Saturday, December 18, 2010

What "The People" "Want", Part Three: Voting Rules Gone Bad

Last time, I introduced Arrow's Theorem, which states, essentially, that we can't have our voting cake and eat it too. I also showed how plurality rule fails to give us one thing we’d like, transitivity.
Today I want look at the other classic problem: the Borda count and independence of irrelevant alternatives. First, let's review a little bit.

Tuesday, December 7, 2010

Feeling Blue? Try a Dose of Blue Light at New Scientist

After a bit of a lull, it's been a busy week (and day) at Nathan Explains Science. This afternoon I have a new story over at New Scientist (link below) on using a blue-light activated, algae-derived protein called Channel Rhodopsin 2 (ChR2) to cure depression in mice.

Fielding Reader Questions: The Strength of Voter Preference

Reader F. Tyler asks the following (slightly edited) question regarding the Borda count, a voting method in which people rank alternatives, higher-ranked alternatives get fewer points, and the option with the fewest points wins, just like golf (see this post and its follow-up on basic problems with voting):

What "The People" "Want", Part Two: It Gets Worse.

Last time I talked about what the people want, there were two main points.

First, there are always more than two options. The point of this is that if even in seemingly two-party systems such as that here in the US, there are so-called third parties, and the presence of third-party candidates is sometimes consequential. The big scary example is Allende in Chile in the 1970s; the less scary but more proximate example (for US readers) is Perot in the 1992 US presidential election.

Second, once there are more than two options, what the people "want" is hard to define. Using the Borda count and plurality rule voting methods, I showed how society's first choice depends on the manner in which people decide.

In the academic literature on "social choice," as it's called, the issue is one of preference aggregation and whether it's possible to aggregate preferences in a rational, fair way.

Today, I'll start with a statement of Arrow's Theorem, which answers that question with a resounding "No, it's not possible. Sorry." I'll follow with some intuition, and in future posts I'll flesh out the ideas.

Monday, December 6, 2010

Light "Flight" at ScienceNOW

Nifty brief on using the momentum carried by light rays to get a piece of glass to move perpendicular to the light. Puzzled? Read more here. I'll give a more thorough explanation later today.

- Posted using BlogPress from my iPhone