The SP algorithm requires the voters to predict other voters' report in the form of a full probability distribution over all rankings of alternatives.

This paper proposes to establish the distance between partial preference orderings based on two very different approaches. The first approach corresponds to the brute force method based on combinatorics. It generates all possible complete preference orderings compatible with the partial preference orderings and calculates the Frobenius distance between all fully compatible preference orderings. Unfortunately, this first method is not very efficient in solving high-dimensional problems because of its big combinatorial complexity. That is why we propose to circumvent this problem by using a second approach based on belief functions, which can adequately model the missing information of partial preference orderings. This second approach to the calculation of distance does not suffer from combinatorial complexity limitation. We show through simple examples how these two theoretical methods work.

We consider the problem of recovering the ground truth ordering (ranking, top-$k$, or others) over a large number of alternatives. The wisdom of crowd is a heuristic approach based on Condorcet's Jury theorem to address this problem through collective opinions. This approach fails to recover the ground truth when the majority of the crowd is misinformed. The surprisingly popular (SP) algorithm cite{prelec2017solution} is an alternative approach that is able to recover the ground truth even when experts are in minority. The SP algorithm requires the voters to predict other voters' report in the form of a full probability distribution over all rankings of alternatives. However, when the number of alternatives, $m$, is large, eliciting the prediction report or even the vote over $m$ alternatives might be too costly. In this paper, we design a scalable alternative of the SP algorithm which only requires eliciting partial preferences from the voters, and propose new variants of the SP algorithm. In particular, we propose two versions -- Aggregated-SP and Partial-SP -- that ask voters to report vote and prediction on a subset of size $k$ ($\ll m$) in terms of top alternative, partial rank, or an approval set. Through a large-scale crowdsourcing experiment on MTurk, we show that both of our approaches outperform conventional preference aggregation algorithms for the recovery of ground truth rankings, when measured in terms of Kendall-Tau distance and Spearman's $\rho$. We further analyze the collected data and demonstrate that voters' behavior in the experiment, including the minority of the experts, and the SP phenomenon, can be correctly simulated by a concentric mixtures of Mallows model. Finally, we provide theoretical bounds on the sample complexity of SP algorithms with partial rankings to demonstrate the theoretical guarantees of the proposed methods.

A fundamental problem in multi-agent systems is resource allocation. Specifically, the problem of assigning a number of indivisible objects to agents with different preferences has been widely studied not only in multi-agent systems, but also in economics [21] and theoretical computer science [12]. The focus of our work is the special case of allocating n objects to n agents (so each agent is matched to a single object), which models many real-world applications. For example, imagine allocating office spaces to faculty members in a new building. Instead of asking each faculty member to report a full preference ranking over the available offices, the department head may ask faculty members to reveal their top choices, and then if need be, he may ask individual faculty members to reveal their next best choices, and so on. The goal of the department head is to learn a matching that satisfies some form of "economic efficiency" while asking as few queries as possible.

We propose multi-type probabilistic serial (MPS) and multi-type random priority (MRP) as extensions of the well known PS and RP mechanisms to the multi-type resource allocation problem (MTRA) with partial preferences. In our setting, there are multiple types of divisible items, and a group of agents who have partial order preferences over bundles consisting of one item of each type. We show that for the unrestricted domain of partial order preferences, no mechanism satisfies both sd-efficiency and sd-envy-freeness. Notwithstanding this impossibility result, our main message is positive: When agents' preferences are represented by acyclic CP-nets, MPS satisfies sd-efficiency, sd-envy-freeness, ordinal fairness, and upper invariance, while MRP satisfies ex-post-efficiency, sd-strategy-proofness, and upper invariance, recovering the properties of PS and RP.

We develop a novel framework that aims to create bridges between the computational social choice and the database management communities. This framework enriches the tasks currently supported in computational social choice with relational database context, thus making it possible to formulate sophisticated queries about voting rules, candidates, voters, issues, and positions. At the conceptual level, we give rigorous semantics to queries in this framework by introducing the notions of necessary answers and possible answers to queries. At the technical level, we embark on an investigation of the computational complexity of the necessary answers. We establish a number of results about the complexity of the necessary answers of conjunctive queries involving positional scoring rules that contrast sharply with earlier results about the complexity of the necessary winners.

Lu and Boutilier proposed a novel approach based on "minimax regret" to use classical score based voting rules in the setting where preferences can be any partial (instead of complete) orders over the set of alternatives. We show here that such an approach is vulnerable to a new kind of manipulation which was not present in the classical (where preferences are complete orders) world of voting. We call this attack "manipulative elicitation." More specifically, it may be possible to (partially) elicit the preferences of the agents in a way that makes some distinguished alternative win the election who may not be a winner if we elicit every preference completely. More alarmingly, we show that the related computational task is polynomial time solvable for a large class of voting rules which includes all scoring rules, maximin, Copeland α for every α ∈ [0,1], simplified Bucklin voting rules, etc. We then show that introducing a parameter per pair of alternatives which specifies the minimum number of partial preferences where this pair of alternatives must be comparable makes the related computational task of manipulative elicitation NP-complete for all common voting rules including a class of scoring rules which includes the plurality,  k -approval, k -veto, veto, and Borda voting rules, maximin, Copeland α for every α ∈ [0,1], and simplified Bucklin voting rules. Hence, in this work, we discover a fundamental vulnerability in using minimax regret based approach in partial preferential setting and propose a novel way to tackle it.

Within the field of Artificial Intelligence (AI) research, Vote (STV) select winners from sets of ballot. For example, the subfield of Computational Social Choice considers under plurality candidate X has won this election by virtue the application of AI techniques to problems in Social of having being at the top of the largest number of ballots. Under STV Y would win instead. Starting in the early 1990's, computer scientists began to In this work, we model voters as having partial orderings take an interest in social choice. Initial work was concerned over the candidates for their preferences, instead of linear with circumventing the impossibility results implied orderings.

While stable matching problems are widely studied, little work has investigated schemes for effectively eliciting agent preferences using either preference (e.g., comparison) queries for interviews (to form such comparisons); and no work has addressed how to combine both. We develop a new model for representing and assessing agent preferences that accommodates both forms of information and (heuristically) minimizes the number of queries and interviews required to determine a stable matching. Our Refine-then-Interview (RtI) scheme uses coarse preference queries to refine knowledge of agent preferences and relies on interviews only to assess comparisons of relatively “close” options. Empirical results show that RtI compares favorably to a recent pure interview minimization algorithm, and that the number of interviews it requires is generally independent of the size of the market.