Related papers: Random Popular Matchings with Incomplete Preferenc…
We consider a variant of socially stable marriage problem where preference lists may be incomplete, may contain ties and may have bounded length. In real world application like NRMP and Scottish medical matching scheme such restrictions…
Two-sided popular matchings in bipartite graphs are a well-known generalization of stable matchings in the marriage setting, and they are especially relevant when preference lists are incomplete. In this case, the cardinality of a stable…
We investigate majority rule dynamics in a population with two classes of people, each with two opinion states $\pm 1$, and with tunable interactions between people in different classes. In an update, a randomly selected group adopts the…
We propose the Pseudo-Mallows distribution over the set of all permutations of $n$ items, to approximate the posterior distribution with a Mallows likelihood. The Mallows model has been proven to be useful for recommender systems where it…
We study distributed plurality consensus among $n$ nodes, each of which initially holds one of $k$ opinions. The goal is to eventually agree on the initially dominant opinion. We consider an asynchronous communication model in which each…
A $k$-uniform, $d$-regular instance of Exact Cover is a family of $m$ sets $F_{n,d,k} = \{ S_j \subseteq \{1,...,n\} \}$, where each subset has size $k$ and each $1 \le i \le n$ is contained in $d$ of the $S_j$. It is satisfiable if there…
We consider the Moran process, as generalized by Lieberman, Hauert and Nowak (Nature, 433:312--316, 2005). A population resides on the vertices of a finite, connected, undirected graph and, at each time step, an individual is chosen at…
In this paper, we focus on ordered $k$-flaw preference sets. Let $\mathcal{OP}_{n,\geq k}$ denote the set of ordered preference sets of length $n$ with at least $k$ flaws and $\mathcal{S}_{n,k}=\{(x_1,...,x_{n-k})\mid x_1+x_2+...…
A preferential domain is a collection of sets of preferences which are linear orders over a set of alternatives. These domains have been studied extensively in social choice theory due to both its practical importance and theoretical…
This paper examines the problem of ranking a collection of objects using pairwise comparisons (rankings of two objects). In general, the ranking of $n$ objects can be identified by standard sorting methods using $n log_2 n$ pairwise…
The stable matching problem has been the subject of intense theoretical and empirical study since the seminal 1962 paper by Gale and Shapley. The number of stable matchings for different systems of preferences has been studied in many…
Recommender Systems (RS) often suffer from popularity bias, where a small set of popular items dominate the recommendation results due to their high interaction rates, leaving many less popular items overlooked. This phenomenon…
Ranking and comparing items is crucial for collecting information about preferences in many areas, from marketing to politics. The Mallows rank model is among the most successful approaches to analyse rank data, but its computational…
Matching plays a vital role in the rational allocation of resources in many areas, ranging from market operation to people's daily lives. In economics, the term matching theory is coined for pairing two agents in a specific market to reach…
This paper develops a framework to study the statistical power of revealed-preference tests. With randomly sampled budgets and mild smoothness of demand, statistical learning implies that any model consistent with the data must approximate…
Sequential recommendation refers to recommending the next item of interest for a specific user based on his/her historical behavior sequence up to a certain time. While previous research has extensively examined Markov chain-based…
Many projects (both practical and academic) have designed algorithms to match users to content they will enjoy under the assumption that user's preferences and opinions do not change with the content they see. Evidence suggests that…
A preference profile with m alternatives and n voters is 2-dimensional Euclidean if both the alternatives and the voters can be placed into a 2-dimensional space such that for each pair of alternatives, every voter prefers the one which has…
We study the implementability of stable matchings in a two-sided market model with one-sided incomplete information. Firms' types are publicly known, whereas workers' types are private information. A mechanism generates a matching and…
Popular matchings provide a model of matching under preferences in which a solution corresponds to a Condorcet winner in voting systems. In a bipartite graph in which the vertices have preferences over their neighbours, a matching is…