Down with Plurality!

Hi friends,

As some of you may know, in general I don’t hold our country’s voting methods in very high regard. Think about the way we vote for president, for instance. Aside from not asking voters to state any preferences at all, it’s difficult to do worse than our current system: we can only show our support for a single candidate, when in fact our preferences may be more nuanced. Moreover, since we can only vote for a single candidate, there’s little incentive to vote for our favorite one, unless our favorite happens to be a front-runner. This is known all across the universe, as evidenced by the Presidential runs of Kang and Kodos:

Even worse, a third party candidate who garners a decent amount of support may end up hurting his own party and parties more closely aligned to it by acting . . . → Read More: Down with Plurality!

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Math in Books: Who’s #1?

In an earlier post, I closed by hinting at the mathematics of ranking. In this modern era, the topic is particularly relevant: the ranking algorithms are hard at work whenever you type something into a search engine, rate a movie on Netflix, or look at a product on Amazon. It’s also a popular area of study among sports enthusiasts, for whom accurate rankings of the relative strengths of teams can make all the difference in a fantasy league or a betting pool.

Because of all of these accessible applications, it should come as no surprise that the mathematics of ranking is the subject of a new book, titled Who’s #1? The Science of Rating and Ranking. Written by applied mathematicians Amy N. Langville and Carl D. Meyer, the book tackles a variety of methods used to extract ratings or rankings given some collection of input data.

Front Cover!

This . . . → Read More: Math in Books: Who’s #1?

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CNN Light Years guest post: Why a different voting system might be better

Hi Everyone,

In an attempt to spread the joy and cheer of mathematics to a broader audience, starting this month, I will occasionally be writing articles for CNN’s new science and technology blog, Light Years. Fear not, most of my content will still be appearing at Math Goes Pop, and every time one of my guest posts goes live, I will let you know about it here as well. Today the topic is voting systems, something I have discussed on this blog before. Here’s a piece of the intro to pique your interest:

When the results of an election (primary or otherwise) run counter to our desires, it is easy to scapegoat the political process. The right person didn’t win, we may argue, because the system itself is broken. The two-party system, for example, is sometimes cited as a leading cause of the current dysfunction in Washington. But perhaps much . . . → Read More: CNN Light Years guest post: Why a different voting system might be better

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And the Award for Best Voting System Goes to…

Last year, the Center for Election Science wrote up a quick blog post on the Oscars to motivate a discussion of voting reform. Since 2009, the Oscars have used Instant Runoff Voting (IRV) to decide the winner of the prestigious Best Picture award, but there is growing backlash against this voting system because of a number of strange properties it possesses. For example, the winner of an IRV election may not be the most favored candidate among the voters; for another strange example, it can sometimes be to your advantage to rank your preferred candidate last instead of first. Here’s a video explaining some of these weird features:

Instead of using IRV, a strong argument could be made for using Score voting (also known as Range voting). I’ve discussed these voting systems before (see here for a discussion of the 2010 Oakland mayoral race, for example), so . . . → Read More: And the Award for Best Voting System Goes to…

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MTV/Oscar Showdown

For many of us, summer is thought of as the time between Memorial Day and Labor Day. For folks of a younger generation, though, trendier bookends are provided by two MTV Award shows: The Movie Awards at the beginning of the summer, and the Video Music Awards at the end. Continuing this noble tradition, the 20th iteration of the MTV Movie Awards was broadcast this weekend. If you missed it, don’t worry; I’m sure it will be shown another 300,000 or so times before the summer is out.

As a shining beacon of what is hip, MTV has a responsibility during its movie awards to highlight the most popular films of the year. This is in stark contrast to the priorities of higher brow award shows such as the Oscars, for which artistic achievement is placed on the highest pedestal. This is not to say that these two goals need . . . → Read More: MTV/Oscar Showdown

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Instant Runoff Voting in Oakland

Earlier this month, Oakland elected its first Asian American to the less than coveted role of city mayor. Jean Quan emerged victorious this election day, although at one point she was trailing her opponent by 11 percentage points. Understood in context, however, her victory is perhaps less surprising – rather than winning by Plurality, Quan won under Oakland’s Instant Runoff Voting system.

I don't know much about Oakland politics, but this picture sure makes her look ready for business.

What’s the difference? For most elections in the United States, voters are instructed to cast their vote for the individual who they would most like to see get elected. These votes are tallied, and the one with the most votes is declared the winner. In contrast, the Instant Runoff Voting system asks voters to rank several candidates at once – this extra information is used to automatically determine the outcome . . . → Read More: Instant Runoff Voting in Oakland

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Math Gets Around: Politics, Part 3

As promised, in this thrilling final installment to the relationship between math and voting (the first two parts can be found here and here), we will look at what many people see as the holy grail of voting systems: Range voting.

The concept of range voting is simple. Given a set of candidates, in a range voting system you simply put a score next to each name that reflects how strongly you support that candidate. Of course, this is quite different from our current voting system, where we only get to vote for one candidate, but more importantly, it differs significantly from other voting systems where you are just asked to rank candidates in order of preference, because a ranking gives no information about the degree to which your support varies from candidate to candidate.

For example, if Anna, Bob, and Charlie are all running for President, you and I . . . → Read More: Math Gets Around: Politics, Part 3

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Math Gets Around: Politics, Part 2

As you may recall, I have already discussed certain perils associated with different voting systems. However, given all the commotion this election is causing, I thought it may be worthwhile to discuss voting in a bit more detail.

There is plenty of information online regarding the relationship between math and voting, for those with interest enough to seek it out. But perhaps the best centralized internet location on this topic comes from this year’s Mathematics Awareness Month website.

In April of every year, mathaware.org hosts a Mathematics Awareness month, complete with articles and contests related to the year’s theme of forging a bridge between mathematics and what is often times a seemingly disparate discipline. It was no doubt with tremendous foresight that they selected “Mathematics and Voting” for this year’s theme.

A good way to kill a few minutes is with their voting methods simulation. On this page, you can . . . → Read More: Math Gets Around: Politics, Part 2

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