Thoughtful Thursday, a second Review of Constitution for a Future Country by Dr. Martin Bailey

Martin J. Bailey, Constitution for a Future Country, part Two

In Chapter Four, Dr. Baylor pointed out--as I have long felt--that when a new government was forming, the leaders were only given the U. S. Constitutions or the parliamentary system to serve as a guide. There has been no improvement in government for two hundred years. He recognizes that a country does not throw out its old Constitution and put in a new one just because logic or economic theory or public choice theory says this one is better. But when there is a situation like the collapse of the Soviet system in Eastern Europe or Afghanistan forming a new government, the leaders of the transition might ask for help looking for a better way.

Dr. Baylor wrote this book in his dying days to provide that help. It is my goal to provide this help also, but in the form of computer programs. We simulate things on the computer before we build them, whether it be the finite element analysis of a bridge resisting the forces of winds and the trucks riding upon them or the robustness of a electric grid as loads change and generators or alternative power sources upon them. The people who must ratify a constitution should be able to simulate it. Just as a pilot practices emergency moves such as an engine stall in a simulator, the people must practice dealing with budgeting during a depression, handling a natural disaster like Katrina. And the judicial system must be practiced as well. How would a one-state solution to the Palestinians and Jews in the Middle East deal with a Palestian Police Officer shooting an Orthodox Jew or the other way? A Law Enforcement class might enact a trial to learn criminal procedure. The people will first vote on a judicial code under a trial constitution. Then, they will have whatever election process that would include for judges. Then the judges and the jury, if their constitution so provides, will try moot cases. This would definitely include staged charged situation of one ethnic group shooting a member of the other. If they can't do it in a mock trial--is there any reason to believe they could accept the results when it happens for real. And we should do it in the more quotidian cases such as those that one might see in Judge Wapner's People's Court.)

As an economist, Dr. Bailey is very concerned that government expenditures are handled efficiently. And he starts with Lindahl taxes. Each possible group, doctors living in Wyoming, wealthy financiers living in tony Connecticut towns, coal miners in Apalachia, single people, married families, will be represented by random samples from their numbers. These will be chosen randomly, what Dr. Bailey refers to as a stratified sample. They will each propose a tax to fall on their group proportional to their marginal benefit. Dr. Bailey that each group can be divided into other groups. But each division would be based on some objective criteria, such as gender, race, occupation group, income or the like.

And taxes would be either based upon property or income and have a tax schedule. The taxes would be categorized by budget category. Thus, there might be a property tax on automobiles to fund the highway system. The goal is to get a near unanomous vote. Also, every two years, there should be the opportunity to vote for a minimal budget for basic public safety needs--equivalent to the partial shutdown of the government that were used during budget stalemates in some states.

As each funding proposal comes through, citizens vote their uninsured harm (VCG taxes) and also can purchase Thompson Insurance for monetary losses. Dr. Bailey proposes limits of about ten to twenty percent of income for these. This means there is no way for a citizen to express extreme concern-- for example a pro-lifer expressing extreme concern about legalized abortion, or a Native American expressing extreme concern about a mine on a sacred burial ground.

And Dr. Bailey proposes a complicated formula for legislative pay which includes a variety of incentives. (See below.) The first is at the start of the public good chain. If their estimate of Lindahl Dr. Bailey believes that legislators should be sequestered like juries in major cases. They should only get information in an organized way through formal hearings and not emotional impacts. More importantly, there would be no way to lobby legislators. Legislator's wealth would be replaced by a mutual fund weighted like theinvestments of their demographic groups. Thus, a physician representing his fellow physicians would sell their investments and be given a set of investments that matches what an average physician has. Cumulanis' Constitution (that's what Dr. Bailey calls his hypothetical State) specifies that legislators shall vote the amount of money they and their family would pay to put through or stop a certain legislature.

And Dr. Bailey believes in referenda, anyone including corporatins can put a referendum on the ballot if they pay the costss including evaluation. Dr. Bailey calls for impartial statisticians to estimate the possibility of referenda passing--I guess after polling. If the odds are ten percent ormore Obviously, there are various technical correction bills that are not controversial. The statistical groupo could find which ones have a 95% chance of passing and these could be grouped in a single up or down vote. He furthermore proposes that referenda be voted on twice, with the first vote just to see if there is interest and requires 25 per cent of the vote. If a legislature makes a proposal rejected by 75 per cent of the people shall have the costs of the ballot deducted from their incentive pay.

Of course legislators have important roles, including determining the size of ebverybody's taxes--although with his mechanisms less of a role than currently. But many other jobs including the election commissioners that administer the non-trivial software systems, the statisticians are critical. And, what about those making decisions about deep oil drilling equipment. Or those administering large contracts for the government.

Dr. Bailey realizes that the VCG mechanism although a Nash equilibrium is not immune to collusion. Cumulanis' constitution simply says that attempt to organize voters to misrepresent their harms that would defeat the nice economic properties of VCG taxes is a felony! Dr. Bailey notes that under the bill of Rights, it is perfectly legal to encourage voters to vote strategically, e. g. a citizen could take out adds encouraging Republicans to cross over and vote in the Democratic Party and vote to nominate an extremely liberal candidate so the Republican party candidate wins.

Dr. Bailey believes legislatures should be paid on a contractual basis with the voters who are sovereign. Thus, every bill should have measures of success. The education bill should state that 70% of the children shall read at grade level for example. The legislature making the education proposal would be responsible for contracting out the education function and monitoring it. If the education system got only 65%--then any citizen can sue them. "The criteria for standing admissibility of suits shall be identical to those for suits against private parties as specified by the laws of torts and contracts." Now, who would have the right to sue here. Would I as a taxpayer or simply a citizen who cared that kids get a good education or a professor who felt that I want students who know how to read and write in my class have the right to institute a suit? (The Supreme Court has restricted this right. Taxpayers do not have the right to pursue a generalized claim that their funds are being mispent. Parents of a particular ethnic group could not sue regarding giving tax exempt treatment to schools that discriminated against their children. And lastly individuals could not sue on behalf of animals under the Endangered Species Act. A generalized claim that the person might not see the animal when they are traveling is not sufficient.)

In the same article, Dr. Bailey proposes mechanisms to make budget estimates more accurate and realistic. Each tax schedule shall have an estimate of how much revenue it will bring in. (And he provides for macroeconomic downturns that are not the estimator's fault.) Legislators cold be sued when their budget estimates were simply incorrect--presumably discouraging the budget shenanigans we say at the state and federal level in the United States. (I have pointed out that there are ways of organizing the budgeting structure constitutionally without budget estimates. One specifies the tax schedule and whatever it brings in is what that government has. Also, one can specify an expense and the people who shall bear it. They compete on a goodness or badness basis before sortition jurors to determine who should pay it. For example, the car owners shall be required to pay for the highway expenses. Each goes before a tax sortition juror and pays a tax based upon how safe they drive, how much they needed to drive (those who lived on a farm out in the boonies might have no choice but to use their vehicle and the sortition jury would assign them a small share of the highway taxes. But someone who might use their vehicle when the Greyhound bus went where they needed to or who drived for vacations.)

One can also use approval voting to determine expenditures. That which 100% vote for gets funded first, then what 99% vote for, etc. The tax schedule brings in whatever it brings in. The things wanted by the most people gets funded first.

Thompson Insurance

A street project would improve the value of some people's property. It would lower the value of others. Every proposal would be associated with a Thompson insurance. The first parties could take out insurance against the proposal failing. The other parties would take out insurance against it passing. A neutral government body must offer this. Dr. Bailey cited work in the law and economics literature that insurance really doesn't work for intangibles such as pain and suffering. And a majority could keep proposing the same thing, bankrupting a minority. That is if the majority might keep proposing the mine on the ethnic group's grave field. The ethnic group would take out insurance against the bill passing, defeating it. However, they would eventually run out of money.

Thus, this really does not deal with the pro-life individual concerned about legalizing abortions or the pro-choice concerned about a proposal to restrict abortion. Dr. Bailey's constitution would have would have limits that would not allow a person to declare the severe harm for their ethical sensibilities. Dr. Bailey realizes this and he says that his mechanisms could not handle it. He says, "The performance of a country with our proposed constitution could be almost an arbitrary and capricious on this issue as the ... United States has been. That is a pity, and if the reader can think of a constitutional order that would arrive at sound policy on such issues more reliably than that proposed, please publish it." I have an idea--and will be posting it shortly here. I should also mention Dr. Bailey's concern about entry into war on spurious grounds. He mentioned the Gulf-of-Tonkin resolution that got the United States escalated in the Vietnam war and the less-disastrous Spanish American war. This book was published and Dr. Bailey passed away before the entry into IRAQ, a situation that has been compared. And Dr. Woodruff discussed the problem in the Greek invasion of Syracuse. system. (I proposed a solution of waiting to reward our statespeople and military leaders.)

Appendix -- Incentives for Legisltuares

Section Eleven includes detail for all legislators. Here are some of the formulas to give a flavor: "0.1 percent of the budget amount contained int he proposal plus thirty percent of the total declared insured and uninsured harm from non-adoption, net of the declared harm from adoption, relative to the next most valuable distinct and differeent proposed by another legilature, less five percent of the net inferiority of these proposals, relative to distinct and different alternatives of the ballot, for each population that on net would have supported an alternative proposal int he group, under the legislature's proposed taxes and accurate taxes for the alternative."

Thoughtful Thursday, Lindahl Equilibrium

We use the concept of marginal benefit and total benefit from a public good. The classical situation in public goods analysis is security guards in a coop. (Or on a national level, the number of Poseidon missiles, Buchanan) Each cooperator is asked how much would you pay, or how much is it worth to you, if there were one security guard, two security guards, three security guards, etc. the question then, is how do we take this information and decide:

1. how many security guards to hire
2. how much to charge each cooperator.

Some coooperators might want more security guards and pay for all of them. Yet all cooperators will have the benefit, even if they don't actually care, of whatever protection the security guards provide.

In the table below we show what each cooperator says is ther total benefit. Dr. James M. Buchanan talk about this type of schedule in Chapter Two and Three of his book, Public Finance in Democratic Process, (on which I hope to have one of my next Thoughtful Thursday series).

Number Security Guards	Citizen 1	Citizen 2	Citizen 3
0	7	8	9
1	12	15	11
2	17	21	13
3	22	27	14
4	28	33	15
5	32	38	16
6	36	43	17
7	40	48	18
8	43	52	0
9	45	55	0
10	47	58	0
11	48	0	0

We compute the marginal benefit, which is the benefit from each new security guard. Which is simply the amount of benefit they get from each additional security guard. Or how much they would pay to have one more security guard in their cooperative.

Number Security Guards	Citizen One	Citizen Two	Citizen Three
Security Guards	1	2	3
0	5	7	2
1	5	6	2
2	5	6	1
3	6	6	1
4	4	5	1
5	4	5	1
6	4	5	1
7	3	4
8	2	3
9	2	3
10	1
11
12
13
14
15
16
17
18
19

For example, when citizen three goes from paying nine dollars to eleven dollars, that is a difference of two dollars.

My program reads in these tables and computes the second. It reads from the keyboard the cost of a secuirty guard. When I entered the cost of five dollars, the program says that we should buy eight security guards. If we add the marginal benefits for eight security guards (2, 3,0) adds up to five. That is the answer to the first question. Under Lindahl Equilibrium we divide the total cost for eight security guards proportional to the marginal equilibruium at that ponit so Citizen One pays sixteen dollars and Citzien Two pays twenty-four.

If we entered twelve for the cost of one security guards, the program tells us that the Citizen One pays ten dollars, Citizen Two pays twelve dollars and two dollars for the Third Citizen. (Notice that this doesn't quite add up to fourty-eight. Our program does not divide the integer to the cost.

We have two citizens, whose benefits from the public good can be read from the two figures below. That is citizen A gets ten units of benefits for one additional item going from zero to one item down to zero units of benefit after the fiftieth item and intermediate five units of benefit after twenty five item.

Citizen B gets 30 units of benefit for the first item, but gets no more benefit after twenty units.

Assume that it costs twenty dollars per unit. then, we read from the curve that the city shoudl get twelve units of benefit. At twelve units of benefit, we read back from the individual citizen curves that Citizen B should pay 10.5 per unit of benefit and citizen A should pay eight units of benefit.

Calculating this out, that meens that citizen Two would pay $126.00 in tax for this public good and citizen One would pay ninety six dollars in tax.

Within margin of error from reading things graphically, that is close to the $240.00 that it actually costs.

I like to use Maple to do my economics calculations. It becomes much clearer and more precise than diagrams. More importantly, I make so many stupid algebraic/arithmetic errors I cannot get the right answer on problems in engineering, physics, etc. I found the solution, at least for homework, is to do the calculations in a symbolic math system like Maple. Last century, my research area was symbolic math in Mechanical Engineering Computer AIDed Design. It was the topic of my Ph.D. dissertation. When I had an engineering course, I used symbolic math to do my homeworks.

One can plot the marginal benefit of each additonal unit as a function of quantity for a particular user. Or, how much would they pay if that was sufficient to get the government, the public at large, to supply one more acre of farm land. For user One, we have (blogf.jpg) -Q + 40. BlogF.jpg

This idea came from Hyman's book but was far better explained by my Public Fianance Professor, Dr. Warren Jones, who arranged for a Summer videotape class. To keep things simple, we assume each user has a linear curve that ends when it crosses the x-axis, or in the computerese we say that the demand for User One that the max (-Q + 40, 0). This example has two other citizens. The formula for Citizen Two is max (0, -Q/2 + 30) and the formula for the Citizen Three is max (0, -Q/3+30). These three graphs are shown in (blogg.jpg). BlogG.jpg BLog H.jpg BlogI In Lindahl equilibrium, we sum these marginal curves (blogh.jpg) and (blogi.jpg). Assume our good costs twenty dollars per unit. I asked Maple to solve for this function (blogi.jpg) and twenty, and we get fourty-eight units purchased. At this number of units, Citizen One, function F1 pays nothing-- substitute Q=48 into the equation for Citizen One (max(-Q+40,0)). Plugging into F2 and F3, we see that Citizen Two pays six dollars and Citizen Three pays fourteen dollars per unit.

Lindahl Equilibrium is a metric of success for an algorithm and voting procedure to determine the tax rate for each group of citizens. I described

And blogG.jpg shows the curves for Citizens One, Two and Three.) Assume that is the netire public. The total demand for the units of parkland is given by BLOGH.JPG as a sum of these curves, and alone s blogI.jpg

If we assume the cost of an acre of parkland in our city is always twenty units, we can ask Maple to solve for us to find out how much we will buy. (48 units)

Genetic Algorithms (Thoughtful Thursday Post)

In genetic algorithms, one represent information as a Chromosome, a series of values. E. G., assume we are optimizing a gas pipeline, that has five pumping stations each with a pressure differential and we have five pipe diameters between them. Thus we would have for two possibilities. I will refer to them as Configuration A and Configuration B.

P(1) P(2) P(3) P(4) P(5) D(1) D(2) D(3) D(4) D(5)

300  200  150  75    80   1.2  1.5  1.3  2.2  3.3

P(1) P(2) P(3) P(4) P(5) D(1) D(2) D(3) D(4) D(5)

275  300  125  140   140  1.8  1.2  1.4  2.1  3.1

This might represent the following real world configuration where the p(1)..p(5) in boxes are the pressure of the pumping stations and the d(1) to d(50 are the diameter of the pipes:

                           d(3)
_____      ______    _____   _____     _____
|    |d(1) |    |d(2)|    |  |    |d(4)|    |d(5)                               
|P(1)|==== |p(2)|=== |p(3)|==|p(4)|=== |p(5)|===
|    |     |    |    |    |  |    |    |    |                             
_____      ______    _____   _____     _____

The most important operation is crossover, where two possible pipleine configurations "mate" and produce two offspring. The system randomly chooses a point in the chromose, and the two mates get switched at that point. Assume the random number generate says cross over after D(2). The two children in the next set would be:

P(1) P(2) P(3) P(4) P(5) D(1) D(2) D(3) D(4) D(5)

300  200  150  75    80   1.2  1.5  1.4  2.1  3.1

P(1) P(2) P(3) P(4) P(5) D(1) D(2) D(3) D(4) D(5)

275  300  125  140   140  1.8  1.2  1.3  2.2  3.3

The second important operation is fitness evaluation and preferring high fitnesses. In the pipeline scenario, this fitness would probably the inverse cost. Thus, assume the two original configurations had costs of $100.00 and $75.00. Assume that there were two other configurations, call them Configuration C and Configuration D, with costs of $300.00 and $150.00.

The genetic algorithm uses random number generators to determine the chance of each configuration mating and thus contributing to the next set of chromosomes, the population in the terms of the Illigal algorithms. Then configuration B would have four times the chance of mating as C and D would have half the chance of mating as configuration C.

Application to taxation and budgeting

In our project, the chromosome will include the various tax rates. These are the marginal tax rates for each quintile of income (with a few special ones for the richest.

R(1) - tax rate for those in the bottom twenty percent of income
R(2) - tax  rate for those in the twenty to fourty percent of income
R(3) - tax rate for those in the fourty to sixty percent of income
R(4) - tax rate for those in the sixty to eighty percent of income
R(5) - tax rate for those making between eighty to ninety-five percent
       of income
R(6) - tax rate for those making between ninety-five percent and
       ninety percent of the income
R(7) - tax rate for those in the top one percent of income

And then, we have the budget amounts, how much to be spent on:

R(8) - social security
R(9) - defense
R(10) - education
R(11) - medicare
R(12) - transportation
R(13) - agriculture
R(14) - aid to low income families
R(15) - training labor and unemployment
R(16) - international affairs

Schemata

David Goldberg's book very nicely explains schemata (Genetic algorithms in search, optimization, and machine learning / by David E. Goldberg. Published: Reading, Mass. : Addison-Wesley Pub. Co., 1989, which is where I got the information in this article ). Schemata represent that we have chosen several fields. The other's have not been chosen yet. In our first example, the schemata

P(1)=300 * * * * * D(1)=1.2 * * * * *

represents a specific value for the pressure in pumping station one and a specific value for the pipe to its right. The schemata,

P(1)=300 P(2) = 200 * * *  * * * * *

represents all the possible configurations with pumping station one having pressure of 300 and pumping station two having pressure of 200.

In crossover, which schemata is most likely to be disrupted by the crossover which occurs each cycle, it is the first with about a fifty percent chance of getting disrupted. The second schemata has only a ten percent chance of getting disrupted as of the ten possible divisions only one will disrupt the schemata.

(These are approximations as most genetic algorithms use scaling to get better performance to prevent random variations that happenn to fit from dominating in the early stages and to magnify differences for fine tuning at the end of the optimization, but that doesn't concern the main idea of what we are doing in social choice.)

In taxes, schemata might represent

R(1) = 0.1 R(2) = 0.2 * * * *  * * * * *  * 

The tax rates forthe two lowest income quintiles thus constitute a schema, and since they are next to each other on the chromosome, they would be most likely preserved. On the other hand, a relationship between the tax rate on the lowest quintile and the money for welfare (aid to low-income persons) would not likely to be preserved. , e.g.

R(1) = 0.1 * * * *   * * * * *  * * * R(14) = 10.0E6 *  *

That is because the first is on R(1) and the second is on R(14). Practically every cross-over will ruin this connection.

There are two other operators, mutation, which is randomly changing one value in the chromosome and inversion which is changing the order of operations. In this space, we could allow individuals to make proposals of new chromosomes or changes. Mutations thus introduce new possible budgets into the mix.

An interesting twist would be to proceed the genetic algorithm by a process where individuals give their degree of associativeness between two characteristics. This would be a pseudo-inversion.

MR. Lessard, a graduate student in our department, has started two programs in that direction: He implemented a web system for the above genetic algorithm.

1. After logging in and do "informed consent" stuff, the participants enters their ideal budget. Thus, the initial population consists of everyone's ideal budgets.
2. When the system has everyone's ideal budget (or at least from enough people), it will cross them over. Each of these will be presented for rating.
3. The users will rate five budgets each.
4. The system will do cross over on the results. These will be based on the fitness ratings in step three.
5. Return to Step Two

Simulation of the strategic behavior will start from the software provided The second step will be a simulation starting from the University of Illinois Library. I have marked the modifications so that we can test strategic behavior. What happens if one or two sets of raters don't give their honest rating, but attempt to give (strategic behavior in the game theory and algorithmic mechanism design literature) a rating that is more likely to have them end up with a budget more to their liking.

Of course, a more basic question is whether the genetic algorithm will converge to a Lindahl Equilibrium. Thus, the first experiment will be to run the genetic algorithm with no strategy. The fitness chromosome will simply the taxation for each group. Each group will have a linear fitness function to give the d U / dTax = M * Tax + b where U is the utility. Each group will be assumed to rate the tax level proportional to the total benefit it receives from the total tax revenue. Thus, the benefit is the integral of the above function up to the total tax on all groups. Then, we will try strategic voting and a genetic algorithm where the chromosome represents a tax which is a piecewise linear function of the Income.

(I really appreciated the lecture of Dr. Warren Jones of this University on Lindahl Equilibrium when I took his Summer Public Finance course. It is on my to do list to write a more detailed Thoughtful Thursday piece on Lidnahl Equilibrium. The next best is the presentation in David N. Hyman, Public Finance, Fifth Edition page 136 to 144,)