Gaming the Vote is a book so ambitious it has a title, subtitle, and sub-subtitle. In full, it appears on my cover like this:
Why Elections Aren’t Fair
(and What We Can Do About It)
Social choice theory—the field of mathematics that asks how to best fit a single “social choice” or “social preference” to a collection of conflicting individual preferences, usually in the form of an election—is a hobby horse of mine. After reading a lot of online articles and a handful of math papers about it, I was hoping to find a more cohesive introduction without having to wade through hundreds of pages of mathematical theorems. With Gaming the Vote, I was not entirely disappointed.
Poundstone writes for a predominantly American audience, which means that his top priority is convincing you that the American-style plurality election system is an idiotic way to determine the will of the people. A very strong case along these lines could probably be made in less than ten pages, but Poundstone explores the subject through historical exposition, which brings the length up by over an order of magnitude. Some of the history is interesting, but it is largely repetitive and superficial. A great deal of time is devoted to the problem of vote splitting, which is likely the worst problem with plurality voting but by no means the only one. Further, vote splitting is easy enough to fix that it seems disproportionate to worry about it so much. What makes the study of voting systems interesting is that, as Donald Saari says, “you find flaws in anything.” It is not enough to fix a single problem and move on. Since every voting system has flaws, the task is to select the option whose flaws are least egregious. This involves some clearing up of facts in the form of mathematical theorems, but by far the most difficult problem is deciding in the first place which flaws are less egregious than the others. Social choice theory itself is therefore like a more abstract version of the elections it hopes to describe. These fascinating subtleties are obscured by the fact that only a single voting system is discussed for over a hundred pages.
The historical approach is also susceptible to indulgence in morality plays. We’re treated to the story of “the wizard and the lizard,” a modern American election culminating in the description, “In one sense only, the American system worked. Now that they are convicted felons, neither Edwin Edwards nor David Duke can ever run for U.S. public office again.” This seems slightly disingenuous to me. Although our voting system does sometimes elect the “wrong” candidate, any severely pathological elections like this one can only occur with a pathological electorate. I agree that George Bush should have lost to Al Gore in 2000 based on the distribution of voter preferences, but he still never would have won without substantial, near-majority support. Poundstone hyperbolically describes this situation as a “catastrophic failure” of the system. The equivocation between the morally correct and mathematically correct winner is also muddied by examples like the 1860 election, where Abraham Lincoln couldn’t have won without vote splitting. Poundstone counts this election as a catastrophic failure as well, despite the fact that Lincoln also had substantial support and turned out to be one of the most celebrated presidents in the history of the country.
Several chapters focus on the development of modern campaign tactics, reviewing historical examples I knew nothing about, but not contributing any big ideas that don’t seem mostly obvious to me. Poundstone makes the case that dirty campaign tactics exploit weaknesses in our voting system, with the implication that a better system would help to clean up campaigns. I agree that Republicans supporting Greens and Democrats supporting conservative Libertarians would cease to be profitable if vote splitting were eliminated, but this seems little more than a drop in the swill bucket of political tricks. Campaigns will likely be manipulative and dirty under any system, and I wasn’t especially moved by the prospect of fixing them.
The discussion of voting systems themselves then begins, still keeping a historical approach. This is where my interest picked up, if only because mathematicians are much more interesting people than politicians. A particularly entertaining section speculates that Charles Dodgson, better known by his pen name of Lewis Carroll, might have begun to develop voting theory as a way of manipulating university committees to shut down the pet projects of Henry Liddell, the father of the real-life Alice, who forbade Dodgson from seeing his daughter after a series of unsettling events.
A variety of systems are described, along with their weaknesses: the Borda count, which seems susceptible to unparalleled strategic abuse; Condorcet systems, which in their most basic form are not well-defined enough to always select a winner; instant-runoff voting, which can punish voters with a less desirable election outcome for showing up to vote instead of staying home; approval voting, which can end up with different results depending on how voters interpret the rules; and range voting, which Poundstone endorses almost without qualification. Range voting is the system that online reviews has popularized: give any candidate any rating within a well-defined range, based on how much you like her, and the winner is the one with the best average. Some compelling objections to range voting do exist; for example, the best strategic vote in the absence of information about other voters’ preferences turns out to not be an honest vote. However, to Poundstone (and to myself), these objections are not as fatal as objections to other systems. It is also emphasized that range voting evades Arrow’s famous “impossibility theorem,” which can be formally stated in mathematical terms but is sometimes summarized as “no perfect voting system exists.” As long as Arrow’s theorem is stated formally, this evasion is an important point; however, it seems that range voting remains an imperfect system for reasons outside of the scope of Arrow’s scheme.
These chapters are not an efficient way to learn about voting theory, but they do give a compelling look at the human element of the field. The mathematicians working on social choice theory move in a small world and blur the line between competitors and collaborators. Poundstone gives us a strong impression of the personalities and alliances involved, as well as what this means for the prospect of finding an “answer” to the voting system problem.
The most interesting part of the book to me was the end, where attempts at voting reform are described. One inherent difficulty is succinctly expressed:
“Academics probably are not the best sales people” Brams and Peter Fishburn wrote wistfully, as “they squabble among themselves. Because few if any ideas in the social sciences are certifiably ‘right’ under all circumstances, squabbles may well be grounded in serious intellectual differences. Sometimes, however, they are not.”
The other obstacle to reform is that politicians and campaign strategists—in other words, the people with power—have already mastered the manipulation of our voting system, and they are not eager to work within a different one. Anything that breaks the two-party dominance is likely to be resisted by politicians currently in office. Even fair-minded voters are reluctant to accept reform that’s too dramatic. Instant-runoff voting has made the largest strides toward replacing our plurality system in the United States despite being one of the most pathological ways to vote that anyone takes seriously.
This is where the book’s title (or rather, sub-subtitle) fails to deliver. Poundstone leaves it up to the public to mobilize in favor of a more sensible electoral system without explaining how they might overcome the formidable social dynamics at play. The book ends with a question: “Surely there are a few American communities willing to volunteer?” But Poundstone should know better than to ask this; after all, it was asking the wrong question that led to Arrow’s theorem and sent social choice theory into a dead end for fifty years. Yes, there surely are a few American communities willing to volunteer to fix our elections. How they can acquire the power they need to enact change, however, is a question with no clear answer.