Surprise in Elections

TL;DR

This paper models how local perceptions and social network biases influence election surprises, especially in close contests, and analyzes how different voting rules impact the likelihood of surprise outcomes.

Contribution

It introduces a mathematical model linking local bias estimates and network structure to election surprise, highlighting the limitations of a single voting rule across diverse population segments.

Findings

Surprising outcomes are linked to closely contested elections.

Different voting rules perform variably in reducing surprise.

Model predictions align with Brexit referendum data.

Abstract

Elections involving a very large voter population often lead to outcomes that surprise many. This is particularly important for the elections in which results affect the economy of a sizable population. A better prediction of the true outcome helps reduce the surprise and keeps the voters prepared. This paper starts from the basic observation that individuals in the underlying population build estimates of the distribution of preferences of the whole population based on their local neighborhoods. The outcome of the election leads to a surprise if these local estimates contradict the outcome of the election for some fixed voting rule. To get a quantitative understanding, we propose a simple mathematical model of the setting where the individuals in the population and their connections (through geographical proximity, social networks etc.) are described by a random graph with connection probabilities that are biased based on the preferences of the individuals. Each individual also has some estimate of the bias in their connections. We show that the election outcome leads to a surprise if the discrepancy between the estimated bias and the true bias in the local connections exceeds a certain threshold, and confirm the phenomenon that surprising outcomes are associated only with {\em closely contested elections}. We compare standard voting rules based on their performance on surprise and show that they have different behavior for different parts of the population. It also hints at an impossibility that a single voting rule will be less surprising for {\em all} parts of a population. Finally, we experiment with the UK-EU referendum (a.k.a.\ Brexit) dataset that attest some of our theoretical predictions.