Contributions to modeling with set-valued data: benefitting from undecided respondents

Kreiß, Dominik (2023): Contributions to modeling with set-valued data: benefitting from undecided respondents. Dissertation, LMU München: Fakultät für Mathematik, Informatik und Statistik

Abstract

This dissertation develops a methodological framework and approaches to benefit from undecided survey participants, particularly undecided voters in pre-election polls. As choices can be seen as processes that - in stages - exclude alternatives until arriving at one final element, we argue that in pre-election polls undecided participants can most suitably be represented by the set of their viable options. This consideration set sampling, in contrast to the conventional neglection of the undecided, could reduce nonresponse and collects new and valuable information. We embed the resulting set-valued data in the framework of random sets, which allows for two different interpretations, and develop modeling methods for either one. The first interpretation is called ontic and views the set of options as an entity of its own that most accurately represents the position at the time of the poll, thus as a precise representation of something naturally imprecise. With this, new ways of structural analysis emerge as individuals pondering between particular parties can now be examined. We show how the underlying categorical data structure can be preserved in this formalization process for specific models and how popular methods for categorical data analysis can be broadly transferred. As the set contains the eventual choice, under the second interpretation, the set is seen as a coarse version of an underlying truth, which is called the epistemic view. This imprecise information of something actually precise can then be used to improve predictions or election forecasting. We developed several approaches and a framework of a factorized likelihood to utilize the set-valued information for forecasting. Amongst others, we developed methods addressing the complex uncertainty induced by the undecided, weighting the justifiability of assumptions with the conciseness of the results. To evaluate and apply our approaches, we conducted a pre-election poll for the German federal election of 2021 in cooperation with the polling institute Civey, for the first time regarding undecided voters in a set-valued manner. This provides us with the unique opportunity to demonstrate the advantages of the new approaches based on a state-of-the-art survey.

• Dokumententyp: Dissertationen (Dissertation, LMU München)
• Keywords: Set-Valued Data, Modeling, Consideration Set, Undecided Voters
• Themengebiete: 000 Allgemeines, Informatik, Informationswissenschaft ; 000 Allgemeines, Informatik, Informationswissenschaft > 004 Informatik
• Fakultäten: Fakultät für Mathematik, Informatik und Statistik
• Sprache der Hochschulschrift: Englisch
• Datum der mündlichen Prüfung: 11. Oktober 2023
• 1. Bericht­erstatter:in: Augustin, Thomas