preference aggregation, but seminal results have shown that all general voting protocols are…
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.
Understanding the characteristics of neural networks is important but difficult due to their complex structures and behaviors. Some previous work proposes to transform neural networks into equivalent Boolean expressions and apply…
We view voting rules as classifiers that assign a winner (a class) to a profile of voters' preferences (an instance). We propose to apply techniques from formal explainability, most notably abductive and contrastive explanations, to…
We study the voting game where agents' preferences are endogenously decided by the information they receive, and they can collaborate in a group. We show that strategic voting behaviors have a positive impact on leading to the ``correct''…
Power indices are essential in assessing the contribution and influence of individual agents in multi-agent systems, providing crucial insights into collaborative dynamics and decision-making processes. While invaluable, traditional…
Participatory budgeting refers to the practice of allocating public resources by collecting and aggregating individual preferences. Most existing studies in this field often assume an additive utility function, where each individual holds a…
The traditional axiomatic approach to voting is motivated by the problem of reconciling differences in subjective preferences. In contrast, a dominant line of work in the theory of voting over the past 15 years has considered a different…
Democracies are built upon secure and reliable voting systems. Electronic voting systems seek to replace ballot papers and boxes with computer hardware and software. Proposed electronic election schemes have been subjected to scrutiny, with…
Let $V$ be a set of $n$ points in $\mathbb{R}^d$, called voters. A point $p\in \mathbb{R}^d$ is a plurality point for $V$ when the following holds: for every $q\in\mathbb{R}^d$ the number of voters closer to $p$ than to $q$ is at least the…
Voting is a game with a no-go theorem. New proofs of Arrow's impossibility theorem are given based on quantum information theory. We show that the Arrowian dictator is equivalent to the perfect cloning circuit. We present…
We introduce quantum XOR games, a model of two-player one-round games that extends the model of XOR games by allowing the referee's questions to the players to be quantum states. We give examples showing that quantum XOR games exhibit a…
We study the computational power of polynomial threshold functions, that is, threshold functions of real polynomials over the boolean cube. We provide two new results bounding the computational power of this model. Our first result shows…
Aggregating agent preferences into a collective decision is an important step in many problems (e.g., hiring, elections, peer review) and across areas of computer science (e.g., reinforcement learning, recommender systems). As Social Choice…
Consider a distributed graph where each vertex holds one of two distinct opinions. In this paper, we are interested in synchronous voting processes where each vertex updates its opinion according to a predefined common local updating rule.…
An important aspect of AI design and ethics is to create systems that reflect aggregate preferences of the society. To this end, the techniques of social choice theory are often utilized. We propose a new social choice function motivated by…
Election rules are formal processes that aggregate voters preferences, typically to select a single candidate, called the winner. Most of the election rules studied in the literature require the voters to rank the candidates from the most…
Consider the decision-making setting where agents elect a panel by expressing both positive and negative preferences. Prominently, in constitutional AI, citizens democratically select a slate of ethical preferences on which a foundation…