DS-2021-06: Collective Decisions with Incomplete Individual Opinions

DS-2021-06: Terzopoulou, Zoi (2021) Collective Decisions with Incomplete Individual Opinions. Doctoral thesis, University of Amsterdam.

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In the modern world, people make decisions together every day: they participate in elections, boards of companies, juries of courts, and social activities amongst friends. Accurately capturing such fine-grained human behaviour is essential, not only for directly improving the choices made by people, but also for developing AI (multiagent) systems that work efficiently and safely with collective decisions. Social choice theory, a sub-area of (micro)economics, is concerned with the analysis of mechanisms that groups use to make decisions; its far-reaching themes transcend neighbouring disciplines, like political science, law, and artificial intelligence. The much younger field of computational social choice investigates problems traditionally studied in social choice theory with powerful tools from computer science.

Much research to date in computational social choice has been resting on a rather stringent hypothesis - namely, that people are able to form concrete opinions about all issues at stake in a given decision problem (such opinions are called complete). But in recent years, people make decisions increasingly in online settings, where the abundance of available options often makes them prohibitively difficult to critically evaluate. This thesis concerns collective decisions where the agents may hold intrinsically incomplete opinions (that is, they may lack an opinion about some issues in question). For example, on a travel website where users rank hotels according to their experience and preferences, most people will not have an opinion about all offered listings. We need aggregation mechanisms that allow for incomplete inputs and produce reasonable collective outcomes. This thesis proposes such mechanisms in three contexts, where we care about (i) reaching a consensus between the diverse opinions of the group members for issues that are subjective in nature (like in the example about the travel website); (ii) avoiding skewed outcomes caused by the strategic behaviour of selfish agents (like in election problems); (iii) discovering the ground truth with respect to a number of objective issues (like in crowdsourcing experiments).

First, how can we achieve a sufficiently good compromise for a group of agents with diverting opinions? One way, typically employed by the social choice community, suggests the use of axioms, i.e., properties of aggregation mechanisms that are normatively appealing. Such axioms are well-studied in the standard frameworks where completeness is assumed, but present numerous open questions when incompleteness comes into the picture. By restricting attention to different axioms, we obtain distinct mechanisms for collective choice - including mechanisms that weigh individual opinions relying on their size, mechanisms that assign scores to alternatives with respect to their position in the individual preferences, as well as mechanisms that are associated with given acceptance thresholds. The various axioms that we consider lead to different notions of compromise. Depending on those one finds compelling, one can argue for the use of the corresponding mechanisms that satisfy them.

Second, under what mechanisms for collective decision making are the members of a group tempted to misrepresent their individual opinions in view of obtaining a better outcome for themselves? Agents that have the freedom to report incomplete opinions may lie in three ways: by hiding their sincere opinion; by inventing a new insincere opinion; or by reversing their sincere opinion. Such acts pose threats to our everyday life, bringing out the risk of obtaining non-representative, undemocratic collective decisions. In many cases, we show that it is possible to find mechanisms that are immune to this kind of strategic behaviour. However, we also prove impossibility results stating that strategic manipulation is, sometimes, inescapable. Furthermore, when agents are allowed to change their opinions in rounds, we examine whether - and how fast - relevant procedures of iterative decision making are guaranteed to terminate.

Third, suppose you need to determine the correct answer to a question (e.g., whether a colleague should get promoted) that depends on two independent premises (e.g., whether the colleague is excellent at her work and whether she is a good team player). Will you ask the members of a group to each evaluate just one of those premises (which can be done with relatively high accuracy) or both (in which case their need to multitask will lower their accuracy)? In scenarios like this, we present an optimal mechanism for making collective decisions, we determine how many agents one should ask for how many of their opinions, and we provide an extensive analysis of strategic incentives that may arise from the point of view of the group members.

In a nutshell, spanning across ample contexts motivated by real-world applications, this thesis discusses several promising ways for making collective decisions when individual opinions are expected to be incomplete.

Item Type: Thesis (Doctoral)
Report Nr: DS-2021-06
Series Name: ILLC Dissertation (DS) Series
Year: 2021
Subjects: Computation
Depositing User: Dr Marco Vervoort
Date Deposited: 14 Jun 2022 15:17
Last Modified: 14 Jun 2022 15:17
URI: https://eprints.illc.uva.nl/id/eprint/2192

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