# June 29, 2008

## New book applies game theory to vote counting methods

In his new book, *Gaming the Vote*, author William Poundstone applies an area of mathematics called game theory to various alternatives to the current winner-takes-all method of counting the vote. This provides a useful perspective that is far different from the rhetorical chest-pounding about “increased democracy”, or “more choices for the voter” that usually accompanies discussions of IRV, STV or other variants of ranked choice voting.

In a review of *Gaming the Vote*, Berylium Sphere writes on Technocrat http://technocrat.net/d/2008/6/28/44675

…the book talks about the nature, the history, and especially the malfunctions of alternatives such as instant runoff voting, approval voting, Condorcet voting and Borda voting. It covers the (often incandescent) theoretical debates about whether the problems of each are significant in real life, in enough detail to be accurate but while remaining clear to a non-specialist. He explains the theorem that all ranking-based voting systems have paradoxes (the Arrow Impossibility Theorem). Most of the alternatives, except for approval voting and the system Poundstone saves for the end as the best choice, involve letting the voter rank all the candidates in order of preference.

**Instant Runoff Voting**

Poundstone finds that Instant Runoff Voting (IRV) often leads to flawed outcomes. The reviewer summarizes the Poundstone’s critique of IRV as follows:

Instant runoff voting takes the rankings and checks whether any candidate has a majority of first-place rankings. If not, you repeatedly eliminate candidates based on their getting the fewest first-place rankings, and reallocate their supporters’ votes to the supporter’s second choices until a winner emerges. This way, there’s no disincentive to putting your first choice first, and maybe enough people will realize that so that vaccination will actually win.

Poundstone points out analysis by voting theorist Donald Saari that IRV could have led to a “bad” outcome in the Lousiana election that pitted a crook against a Klansman. Other problems show up in theory. Popular moderates can be eliminated early if they’re crowded out of first place by ideologues. An apparent paradox, which Poundstone explains, is that ranking a candidate higher in some configurations can cause that candidate to lose. There’s also a practical problem: the “instant” in the name isn’t quite accurate because you have to total up all the votes before you can begin the actual selection. The more serious effect is that you’re completely dependent on a central counting authority.

**Condorcet and Borda**

Then the reviewer takes a brief look at two lesser-known voting methods — Condorcet and Borda — and finds them with different but fatal flaws.

Condorcet voting takes the rankings and runs pairwise contests using them….The drawbacks, which Poundstone illustrates with a real-life Wikipedia vote, include the risk of getting into a rock-paper-scissors cycle with no clear winner.

Borda counting awards points to each candidate based on the candidate’s rank position, and adds those up across all ballots. It suffers from the problem that it encourages dishonest ballots.

**Approval voting and range voting**

The final two voting methods considered by Poundstone are approval voting and range voting, with Poundstone finally finding a method that he really likes — range voting.

Approval voting does away with rankings entirely, and is therefore exempt from the impossibility theorem. Each voter says “OK” or “not OK” of each candidate….This sounds simple and fair but is the subject of bitter academic controversy. The easiest problem to understand is that it doesn’t rank preferences: a candidate just barely tolerable enough to approve for most people can beat a candidate who is the enthusiastic favorite of many.

This would not be a desirable result. So what does Range Voting offer that these other methods do not?

So what are we supposed to do? Poundstone closes by advocating “range voting”, which captures the information other systems miss by having voters give each candidate a rating from 1 to N. Instead of clicking a checkbox or picking a ranking, you can say how much you approve or disapprove of each candidate. Researcher Warren Smith has run simulated elections pitting voting systems against each other on a scale of “Bayesian regret”, a measure of how unhappy the simulated voters are with the simulated results. Range voting consistently comes out best.

This is an interesting conclusion but has two real-world problems that may not have been addressed by the mathematically-focused Poundstone. Voters may not have sufficient information about all the candidates in a large field to pick a ranking. For instance, in a recent mayoral race in Portland, Oregon, there were 17 candidates, most of whom were completely unknown and several who were clearly on the lunatic fringe. Most voters would be inclined to express an opinion about the candidates that they had some knowledge of and would not want to be required to rank the rest of the field. With such an abundance of candidates the voters’ inclination is simply to pick the one they like best and move on to the next race on the ballot.

The other problem with range voting — and one that is shared with all these other alternative voting methods — lies in the computational complexity. The calculation method is not transparent to the average voter and they must be willing to trust experts that everything was done properly. So then we come to the “trust but verify” conundrum. Not only do voters have to trust the experts for the first count, they must trust another group of experts to verify that the first count was correct. This process of verification is usually done in the course of a post-election audit.

A post-election audit should be an essential part of the electoral process. But because of the additional computation that is an intrinsic part of all these alternative counting methods, it will be more difficult to design and perform a robust, statistically sound audit of these results. Furthermore, the lack of transparency of the original count will be compounded by the audit which may increase the opaqueness of the elections process.

In a democracy it is essential that voters understand how their vote was counted and must believe that the process is fair. If the process is too mathematically complex for the average voter to understand, then an underlying premise of democracy is lost.

*Gaming the Vote*, William Poundstone, Hill and Wang 2008. ISBN 978-0-8090-4983-9

Tactical Manipulation of IRV Using Voting Theory Mathematics (applying statistical analysis to others’ votes to choose one’s vote) « Geanark said,

March 31, 2010 at 3:32 pm

[…] A good example is this review of a recent bookÂ applying game theory to various voting methods. […]