Monday, November 12, 2012

Goldilocks and the Median Voter Theorem

Since two of my vertebrae are now kissing that have no business kissing, I'm going to be teaching from a seated position a lot more, and that means relying a lot more on PowerPoint and other such abominations to teach class. Since the power goes out a lot, it would be useful to have a backup. So I'm going to finally resurrect this blog to put up some notes for my classes that they can turn to during class on their smartphones if the power goes out. This post is for ECO 303 - development - and is an easy introduction to the Median Voter Theorem for our political economy section.

Political economics is the study of how governments make decisions using economic tools. One of the earlier and easier examples is the Median Voter Theorem.

To understand what the Median Voter Theorem is, remember the story of Goldilocks and the Three Bears. In the original story, every bear could have porridge, chair, and bed ideally suited to his or her preferences. This is one of the good things about the market system: everyone can have exactly what they want. With government making decisions, that may not be the case at all. We are much more likely to get one-policy-fits-all. But which policy will we get?

Suppose the three bears' government will only supply one type of porridge, one type of chair, one type of bed. What will the temperature of their porridge be? How hard will their chairs and beds be?

If the three bears decide things democratically, the Median Voter Theorem tells us the answer: it's whatever Baby Bear wants!

"Proof" by example: Suppose at first Mama Bear has insisted everyone eat cold porridge. Papa Bear then proposes a vote: "Let's raise the temperature of the porridge a little." Who votes for raising the temperature a little? Mama Bear is opposed, but Baby and Papa agree, so the temperature gets raised. Papa Bear then grumbles that it's not hot enough yet, so they should raise it a bit more. Baby and Papa Bear still vote Yes and the temperature is raised. Still not warm enough for either of them, they continue to outvote Mama and raise the temperature. UNTIL it gets to be the temperature Baby Bear wants. Now when Papa Bear proposes raising the temperature even higher, Baby Bear joins Mama Bear in opposing the vote and it stays at the temperature Baby Bear likes.

This example works equally well in revere. If we start with hot porridge, Mama Bear will propose letting it cool down before everyone eats and Baby Bear seconds the motion. Baby Bear continues to side with Mama until the porridge gets down to the temperature the Baby likes and then they all eat it at Baby's preferred temperature.

The same things happens with their furniture: not hard enough for Papa, not soft enough for Mama, just right for Baby. Any motion to make the chairs harder only has one vote and any motion to make the chairs softer has only one vote. 

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