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Three word explanations
Median voter theorem.
It's my first-cut account of a lot of what is going on in the newspaper headlines. Yet somehow I rarely see it mentioned, even when I read very prominent social scientists commenting on current policy.
I thank Garett Jones for a useful conversation behind this blog post.
Posted by Tyler Cowen on June 22, 2009 at 02:07 PM in Political Science | Permalink
Comments
When I was TAing Microeconomics last fall, I could not find any good and intuitive explanation of median voter theorem online or in a microeconomics textbook. It was very frustrating. I would find articles in Econ or Public Policy journals with lots of math, but not one intuitive explanation. Could you point to any sources to read up on it?
Posted by: Irina I at Jun 22, 2009 2:41:42 PM
Irina: Perhaps I've done statistics for too long, but the median voter theorem looks so straightforward to me that an explanation consists of little more than a definition of terms. Is there some more complicated median voter theorem I don't know about?
Posted by: David Wright at Jun 22, 2009 2:58:42 PM
There's a great discussion of the Median Voter Theorem in the third lecture from Yale's open course on game theory:
http://oyc.yale.edu/economics/game-theory/contents/downloads
Posted by: John Myles White at Jun 22, 2009 3:10:26 PM
Here's what Paul Krugman says in his NY Times column today:
The real risk is that health care reform will be undermined by “centrist” Democratic senators who either prevent the passage of a bill or insist on watering down key elements of reform. I use scare quotes around “centrist,” by the way, because if the center means the position held by most Americans, the self-proclaimed centrists are in fact way out in right field.
Tyler, do you disagree with Paul Krugman about the preferences of the median voter in the U.S. or do you mean the theorem to apply to the median senator (or median lobbyist) instead?
Or are you perhaps referring to a different set of newspaper headlines?
Posted by: a student of economics at Jun 22, 2009 3:12:04 PM
Here's the full Krugman column, by the way, with more details on why he believes the median Senator is very different than the median voter w.r.t. health care and especially the "public option": http://www.nytimes.com/2009/06/22/opinion/22krugman.html
See also this poll or similar polls summarized by Nate Silver recently:
http://www.nytimes.com/2009/06/21/health/policy/21poll.html
Posted by: a student of economics at Jun 22, 2009 3:15:41 PM
@student:
If the median voter hasn't changed her position much in the last year or two, then by the MVT the policy outcome won't change much. Whether the median voter is the "median member of Congress" or the "median voter at the booth" is a minor question at that point.
The Dems have picked up a lot of culturally-conservative seats so the median member of Congress probably hasn't changed her views all that much. When you hear "The Dems won a seat that had been GOP for decades" you should probably think Blue Dog.
And on Krugman's alleged evidence of unmet demand for health care reform: As Larry Bartels's resarch shows, voters always say they want more government services and lower taxes: They want more for less, no surprise to economists. This is true even in Sweden. Voters leave it to the legislators to figure out how to optimize their re-election chances subject to those preferences and the government budget constraint. Is there also a massive unmet need for tax cuts?
As the link in my name shows, support for massive health care reform is lower now than in 1993: The median voter---whether in the booth or on the floor on the House--is probably less supportive of massive change than in 1993. Bad news for universal health care, if the MVT is roughly true.
Posted by: Garett Jones at Jun 22, 2009 3:39:42 PM
SGS about the median voter or the median Senator? When the politicians and their lackeys start trotting out the polls, especially those as contradictory as the NYT poll...
"While 85 percent of respondents said the health care system needed to be fundamentally changed or completely rebuilt, 77 percent said they were very or somewhat satisfied with the quality of their own care."
"Three of four people questioned said unnecessary medical tests and treatments had become a serious problem, suggesting that they would support calls by health researchers for a payment system that would better reward appropriate care. But an even higher number, 87 percent, said the inability of people to have the needed tests and treatments was a serious problem."
...it's a clue that they are substituting populism in place of principle and accuracy.
"Half of those questioned said they thought government would be better at providing medical coverage than private insurers, up from 30 percent in polls conducted in 2007. Nearly 60 percent said Washington would have more success in holding down costs, up from 47 percent."
Damn, the gov't got a lot better in 2 years.
Posted by: Andrew at Jun 22, 2009 3:49:55 PM
Thanks, Garrett. Good answer.
Posted by: a student of economics at Jun 22, 2009 3:50:07 PM
Tyler, do you disagree with Paul Krugman about the preferences of the median voter in the U.S. or do you mean the theorem to apply to the median senator (or median lobbyist) instead?
He's quoting the parts of the polls that shows that people want free stuff, but not the parts that show that they don't want to pay for it.
In addition, student, you can note from various polls that one of the things that people emphatically say in polls that they don't want are precisely the types of cost controls and equalization of spending that the studies seem to suggest that we should do and could do without harming care.
It's easy to cherry-pick part of the polls. What's generally true:
* People would like to cover the uninsured, but
* They don't want their own coverage to be changed (leading Obama to overpromise that no one will lose employer coverage against their will under his plan, something that can't be done with an efficient and cost-effective plan)
* People don't want to pay more in taxes or pay more for treatment or insurance premiums, but
* They don't want any claim to be denied, even if science demonstrates that it's useless or that their area spends 30% more for no better care.
* They agree that there are unnecessary spending and tests, but
* Certainly not anything that their doctor would ever recommend.
* They trust the government more than insurance companies to hold down costs, but
* Their idea of how to hold down costs is not at all what Orszag is proposing.
The median voter is either irrational, or believes that health care costs are all a conspiracy.
Posted by: John Thacker at Jun 22, 2009 4:15:13 PM
@andrew: of course 60% of voters approve of the job their congressional representative is doing yet as a whole congress has only 18% approval ratings. the same mindset is at work here
Posted by: wriufqrfh at Jun 22, 2009 4:17:00 PM
My three word explanation
Something for Nothing
can be reduced to the two word explanation
Free Lunch
While the recent survey indicated that a majority said they would support paying more in taxes to cover the un/under-insured, I'm not convinced that a majority won't continue voting for politicials denouncing high taxes and promising to cut taxes (justified of course by unspecified fiscal responsibility of cutting waste, fraud, and entitlement reform).
A more serious three word explanation is
Not Evidence Based
The headlines denounce Obama's attempt to take control of your health care so he can ration it and cause your health to suffer. Or the claim that government run health care costs more and is inferior to our health care system, which gives superior care to everyone and is cheaper than in Canada and Britain.
Posted by: mulp at Jun 22, 2009 4:17:28 PM
dang, i thought this was about the median smoker theorem!
Posted by: babar at Jun 22, 2009 4:18:50 PM
Irina,
Median voter theorum is a model that in a democracy, the preferences of the median voter become policy for the nation (because they are the only policies that can attract enough support to pass with a majority).
Posted by: nelsonal at Jun 22, 2009 4:30:12 PM
"60% of voters choose good, fast and cheap while 35% prefer fast, cheap and good"
The NYT is beyond question, but if I were asking the questions, I'd ask "exactly which costs should be reduced?" and "Which one(s) are getting/keeping too much money: doctors, insurance companies, hospitals, consumers, pharmaceutical companies, medical device companies, or government agencies?"
Here's my best shot for Irina. Take a bell-curve. Draw a vertical line through it. On one side of the line are people who vote for A, and the other side are people who vote for B. Since we have a "plurality" candidate system and yea/nay voting on issues, there are only two choices. Now, the job for each candidate is to get 50% + 1 of the vote. The same job is required of a passing policy vote. So, the job of the candidate or the policy advocate is to move that vertical line on the bell curve up to and past the maximum, but not too far past, because to do so you are making concessions to your opposition in return for votes. Now, the interesting part comes in crafting the platform, or in reality, the advertising of the candidate and in hashing out the items in a policy to achieve that total. It gets more complicated when you acknowledge that policies and voters are not linear, so "horse trading" can take place outside the issue at hand.
Posted by: Andrew at Jun 22, 2009 4:39:44 PM
I think the status quo policy matters quite a lot these days. I would argue that becuse the Democrats control everything, the proposed policies are going to start at the median Democrat and schooch to the right until the conservative Dems like the proposed policy more than the status quo. Since most established policies are probably at or to the right of the median Congressman right now, it's going to be a hard sell moving those too far to the left. The status quo default option for climate change and health care may well kill legislation. On something like financial markets where the current policies might be seen as on the far right, we will might see reform land closer to the median Dem than the median voter.
Posted by: david at Jun 22, 2009 7:00:00 PM
1) The median of the median is not usually the median. There is no reason to assume that the preferences of the median voter of the population translates to anything close to the median member of Congress. Even if you assume a single dimension. Congressional districts are not randomly created.
2) No Congress scholar believes that the median voter theorem holds in Congress. There are too many institutional rules in place. The two dominant models are the Party Cartel Model (median of majority party is more important thatn median of Congress) and the Pivotal Politics model (includes the president and key members who have power owing to the Constitution or chamber rules)
Posted by: congress scholar at Jun 22, 2009 9:28:02 PM
If, in fact, Democratic senators are positioning themselves to the right of the median voter, perhaps a modified version of the model provides the best explanation. (I'm not saying that the premise is true -- as John Thacker ably notes, the "typical voter" as revealed through polls is so confused and self-contradictory that it's almost meaningless.)
The two modifications are:
1. There are massive institutional barriers to challenging an incumbent for the nomination. We can model this by assuming that even if a Democratic candidate is to the right of the median, there is only a small chance p(x) that a challenger is able to slip in on the left, where p is an increasing function of x, the distance from the median.
2. The distribution of voters is dynamic and partially unpredictable.
With these two modifications, you can continue to explain the vast majority of political behavior as strategic positioning along a one-dimensional continuum of ideology, but many of the apparent paradoxes disappear. If there is only a small chance that a liberal challenger will capitalize on a Democratic nominee's slight rightward drift (modification 1), it may be optimal for a Democratic incumbent to place himself to the right of the median to hedge against the risk that the median might move to the right in the future. (modification 2).
Posted by: Matt Rognlie at Jun 22, 2009 10:17:39 PM
Irina, the colloquial version of the MVT is called the Ice Cream Vendors on the Beach theorem. If you have two ice cream carts competing on a long and narrow (i.e. one-dimensional) beach, and all kids on the beach go to the cart that's closer to them, then no matter where they start out or how exactly the kids are spread out over the beach, both vendors will end up with their carts right next to each other at the spot where the number of kids on both sides is equal. Note the necessary conditions for this to work: the beach can't be two-dimensional, there can't be more than two carts, and all kids will buy one ice cream cone no matter how far they are from the nearest vendor.
Posted by: ogmb at Jun 23, 2009 4:46:46 AM
Here's another survey of poll results by William Galston showing that, to a first approximation, what the average American wants health care reform to do could be better approximated by taking what Orszag and other experts are proposing and doing exactly the opposite.
See also the Kaiser CEO's The Experts versus the Public on Health Care Reform.
Democrats realize that while certain broad ideas poll well, the public's idea of the details are very different from the experts'. So even something that might be good in the long run may be punished heavily at the polls in the short-run.
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