In this work, we present a novel human-in-the-loop framework to help the human user understand the decision making process that involves choosing preferred options. We focus on qualitative preference models over alternatives from combinatorial domains. This framework is interactive: the user provides her behavioral data to the framework, and the framework explains the learned model to the user. It is iterative: the framework collects feedback on the learned model from the user and tries to improve it accordingly till the user terminates the iteration. In order to communicate the learned preference model to the user, we develop visualization of intuitive and explainable graphic models, such as lexicographic preference trees and forests, and conditional preference networks. To this end, we discuss key aspects of our framework for lexicographic preference models.

In this work, we present a novel human-in-the-loop framework to help the agent understand the decision making process that involves choosing preferred options. We focus on qualitative preference models over alternatives from combinatorial domains. This framework is interactive: e.g., the agent provides her behavioral data to the framework, and the framework ex- plains the learned model to the agent. It is iterative: the framework collects feedback on the learned model from the agent and tries to improve it accordingly until the agent terminates the iteration. In order to communicate the learned preference model to the agent, we focus on visualizing some of the intuitive and explain- able graphic models, such as lexicographic preference trees and forests, and conditional preference networks. To this end, we discuss key aspects of our framework, and demonstrate our prototype ready for lexicographic preference models.

We consider a scenario where a user must make a set of correlated decisions and we propose a computational modeling of the deliberation process. We assume the user compactly expresses her preferences via soft constraints. We consider a sequential procedure that uses Decision Field Theory to model the decision making on each variable. We test this procedure on randomly generated tree-shaped Fuzzy Constraint Satisfaction Problems. Our preliminary results showed that the time increases almost in the number of nodes. This is promising in terms of modeling decision over exponentially large domains. In the future, we plan to compare our results non-sequential approach and with behavioral data to asses our approach both in terms of modeling human decision making over complex domains, and adopting DFT as a means of incorporating a form of uncertainty into the soft constraint formalism.

In both individual and collective decision making, the space of alternatives from which the agent (or the group of agents) has to choose often has a combinatorial (or multiattribute) structure. We give an introduction to preference handling in combinatorial do - mains in the context of collective decision making and show that the considerable body of work on preference representation and elicitation that AI researchers have been working on for several years is particularly relevant. After giving an overview of languages for compact representation of preferences, we discuss problems in voting in combinatorial domains and then focus on multiagent resource allocation and fair division. These issues belong to a larger field, which is known as computational social choice and which brings together ideas from AI and social choice theory, to investigate mechanisms for collective decision making from a computational point of view. We conclude by briefly describing some of the other research topics studied in computational social choice.

Qualitative preferences over outcomes in a combinatorial domain (where many variables jointly describe the outcome) The CP-net visualizer presented is useful for researchers are useful in automated decision making and modeling human eliciting human preferences, building CP-nets for specific preferences in real world domains. Conditional Preference experiments, visualizing generated CP-nets, and for the general Networks (CP-nets), also known as Ceteris Paribus public learning more about preference modeling. It has Networks, are a compact graph-based mathematical formalism an interface consisting of three vertical panels. On the left is for representing such preferences (Boutilier et al. 2004).

We introduce partial lexicographic preference trees (PLPtrees) as a formalism for compact representations of preferences over combinatorial domains. Our main results concern the problem of passive learning of PLP-trees. Specifically, forseveral classes of PLP-trees, we study how to learn (i) a PLP-tree consistent with a dataset of examples, possibly subject to requirements on the size of the tree, and (ii) a PLP-tree correctly ordering as many of the examples as possible in case the dataset of examples is inconsistent. We establish complexity of these problems and, in all cases where the problem is in the class P, propose polynomial time algorithms.

Finally, explore possible methods for decision making in general, have received a lot uses of combinatorial aggregation in sequential voting, of attention in the AI community in recent years. The reasons and discuss theoretical generalisations to more complex logical for this focus are clear: SCT provides tools for the analysis of languages and practical applications. Particularly close to the interests of AI is the to study binary aggregation procedures, inspired by research problem of social choice in combinatorial domains (Chevaleyre in AI. As long as we do not know the intended application of et al., 2008), where the space of alternatives the individuals the model, there is no appropriate set of axioms to concentrate have to choose from has a combinatorial structure. Instead, we prove characterisation results concerning one Definition 1.

Many collective decision making problems have a combinatorial structure: the agents involved must decide on multiple issues and their preferences over one issue may depend on the choices adopted for some of the others. Voting is an attractive method for making collective decisions, but conducting a multi-issue election is challenging. On the one hand, requiring agents to vote by expressing their preferences over all combinations of issues is computationally infeasible; on the other, decomposing the problem into several elections on smaller sets of issues can lead to paradoxical outcomes. Any pragmatic method for running a multi-issue election will have to balance these two concerns. We identify and analyse the problem of generating an agenda for a given election, specifying which issues to vote on together in local elections and in which order to schedule those local elections.

We consider problems where several individuals each need to make a yes/no choice regarding a number of issues and these choices then need to be aggregated into a collective choice. Depending on the application at hand, different combinations of yes/no may be considered rational. We can describe such rationality assumptions in terms of a propositional formula. The question then arises whether or not a given aggregation procedure will lift the rationality assumptions from the individual to the collective level, i.e., whether the collective choice will be rational whenever all individual choices are. To address this question, for each of a number of simple fragments of the language of propositional logic, we provide an axiomatic characterisation of the class of aggregation procedures that will lift all rationality assumptions expressible in that fragment.

In both individual and collective decision making, the space of alternatives from which the agent (or the group of agents) has to choose often has a combinatorial (or multi-attribute) structure. We give an introduction to preference handling in combinatorial domains in the context of collective decision making, and show that the considerable body of work on preference representation and elicitation that AI researchers have been working on for several years is particularly relevant. These issues belong to a larger field, known as computational social choice, that brings together ideas from AI and social choice theory, to investigate mechanisms for collective decision making from a computational point of view. We conclude by briefly describing some of the other research topics studied in computational social choice.