Fun with Modern Election Methods

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Tags: voting, elections, condorcet

I spent the previous week vacationing in the Outer Banks. During the ten-hour drive back home, a friend and I were discussing the topic of the season – the U.S. presidential race. In particular, we both lamented the lack of diversity among the “electable” candidates. Are Bush and Kerry the best leaders that our nation can produce? I hope not. Why, then, are we stuck with them when it comes time to cast a vote?

The problem with plurality voting

One reason is that the U.S.‘s current system of electing officials – the plurality method, in which each voter casts a single vote for a most-preferred candidate – effectively squelches third-party candidates and their ideas, leaving only the increasingly similar, mainstream Democratic and Republican candidates as viable choices. The rub is that any voter who votes for a third-party candidate doesn’t have a say in the race between the mainstream candidates. Because most voters who favor a third-party candidate are also strongly opposed to one of the mainstream candidates, they are faced with a dilemma: to vote for their true first choice (the third-party candidate) or to vote for “the lesser of evils” between the mainstream candidates as a defensive strategy in the all-to-likely event that the third-party candidate cannot win. Neither option gives the voter a fair representation of his or her preferences.

Alternatives to plurality voting

What’s needed is a way for voters to express their true preferences. is a web site that describes voting methods that allow for just that. [The content of the ElectionMethods site has disappeared since I posted this article. —Ed.]

One such method is Approval Voting, a simple extension to plurality voting. Instead of voting for one candidate (the most preferred or the lesser of evils), each voter can vote for all of the candidates of which they approve. Thus our hypothetical voter from above can vote for both the third-party candidate and the lesser-of-evils mainstream candidate. The winner is determined the same as before: Whomever receives the most votes wins.

Approval voting eliminates most of the problems with plurality voting, and yet it is almost entirely compatible with the existing voting infrastructure within the United States. The same ballots and voting machines in use today can be used for approval voting. Only the counting rules need be changed. Further, approval voting is easy for voters to understand: Just select the candidates that meet your approval. For these reasons, approval voting is a realistic option for election reform.

But, what if we’re willing to rethink our voting infrastructure from the ground up? Can we capture voters’ preferences even more accurately than with approval voting? Condorcet voting (sometimes referred to as Ranked Pairs voting, after the name of one popular variant) appears to be the best approximation of the voting ideal. Each voter ranks the candidates in order of preference. The winner is determined by decomposing the rankings into candidate-vs-candidate pairwise preferences whose strengths are determined by the count of voters that support each preference. Finally, the candidates are ranked according to the pairwise preferences (with stronger preferences overruling weaker preferences). The winning candidate is the topmost ranked.

What’s fascinating about Condorcet voting is that it can accurately capture the real-world possibility that subsets of the “majority” can have conflicting opinions. For example, candidate A may be preferred to B, and B to C, and yet C to A. Such a set of preferences is said to contain a cyclical ambiguity.

There are a number of (competing) methods for resolving cyclical ambiguities. Most of them are iterative and either “lock in” preferences, strongest first, or eliminate preferences, weakest first, until an unambiguous set of preferences remains. Which method is the best (all are very good) is still an area of active research. This is one reason why Condorcet voting seems an unlikely vehicle for near-term election reform.

Put Condorcet voting to work for you

Nevertheless, we can take advantage of Condorcet voting for our own purposes. Need to decide upon a restaurant for a group dinner? Select a vacation spot for an annual family retreat? Elect committee members at work? If so, take a look at Andrew Myers’s handy Condorcet Internet Voting Service. Or download a Python implementation of Condorcet voting (and a bunch of other voting methods, all GPL licensed) and put the code to use.

Explore and have fun

Election methods is an interesting realm for exploration, and there are plenty of interesting opportunities for the programming hobbyist. How can your applications take advantage of modern election methods? What about your web site? Dig in, and have fun!

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