OR Forum: Blotto Politics

Introduction

In the July-August (2013) issue of Operations Research Alan Washburn writes about the optimal allocation of money to states in a presidential election campaign in the United States.(Available in online in Articles in Advance http://or.journal.informs.org/content/early/2013/03/19/opre.1120.1142.full.pdf+html

He models the competition between two parties for control of the United States Electoral College.  According to the Federal Election Committee (http://www.fec.gov/press/press2013/20130419_2012-24m-Summary.shtml) in the 2012 election cycle presidential candidates raised and spent approximately $1.4 bln this does not count the similar spending by the major political parties themselves as well as Political Action Committees. As is well known spending is generally increasing rapidly from election to election although the degree to which primaries are contested can cause variation in this trend.  There is considerable public concern about the amount of money spent on elections and its impact on the democratic process. There are laws that regulate election spending and there may be a need for new laws. A better understanding of how money can be used optimally in an election campaign will inform such a discussion.  Washburn’s article “Blotto Politics” is a small step in developing this understanding by modeling the competitive game the two major US political parties are engaged in when making spending decisions and showing the impact that funds imbalances can have.  Elections are an area with rich potential for applications of Operations Research and over the years have attracted interest from a wide range of perspectives.  This article will hopefully spur some more research activity that can help inform the public discussion of campaign finances. 

Invited Comments

While the study of elections by the Operations Research community is relatively limited it is of course a major topic of interest among political scientists.  Therefore the editors have invited comments from several political scientists on this paper.

David Primo is the Ani and Mark Gabrellian Associate Professor of Political Science at the University of Rochester with a joint appointment in the school of business. His areas of expertise and interest are campaign finance, airline safety, airline security, government spending and budgets, judicial appointments, and legislative rules.  He has testified before Congress on constitutional budget rules, and his campaign finance research was cited by the U.S. Supreme Court in a case regarding the public funding of elections. He has a PhD in Political Science from Stanford University.

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David B. Magleby is a Distinguished Professor of political science at Brigham Young University (BYU) and formerly the dean of the College of Family, Home, and Social Sciences at that institution. He is a Senior Research Fellow at the Center for the Study of Elections and Democracy at BYU and is one of its founders. He is an expert on direct democracy and campaign finance. He is the lead editor of a series on presidential election finance, including Financing the 2008 Election. He has also written several works on issues related to soft money in campaigns. In 1990, he served on a bipartisan Senate task force on campaign finance reform and his book on the subject, The Money Chase, was published by the Brookings Institution. Magleby received his Ph.D. in Political Science from the University of California, Berkeley.

Jay Goodliffe is an Associate Professor of Political Science and Associate Chair of the Political Science department at Brigham Young University. He is a Research Fellow at the Center for the Study of Elections and Democracy at BYU. His areas of expertise and interest include congressional campaigns and elections, legislative discipline, interest groups, international human rights treaties, and political methodology. His methodologies of choice are game-theory and econometrics. Dr. Goodliffe holds a Phd in Political Science from the University of Rochester.

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Discussion

In Washburn’s model two sides Blue and Red allocate resources to the 50 states to try to capture the electoral votes for that state.  In this stripped down representation of presidential elections if Blue invests xi resources in state i and Red invests yi and there is an inherent bias toward Blue of zi then if the xi+zi-yi is positive then Blue captures all the electoral votes. Using this core model he explores the strong first mover advantage in this game and how information availability affects the outcomes. 

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As in many competitive games, there is a last-mover advantage: If the first party has allocated all of its resources, and the second party knows where those resources are, then the second party can move its resources to beat the first party.  This disadvantage is so great in this model that the first party must have twice the resources of the second party to be competitive.  However, there are factors in allocating campaign spending that run counter to this advantage. Washburn, like much of the literature, assumes all spending is of equal value.  However, it is not just how much a candidate or ally spends, it is how and when the money is spent.  

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Goodliffe and Magleby

Clearly this model is a simplification of elections abstracting away many important details.  For example the assumed linear relation between spending and votes has not been established and the effect of spending on votes across states is probably not independent.  An example of this non-linearity is pointed out by Goodliffe and Magleby:

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Much of the money spent on campaigns is used for television advertising.  The closer one gets to the election (at least in close races where both parties allocate resources, which are the focus of this model as well), the more expensive that advertising is to purchase. 

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Goodliffe and Magleby

That said, within Washburn’s framework, there are features of real elections that come through.

For example, in his model of continuous public spending he shows how focusing resources on a carefully selected subset of states rather than trying to compete everywhere is an advantageous strategy.  When some states are leaning to one side or another determining the subset of states to focus can be complicated but it is still valuable to do.  We do see this occurring to some degree in practice were a small number of battleground states get disproportionate attention because they are up for grabs.  At the same time the behavior in practice is not as stark as the model projects because reality is more complex. Identifying possible causes for the gap between behavior and the model can also be illuminating.  Blue campaigning in a heavily blue state may be motivated by other goals than the direct influencing of voters.  It can influence fundraising and it can affect other concurrent elections on the local level. As Primo states:

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The models Washburn lays out are, by necessity, stylized.  For instance, the candidate who spends the most money wins the election.  The actual relationship between money and votes is far more complicated. 

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Primo
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Moreover, early money raised and early expenditures are often interpreted as a marker of candidate viability and seriousness (the "money primary") and have been seen as helpful in raising other money by investing in campaign infrastructure

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Goodliffe and Magleby

The title of the article comes from the case of secret spending that is analyzed and strongly resembles a Colonel Blotto game.  The applicability of this case is challenged by Goodliffe and Magleby:

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In most elections, it is very difficult to spend money secretly, at least in efforts to interact with voters, which is the central purpose of campaigns.  Candidates and their allies purchase the services of advertising trackers (such as the Campaign Media Analysis Group) so that they know when new ads are broadcast, and how often those ads are shown (and how much is spent). 

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Goodliffe and Magleby

Washburn does not dispute this point in a response he says:

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I think all of us would agree that my paper is sort of misnamed. The most realistic of the three informational models is Continuous Public Spending, not the Secret Spending model that leads to a Blotto game. But the Blotto game is still interesting, and I just couldn’t resist the title.

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Washburn

At the same time Goodliffe and Magleby point out that:

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But as we move to a more deregulated campaign finance world where some groups do not have to disclose their resources until after the election (so-called IRS Section 501 (c) organizations), players in electoral games may be able to at least partially hide their spending.

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Goodliffe and Magleby

 

What is most intriguing about this paper is more the questions that it raises than the ones it answers. All the commentators raised potential alternative applications or extensions for the work.

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A large “vote buying” literature studies how interest groups build support for or against a piece of legislation.  These models often assume complete information and sequential offers to legislators.  Washburn’s approach for studying elections is easily adaptable to the study of legislative bargaining and could be used to consider more complex environments.

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Primo
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Finally, the article primarily considers presidential general elections, but the puzzle examined here is equally interesting in presidential nominations.  In that setting, the model is complicated by the fact that not all states vote at the same time, adding a temporal element to spending.

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Goodliffe and Magleby

Washburn also sees potential for his model to say something about district gerrymandering:

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Worst Case Blue should also be of interest. It comes closest to gerrymandering, a phenomenon that plagues our elections. To give politicians in power the ability to define electoral districts as they choose is to give away a factor of two in voter registrations!

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Washburn

Primo observes that political science has something the gain from the application of Operations Research techniques.  The tendency in Political Science is to use game theoretic models that are analytically solvable to study the strategic interactions found in election campaigns.  “The disadvantage is that it is often not possible to solve for closed-form solutions without making restrictive assumptions.” Washburn has taken a more computational and algorithmic approach that allows him to go somewhat further in the analysis than most political scientists typically would. 

Comments