Canales, Diego
(2021)
Essays on political economy.
PhD thesis, University of Nottingham.
Abstract
Typically, political phenomena have been the main focus of study for philosophers and political scientists. However, with the advent of mathematicians (e.g., Hotelling, Debreu, and Arrow) to the Economics discipline, there was an increased inclination to utilize advanced mathematical technique to solve complex problems around political science. This dissertation attempts to follow that tradition. In the next two chapters, we analyse political phenomena using economic tools.
In Chapter 2, we start by looking at the concept of a Condorcet winner; which is defined as the alternative that is preferred by a plurality in every pairwise competition. The notion of a k−winner generalises that of a Condorcet winner. The k−winner is the unique alternative that is top-ranked by the plurality in every competition composed exactly of k alternatives, including itself. We use a spatial voting setting to characterise this theoretical concept. More importantly, we show that if a k-winner exists for some k > 2 then the same alternative must be the k’-winner for every k < k’ <=n. Finally, we derive additional results such as sufficient and necessary conditions for the existence of a k-winner for some k >2.
There is a natural link between Chapters 2 and 3: primaries. The concept of k-winners found in Chapter 2 can be further extended to analyse the case of primary elections; more specifically American presidential primaries. In Chapter 3, we use a non-cooperative model where a continuum of citizens vote, according to their ranked preferences, from a sequence of candidates in a sequential series of primary elections. There are two significant exogenous variables: voting rules and delegation size. In every election, there is a fixed number of delegates given to (i) a single winner in the case of plurality rule and (ii)multiple candidates under a proportional representation rule. Moreover, these candidates take sequential turns to decide if it would be optimal to stay in the race giving there is a cost to run in every primary. More importantly, we use this theoretical framework to study two seemingly unrelated political phenomena: momentum and Duverger’s law. The concept of momentum captures the political wisdom which dictates that “doing well” in the early stages is crucial for any candidate. This wisdom translates into a substantial amount of attention drawn to the Iowa caucus. Iowa is the first electoral contest in the primary schedule. Although it does not award a large number of delegates, the majority of the candidates will focus their initial campaign efforts there. Ultimately, the empirical evidence does not seem to support the existence or the effectiveness of the so-called “momentum effect”. The second half of Chapter 3 aims to revise the so-called “Duverger’s law” into the context of the primary elections. This sociological “law” was the product of the 20th-century sociologist Maurice Duverger. He noticed a particular pattern across several countries: the voting system (i.e., voting rules) had a particular effect on the number of parties forming a government. More specifically the law asserts that plurality rules “tend to favour” two-party governments whereas proportional representation rules favour multiple-party governments. In the case of primary elections, the analogous concept will be the number of candidates at a primary contest. Thus, the modified Duverger’s law version for primary elections would assert that primary candidates tend to quit faster or earlier under plurality rule compared to proportional representation. Our theoretical results will characterise conditions under which this assertion can be challenged. More specifically: we find both sufficient and necessary conditions under which, in equilibrium, the number of candidates remaining in the first stages of a sequential primary election, would be strictly smaller under proportional representation compared to plurality rule.
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