Related papers: A Partial Order on Preference Profiles
Earlier papers \cite{VB2022,VB2023a,VB2023b} introduced the notions of a core and an index of a relation (an index being a special case of a core). A limited form of the axiom of choice was postulated -- specifically that all partial…
Selecting a set of alternatives based on the preferences of agents is an important problem in committee selection and beyond. Among the various criteria put forth for the desirability of a committee, Pareto optimality is a minimal and…
We describe multi-objective influence diagrams, based on a set of p objectives, where utility values are vectors in Rp, and are typically only partially ordered. These can still be solved by a variable elimination algorithm, leading to a…
In this paper we consider the collaborative ranking setting: a pool of users each provides a small number of pairwise preferences between $d$ possible items; from these we need to predict preferences of the users for items they have not yet…
We study the trade-offs between strategyproofness and other desiderata, such as efficiency or fairness, that often arise in the design of random ordinal mechanisms. We use approximate strategyproofness to define manipulability, a measure to…
Distributions over rankings are used to model data in various settings such as preference analysis and political elections. The factorial size of the space of rankings, however, typically forces one to make structural assumptions, such as…
The notion of fractional minimal rank of a partial matrix is introduced, a quantity that lies between the triangular minimal rank and the minimal rank of a partial matrix. The fractional minimal rank of partial matrices whose bipartite…
In multi-objective decision planning and learning, much attention is paid to producing optimal solution sets that contain an optimal policy for every possible user preference profile. We argue that the step that follows, i.e, determining…
House Allocations concern with matchings involving one-sided preferences, where houses serve as a proxy encoding valuable indivisible resources (e.g. organs, course seats, subsidized public housing units) to be allocated among the agents.…
We consider the allocation of indivisible objects among agents with different valuations, which can be positive or negative. An egalitarian allocation is an allocation that maximizes the smallest value given to an agent; finding such an…
Many complex systems exhibit a natural hierarchy in which elements can be ranked according to a notion of "influence". While the complete and accurate knowledge of the interactions between constituents is ordinarily required for the…
Many systems, including the Internet, social networks, and the power grid, can be represented as graphs. When analyzing graphs, it is often useful to compute scores describing the relative importance or distance between nodes. One example…
We propose a multivariate extension of the Lorenz curve based on multivariate rearrangements of optimal transport theory. We define a vector Lorenz map as the integral of the vector quantile map associated with a multivariate resource…
Many algorithms for ranked data become computationally intractable as the number of objects grows due to the complex geometric structure induced by rankings. An additional challenge is posed by partial rankings, i.e. rankings in which the…
Post-hoc global/local feature attribution methods are progressively being employed to understand the decisions of complex machine learning models. Yet, because of limited amounts of data, it is possible to obtain a diversity of models with…
Ranking, and inferences based on ranking of a set of entities, are important problems in numerous contexts. This is especially true in small area statistics where there may be only a limited amount of directly observed data from each entity…
In social choice theory, (Kemeny) rank aggregation is a well-studied problem where the goal is to combine rankings from multiple voters into a single ranking on the same set of items. Since rankings can reveal preferences of voters (which a…
Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis (1973) earlier considered such a notion of relative likelihood in the…
When allocating indivisible objects via lottery, planners often use ordinal mechanisms, which elicit agents' rankings of objects rather than their full preferences over lotteries. In such an ordinal informational environment, planners…
We analyze the design of a mechanism to extract a ranking of individuals according to a unidimensional characteristic, such as ability or need. Individuals, connected on a social network, only have local information about the ranking. We…