Essays in Theoretical Political Economy

Mark Winter

Research output: ThesisDoctoral Thesis

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Chapter One

This chapter reports the results of an in-lab experiment to test two design features of two round elections. (1) uncertainty about round two participants and (2) the flexible threshold for first round victory. The chapter finds experimental evidence of the existence of Duverger's Law equilibrium (predominance of two candidates) and the sincere equilibrium in two round divided majority election games with uncertainty and flexible thresholds. The effect of flexible thresholds and uncertainty on the occurrence of these two equilibrium are tested. The chapter finds that the flexible threshold has a greater effect than uncertainty when it comes to Duverger's Law type effects. It is found that in general the effects of threshold and uncertainty are complementary but with a large interaction effect. The Duverger Law equilibrium exists and is more stable than alternative equilibria including the sincere equilibrium. Elections with a lower threshold and or uncertainty have higher levels of minority candidate victory. While coordination levels are in general high enough to mitigate these effects, the lower threshold and uncertainty reduce the room for error and magnify the effect of error. The secondary findings of this chapter are the existence of non-symmetric equilibrium in the experiment that voters do not take dominated strategies in the experiment under these new parameters of uncertainty and a lower threshold, therefore supporting the assumptions necessary for the other results. The second if these is not claimed as a contribution to the literature as others have made the same findings though not under these specific election rules. The non-symmetric equilibrium suggest further study as it questions the assumption of symmetric voting in equilibrium.

Chapter Two

This chapter presents a three candidate election model with the key feature of two 'large' candidates and one 'small' candidate. This design mimics many political systems for example the US and Uk. with two large parties and a number of small parties. under these conditions two voting rules, Plurality and Instant run-off, are analysed. The analysis starts with the sincere equilibrium. It is found to exist for all voter distributions (under the basic conditions of two 'large' candidates) in this model for the instant run-off rule. The plurality rule is found to only have a sincere equilibrium under a set of restrictions. As such the instant run-off is a better system for those that want incentivise sincere voting. It is also found that when sincere voting gives different outcomes for the two rules the instant run-off is preferred by a strict majority of voters. The second part of this chapter is the main contribution to the literature. The application of level-k thinking to the model described above with the assumption of bounded rationality. These finds also support the argument that the instant run-off is a preferable system. It always gives and outcome that is weakly preferred by a strict majority of voters and when the two voting rules give the same outcome the instant run-off reaches this with a weakly lower level of necessary thinking. The sincere equilibrium is found to be the only equilibrium at higher levels of thinking for instant run-off while plurality has 3 possible equilibrium based on the voter distribution: the sincere equilibrium, the Duverger’s Law equilibrium and the non-pivotal equilibrium. The chapter gives supporting evidence for 'wasted' votes that go to candidates that can not win the election coming from voters who are bounded by their rational and have not worked out that they should be strategic.

Chapter Three

The final chapter links the first two together somewhat but primarily aims to give supporting evidence for the assumptions made in the first two chapters. It presents a three candidate election with entry. Two candidates have a first move advantage and a third candidate enters after them. This simple candidate model is analysed for the 4 rules used in the first two chapters. The spatial equilibria that are found under the four rules fit to the assumptions about candidate policy position in the other two chapters with varying success. The plurality rule that is investigated in chapter two fits well and the entry model creates two 'large' candidates who get the first mover advantage. This suggest one rationale for the set up of chapter two is a first mover advantage that creates the 'large' candidates. This rationale is less clear for the instant run-off where the results of the entry game is for the entrant to copy one of the first movers and this creates two 'small' candidates. The two round elections with and without flexible threshold do not fit well into the equilibrium of the entry game. The interesting thing about the two round election with and without a flexible threshold though is that they fit very well with such a game where an entrant makes a small error in their strategy. So the entry game in disequilibrium could explain in part the divided majority set up. This raises questions in the divided majority especially with a flexible threshold; why does the minority candidate not get slightly more moderate to try to win enough votes to win as a minority?
Original languageEnglish
Awarding Institution
  • Royal Holloway, University of London
  • Bade, Sophie, Supervisor
  • Naef, Michael, Supervisor
  • Neary, Philip, Supervisor
Award date1 Mar 2019
Publication statusUnpublished - 15 Mar 2019


  • Economic voting
  • Experimental Economics
  • Political Theory

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