Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Quantitative Economics


Economics and Planning Unit (EPU-Delhi)


Sen, Arunava (EPU-Delhi; ISI)

Abstract (Summary of the Work)

This thesis comprises three chapters on issues in political economy and voting. The first chapter considers a multilevel multidimensional aggregation problem in voting. The second chapter considers a model of party formation where citizens propose links to other candidates. The final chapter considers a model of electoral competition between regional and national parties.We provide a brief description of each chapter below. 1.1 Multilevel Multidimensional Consistent AggregatorsIn this chapter we study gerrymander-proof or consistent aggregation rules in different contexts. There are several papers that have studied the structure of consistent voting rules satisfying various versions of consistency. Virtually all these papers have considered models where voters express opinions about a single alternative which have to be aggregated into a social opinion about that alternative. Our goal in this paper is to investigate the consistency of voting rules in models where voter opions over several alternatives have to be aggregated.We consider a model of aggregation where voter opinions have to be aggregated. Each voter submits an evaluation for each alternative (or component) indicating the intensity with which she likes the alternative. The set of permissible evaluations for any alternative is the closed unit interval. An aggregator considers an arbitrary collection of voter evaluations and transforms them into an aggregate opinion.Voters can be divided into mutually exclusive subgroups. This could be based, for example, on geographical regions/districts or political constituencies. The aggregator generates an aggregate for each subgroup. It can also be used to aggregate subgroup opinions into an opinion for the whole population. Consistency requires the same opinion for the population to emerge (for every possible configuration of voter opinions) irrespective of the way the population is spilt into subgroups. This chapter examines the implications of consistency on aggregators.We characterize component-wise α median rules. These rules are separable, i.e. the outcome for an alternative depends only on voter opinions for that alternative. Moreover, the outcome for each alternative is the median of the minimum utility (across voters), the maximum utility (across voters) and a fixed but arbitrary number αj for each alternative j. Consistent voting rules have also been analyzed in Chambers (2008), Chambers (2009) and Nermuth (1994). Perote-Pe˜na (2005), Bervoets and Merlin (2012) and Plott (1973) also analyze models that are similar in spirit to ours with related notions of consistency. Both the Nermuth and Chambers papers consider a single alternative voting model.Our result is a generalization of the result of Fung and Fu (1975) who prove an α-median characterization result for the one alternative case. There are significant difficulties involved in the extension to the multidimensional case due to its additional richness. However, these are resolved using the same set of axioms as in Fung and Fu (1975) defined suitably for the multidimensional model.


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Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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