Political Analysis: Median Voter Theorem and Voting Systems

In this final, though not very conclusive, post on political analysis, we’re talking voting, voting systems, and ice cream.

The Median voter theorem helps explain the importance of the swing voter. For the MVT there are four elements:

  1. A set of n voters where n is odd (apparently an even number can work too, but we didn’t really talk about it, and, as in Minecraft, odd numbers just work better.)
  2. Unidimensional policy space (i.e. right vs. left, socialist vs. capitalist, more funding vs. less funding)
  3. Voters have quadratic or “single-peaked” preferences that can be represented by the equation U[x] = [x1 – x’]2. So they have one ideal point (x’) and whichever option falls closer to their ideal point is what they’ll vote for.
  4. The group makes decisions by majority rule (and we’ll talk about alternatives to this in a  bit.)

The theorem states that, if every voter in the group has an ideal point, the voter with the median ideal point is an indicator of how the group will vote.

To apply this, here’s an example:

The International Space Committee is voting between two bills to send colonists to Mars. There are seven seats on the committee. Three of them are hardliners who think colonization is a waster of resources, and their ideal point is 0 colonists. On the other end of the spectrum is a sci-fi fan who wants to send a hundred colonists. Then in the middle we have someone who wants to send three colonists, someone who wants to send five, and someone who wants to send twelve. Read More »

Political Analysis: Condorcet Jury Theorem

Last post I introduced the concept of aggregation in political analysis, and how you can’t always make inferences about members of a group based on the character of the group as a whole—or visa versa. This post will go further into that, and also why democracy works.

In college, it’s easy to forget how much smarter you are than everyone, because you’re surrounded by people as smart or smarter than you—but really, a lot of people are highly ignorant. [NOTE FROM THE NOTE-TAKER: This is how Professor Dion introduced the topic, not me just throwing in my own color. But it is kind of true.]

For example, only 74% of Americans believe that the Earth orbits around the sun. As for politics, in 2010 only 54% knew the controlling party of the House of Representatives.

So, is democracy doomed? The idea with democracy is that an individual is the best judge of their own interests, and will elect a good representative for themself. But if people are ignorant, will they really?Read More »