Grand Challenge

The grand challenge of economics is to allow each voter to play with the tax code at a detailed level -- and combine these results in a meaningful way into The Tax Code. That is they should be able to say that a person with an income in the range of $80,000 to $100,000 with two kids in an expensive suburb, whose income, 30% comes from investments and the rest from working should pay thirty four percent in taxes.

We have had many good analyses of how the income tax burden is distributed and whether the wealth or the workers are paying enough, and that half of Americans are not paying any income tax but may be paying Social Security tax as well as state and local taxes.

1. http://www.npr.org/blogs/money/2010/04/inside_the_returns_of_americas.html
2. http://finance.yahoo.com/news/Nearly-half-of-US-households-apf-1105567323.html?x=0
3. And a Dangerous Economist Posting on April Ninth 2010, "Does Everyone Pay Taxes?"
4. http://www.npr.org/templates/story/story.php?storyId=125991138

Our Federal Government is a huge insurance company with an army" as Dr. Krugman put it. Thus, the voters also need to say how much money a Colonel who had fifteen years of active duty when he lost his hand to a road side bomb in Afghanistan, how much money should a eighty-year old man earn from Social Security after working 160 quarters and whose total input was $100,000. And who do these interact and what is the optimal way to have people weigh their desire for public programs and their desire to keep the tax burden down, an issue raised at least half a century ago.

This part would use the best of MultiMedia Learning Theory and visualization. ( I was very impressed by E-Learning and the Science of Instruction: Proven Guidelines for Consumers and Designers of Multimedia Learning by Ruth Colvin Clark and Richard E. Meyer and and Richard E. Mayer, Multimedia Leaarning. There is a science to this, but that is a subject for other posts).

The second part is combining the individual choices and budgets into a tax code and budget. This can be done by Genetic Algorithms, the classical Machine Learning from Examples algorithms (ID3 and C4.5). But another question, building on the grand question of discretion versus the rule of law, is replacing some or all of this tax code by sortition juries who would look at each tax payer's situation holistically, and letting the tax burden be a competition among both businesses and individuals to be "good" as broadly defined by the jury.

Grand Challenges

There are many other grand challenges and grand challenge lists out there:

1. Engineering which is a list of fourteen challenges developed by the National Academy of Engineering by a panel of eighteen indivudals including Google Co-founder Larry Page and J. Craig Venter
2. the DARAPA Grand Challenge to develop autonomous vehicles that can drive off road.
3. Improve Scientific Result and Data Communication
4. global health
5. David Hilbert publishing twenty-three unsolved problems in mathematics in 1900
6. And in the 1980's, a list of challenges for Computer Science

Thoughtful Thursday, Conitzer

I was planning to write a Thoughtful Thursday piece on the Combinatorial Auctions (1) book. But Dr. Conitzer beat me to it and did a better job than I possibly could have done. I was pleased to see "Making Preferences Based on the Preferences of Multiple Agents" in the latest issue of Communications of ACM, March 2010, Volume 53, Number Three, Pages 84 to 94.

A combinatorial auction allows one to say that they value a set of objects that are being offered for auction. Imagine that Ms. Smith was browsing on eBay and saw a set of chairs and a table that she liked and she wanted to buy together for her dining room. However, she doesn't want the table without the chairs or the chairs without the table. There is no way she could do this now. If eBay would implement a combinatorial auction, then Ms. Smith could say or bid that she would pay $150 for both the table and chairs. Assume that Mr. Johnston bids $75.00 for just the table and Mr. Nixon bids $59.00 for just the set of chairs. The combinatorial auction system would realize that the best use (and the most money for the auction company) would happen if the pair of items were given to Ms. Smith. Had Mr. Johnston bid $75.00 and Mr. Nixon bid $76.00 for the set of chairs, the auction system would give each of these to the individual bidders and Ms. Smith would not win anything.

A lot of time in public choice is spent on dealing with multi-candidate elections. How do we deal with an election involving N, B and G and we want to allow people to say I really like N, but if it is a choice between B and G, then give me G? How do people specify their preferences. How does the election system computer decide who won? And how can we make the system strategy-proof? That is, we don't want a person who really prefers N to feel that if they rank N belong B or G, they are more likely to get N elected. One of the impressive things in Dr. Conitzer's article is the Kemeny Rule for elections. Let each person simply give each ranking. The election computer would compute a complete set of ranks that minimizes the total number of disagreements. One "disagreement" occurs when one voter ranking candidate i above candidate j and the election system ranks candidate j above candidate i. It would be great if we could do this for all kinds of things, like which bridge design do the members of the region prefer or what tax code do we prefer. Computing this is NP-complete. That means (I won't go into all the provisos here) any computer algorithm purporting to solve it for all possible sets of rankings will take time proportional to some power of the number of alternatives. In other words, for modest size problems, it is impossible to solve this generally even with computers much faster than the impressive ones that are available today. However, getting a problem proved NP-complete does not mean that an algorithm might not solve it efficiently most of the time or for most practical cases. And Dr. Conitzer reported they use CPLEX for ranking one hundred Ph.D. candidates to their Computer Science department by the Kemeny method. Dr. Conitzer analyzed many voting systems in a masterful Journal of the ACM article. In particular, although he showed that many schemes are NP-compatible to manipulate, that does not mean that one could not find an algorithm that will manipulate most practical elections as he demonstrated with an algorithm at the end of the article.

However, there are many who advocate for simply having each voter assigning a score within a range. say -1 to 1 or 0 to 100, to each candidate and the one with the highest average wins. (I will do a Thoughtful Thursday Post on Wally Smith's simulation and theorems.)

And I was impressed by the work on kidney exchanges. Assume A wants to donate a kidney to B and C wants to donate a kidney to D. Unfortunately A is not compatible with B, C is not compatable with D, but A is compatible with D and C is compatible with B. The computer system at Carnegie Mellon finds the proper matching and constructs a chain out of a set of all the people who would like to exchange kidneys with each other. However, it tries to minimize the chains.

These are examples of choice problems that don't use money. I sometimes wonder, and I will talk about this in another posting, whether this kind of technique could be used to minimize the necessity of money. As a poster on The Oil Drum put it, "Money is the lubricant in the economic engine and without enough of it that engine will seize up as it did in the 1930's when farmers dumped milk they couldn't sell into ditches while others were starving for want of the money to buy food." Could a program such this find the chains between the person working at Intel building parts for computers and the farmer without using a currencies or a numeraire?

Personal Note

Dr. Conitzer is a personal hero of mine since I read his dissertation. Last century, I read Robert Tilove's Disertation on Constructive Solid Geometry that was impressed me for being extremely clear and building up a whole research area. This century, I was amazed at the breadth in Dr. Conitzer's dissertation handling a whole area of combinatorial auctions and the remarkable clarity of his writing. I see the same quality of writing in the Communications of the ACM article on which I reported and his Journal of ACM(2) article!

Reference

1. Combinatorial Auctions edited by Peter Cramton, Yoav Shoham and Richard Steinberg, 2006 Massachusetts Institute of Technology Press
2. Conitzer, Vincent, Sandholm, Tuomas and Lang, Jerome, "When are Elections Hard to Manipulate" Journal of the ACM Volume 54, Number Three, Article 14, June 2007, 1 to 33.