The price of a vote: diseconomy in proportional elections

TL;DR

This paper analyzes how campaign spending impacts votes, revealing a diseconomy of scale where top candidates spend more per vote, and models electoral dynamics to predict turnout rates.

Contribution

It uncovers the diseconomy of scale in electoral campaigns and provides a model linking campaign spending patterns to vote distribution and turnout prediction.

Findings

Top candidates spend more per vote than less successful ones.

Electoral diseconomy arises from inefficient campaign expenditure.

Predicted turnout rate of approximately 63% matches real data.

Abstract

The increasing cost of electoral campaigns raises the need for effective campaign planning and a precise understanding of the return of such investment. Interestingly, despite the strong impact of elections on our daily lives, how this investment is translated into votes is still unknown. By performing data analysis and modeling, we show that top candidates spend more money \emph{per vote} than the less successful and poorer candidates, a sublinearity that discloses a diseconomy of scale. We demonstrate that such electoral diseconomy arises from the competition between candidates due to inefficient campaign expenditure. Our approach succeeds in two important tests. First, it reveals that the statistical pattern in the vote distribution of candidates can be explained in terms of the independently conceived, but similarly skewed distribution of money campaign. Second, using a heuristic argument, we are able to predict a turnout percentage for a given election of approximately 63\%. This result is in good agreement with the average turnout rate obtained from real data. Due to its generality, we expect that our approach can be applied to a wide range of problems concerning the adoption process in marketing campaigns.