A Scientific Look At The Problem With Third Parties

As the 2012 election draws near, I am constantly reminded about third parties. What is interesting however, is that, as the election draws nearer, voter interest in third parties seems to be declining. In fact, the existence of third parties on the ticket may actually benefit Obama.

• Without third parties on the Ballot: Obama 47%, Romney 45% (Gallup 7/1/12 through 7/8/12)
• With third parties on the Ballot: Obama 47%, Romney 40% (Gallup 7/6/12, see "declining" link)

Still the temptation may still be there for just enough voters to swing the election in ways a plurality of Americans do not favor. This is more than just mere speculation. In fact, the evidence for this is actually quite strong. Brian Dunning explains this evidence in his Skeptoid episode entitled "The Science of Voting" (all of the following emphasis is mine):

Democratic voting is only simple if there are just two candidates, or if it's a Yes or No vote. In those cases, any attempt to vote tactically or to create a voting block — casting votes that don't represent your preference — work against you. What we're talking about today are elections where there are three or more candidates. And the idea that all the various systems for running such elections are flawed (subject to results that do not represent the group's preference) is not just a whim or a crazy opinion of mine. It's proven by Arrow's Impossibility Theorem, named for the economist Kenneth Arrow, winner of the 1972 Nobel Prize in economics and the 2004 National Medal of Science. He proved it in 1951 with his Ph.D. thesis at Columbia University.

Arrow's theorem can be simplified into one clear statement: that no fair voting system exists when there are three or more candidates.

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Arrow's theorem applies to election systems that require voters to rank the candidates. This is the case with most voting systems worldwide. Typically, when you vote, you mark an X in the box for one candidate. That's a ranking; you've ranked that candidate first. Arrow's theorem applies to these simple ranking systems, but its richest mathematical complexities come from systems with three or more candidates and the voters rank all candidates in order of preference.

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The ideal outcome in any election is to choose what's called the Condorcet winner. A Condorcet winner, named after the French mathematician and political scientist, is the candidate who would beat all other candidates in a simple two-man majority race. There isn't always a Condorcet winner in every election, but there usually is. The most common voting system is plurality voting, where the candidate with the largest number of votes wins. However, there are numerous situations in which the winner of a plurality vote is not the Condorcet winner who should have been elected. This is most often seen in a vote-splitting situation, where there are two similar candidates and one oddball candidate. One of the similar candidates is often the Condorcet winner; but because of their similarity, party votes are often split between them, and the oddball candidate wins. This is the most obvious failure of election systems, and it's exactly what Kenneth Arrows was talking about.

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A variant of range voting is called approval voting, where you vote either for or against each candidate, but you can vote for as many as you like; even all or none. It's basically range voting with only two choices, 0 or 1. Approval voting also avoids the pitfalls of Arrow's theorem because it does not require ranking. It's simpler than range voting; and in both real-world and simulation examples, it selects the Condorcet winner virtually every time that one exists, in contrast to plurality voting which fails frequently.

This inherent tendency for voting to fail is called the voting paradox, also described by Condorcet. Yet, it's the system that virtually all nations rely upon for most or all of their elections. Something's broken somewhere.

This sounds quite depressing. At this point you may be wondering if third parties work with ANY theoretical voting system. Luckily, Brian Dunning outlines a few voting systems that allow third parties to exist without screwing up the system. Two of them, lottery and range voting, both come with flaws of their own. Perhaps the most intriguing system is saved for last:

A variant of range voting is called approval voting, where you vote either for or against each candidate, but you can vote for as many as you like; even all or none. It's basically range voting with only two choices, 0 or 1. Approval voting also avoids the pitfalls of Arrow's theorem because it does not require ranking. It's simpler than range voting; and in both real-world and simulation examples, it selects the Condorcet winner virtually every time that one exists, in contrast to plurality voting which fails frequently.

This not the full range of possibilities, but it shows that there are alternatives to our rank-based voting system. Third parties have had so little success over the last 150 years. And, given the recent Citizens United decisions, it may be virtually impossible for another Ross Perot to spend the money needed to get the 15% support required to participate in national debates. If we ever hope to establish a clear third party in this country, we need to seriously re-examine our system of voting before throwing our vote away at the expense of the American people.