Should you try to prevent spoilers in your voting system?

Posted by Chris on April 17, 2014
Previous: Should you be using a more expressive voting system?
Next: Mobile voting app use cases: Selecting a logo for your business

If you're building a system that incorporates voting, or helping determine the election rules for an institution, there are a lot of potential voting systems for you to choose. This article explores how "spoilers" can prevent a group from making an optimal choice, and how voting systems that satisfy a property known as “Independence of Irrelevant Alternatives” are more resistant to spoilers.

What’s a spoiler?

A "spoiler candidate" is a candidate whose presence in an election will change the outcome of the election, even though the spoiler himself won’t win. Plurality voting, the system most states use to choose the allocation of their electoral college votes, is especially vulnerable to spoilers that “split the vote” of another candidate. The most famous example of recent years may be the 2000 presidential election, in which Al Gore narrowly lost the Florida vote to George Bush, and thus lost the presidency. In Florida, Ralph Nader received 97,488 votes, and it was widely assumed that he was a “spoiler” -- that is, if he hadn’t been a candidate in the election, a majority of the votes cast for him would have gone to Gore, tipping the election to the other side. The assumption that Nader was “splitting the liberal vote” was strong enough that Republicans even paid for pro-Nader ads.

The point of identifying Nader as a spoiler is not really that "Nader caused Bush to be elected", because in such a close election it’s easy to identify countless small actions that would have changed the outcome. You could make the argument that US society got a sub-optimal outcome in 2000 because of the spoiler effect, but your conclusion will be strongly colored by your political preferences (and remember, Buchanan and Browne may have been “splitting the conservative vote” too). What is clear is that the incentives for voters and politicians are warped by vote-splitting: voters are given a strong incentive to misrepresent their preferences to avoid throwing their vote away on a third party candidate, and political parties can even have a bizarre incentive to campaign for their ideological opponents.

The spoiler problem isn’t limited to hotly-contested political questions.

In fact, whenever there are multiple options in an election and some of the options are more similar to each other than others, spoilers or vote-splitting can be a problem. Consider a group of nine friends trying to decide between four activities:

Bike Riding Hiking Running Watching a Movie
Top-Choice Votes 2 2 2 3

With the votes above, "Watching a Movie" would win, even though two-thirds of the voters prefer an outdoor activity to an indoor activity. We can guess that removing any one of the outdoor activities from the list would probably change the outcome.

Even with all the friends co-operating, it would be difficult for them to avoid the vote-splitting problem. The creator of the poll could try to limit the poll to "one outdoor option and one indoor option", but how would he know which outdoor option to choose? Outdoor-loving voters could try to vote for the “most electable” outdoor option, but how would they know which option that was? As crude as it is, at least the US political system clearly identifies “front runners” on either side of the ideological divide.

How can we prevent spoilers?

Throughout the world, some political systems try to address the spoiler problem by using Instant-runoff voting (IRV), and organizations such as FairVote campaign for increased use of IRV throughout the US political system. In IRV, voters first rank all the candidates. In the first round, the top choice of each voter is used. If one candidate gets a majority, he’s declared the winner. Otherwise, the candidate with the fewest "top choice" votes is eliminated, and the election proceeds to the next round, until one candidate gets a majority of votes.

At first glance, it seems like IRV solves the spoiler problem. After all, if the three candidates were Bush, Nader, and Gore, voters would be free to rate Nader as their top choice secure in the knowledge that once Nader was eliminated, their vote would be counted towards whoever their second choice was. When you look deeper, however, the picture is a little more complicated.

There’s a formal property of voting systems known as Independence of Irrelevant Alternatives (IIA), which you might interpret as meaning that a system is spoiler-proof. If a voting system satisfies IIA, then adding a new candidate “Bob” to an election won’t have any effect on the relative rankings of the original candidates (that is, in the new election results Bob may rank above or below candidates “Alice” and “Charlie”, but Alice and Charlie won’t change their ranking relative to each other). Perhaps surprisingly, IRV doesn’t satisfy IIA, because in some election scenarios it’s possible that misrepresenting your top choice may actually keep your second-choice in the running long enough to defeat your last choice.

Our beloved voting system chart shows us some systems that do satisfy IIA, such as Approval Voting, Range Voting, and Majority Judgment. If you use one of these systems, you’re mathematically safe from spoilers, although human psychology may still get in the way.

Consider a group of friends deciding what to do on a Friday night and choosing between "Watch a Movie" and “Go out and Party”. If you add a third option “Sleep early to prepare for our run tomorrow morning”, it may not theoretically alter the relative ranking of the first two options, but it’s easy to imagine that by changing the voters’ frame of reference it could discourage a late night of partying.

What do I have to give up for my voting system to be spoiler-resistant, and when is it worth it?

As always with voting systems, no desirable property comes for free. For instance, you’re not going to be able to find a voting system that satisfies both the Condorcet Criterion (any candidate that can beat each other candidate in a 1-on-1 election will also will the overall election) and IIA. If for some reason you’re constrained to a rank-order voting system (such as IRV), then Arrow’s Impossibility Theorem actually proves that you can’t satisfy IIA without either having a dictator (who wants that?) or at least ignoring unanimous votes (which doesn’t seem right either).

Why VoteUp uses a voting system that satisfies IIA

VoteUp uses range voting primarily because it’s expressive, and we believe that IIA property of range voting also supports a form of expressivity. Our reasoning is (1) voting systems that are susceptible to spoiler effects have strong incentives for voters to misrepresent their preferences, and (2) being encouraged to misrepresent your preferences reduces how fully you can express yourself.

Additionally, our app is designed for speed and flexibility, so we can’t assume that the options in a poll are carefully chosen to avoid spoiler effects. In fact, we even allow options to be added while polls are in progress (so that voters can get a say in case the creator missed an important option), so we have to use a system that gives reasonable results even when it’s possible that some voters don’t get to vote on all the options.

Comments

{{comment.author}}: {{comment.comment}}
© 2015 Uxor Navium Labs