Jurors doing their own research

It is probably well known that jurors should not independently research the case and evidence presented before them in a trial. Just to make that clear, four jury verdicts were overturned on appeal because a juror did just that--using the internet.

Thanks to the Juries Blog, which I follow, for the lead to this excellent story.

Corporations Running for Congress, Courteous Logic Programming

A corporation is running for Congress in a tongue-in-cheek satire of the Supreme Courts' recent decision allowing corporations to have frankly political ads. If a corporation is a person, why can't it run for Congress?

All kidding aside, if a person can have several representatives, each with different priorities, why can't some of these be organizations. I believe Grosof's courteous logic programming is the basis for that. This allows one to deal with different people creating different rule sets. Each might have a different priorities. Each voter would have several represenatives. Each voter would assign a priority to each represenative. Legislation is a set of rule sets. When they conflict, we look at which representatives voted for each and combine them based upon the priorities they gave them.

In the proposal, many individuals would give their employer as a representative, as they are concerned that it is prosperous. They would also give various entities such as the Sierra Club, their Church, etc. a vote. And they would give a priorities (One could see one giving their Church first, then their employer, and then the environmental group to which they felt most attached.) And, of course, on any bill, one could vote oneself. Thus, the system would extend to try participatory democracy, but only on those bills which one cares enough to read for oneself.

I have played with how to to combine the votes using Dr. Grosof's work. (This will be a subject of another Thoughtful Thursday Posting.)

Conspiracy Theory Aaronovitch Voodo Histories

NPR reviewed Aaronovitch, Voodoo Histories: The Role of the of the Conspiracy Theory. He shows that many people believe in conspiracy theories but are not "wackos." And many of the conspiracy theories have influenced history--In the 1920's the Protocols of the Elders of Zions was popular. The Times of London had an strongly positive introduction to this, but a year later found the evidence to debunk this.

Mr. Aaronovitch also said that a significant portion of the educated Pakistani's believe 9/11 was a hoax put on by the Bush Administration. A former President of Malaysia, Mahathir Mohamad, was in favor of this and said that if the country could make Avatar, they could create this conspiracy theory. The Wikipedia article on 9/11 Conspiracy Theories is very helpful on this subject.

I will put his book on my list of books to review for a Thoughtful Thursday post.

Obviously, one must be concerned about any democracy whether it be participatory of otherwise, when people believe things that are not true. However, I have found no evidence that a participatory democracy would be more affected than a conventional one where demagogues could whip up the frenzy.

Thoughtful Thursday: The ID3 Machine Learing Algorithm

ID3 is an algorithm to generate a decision tree from a set of examples. It is used in machine learning.

Many legal codes are some sort of function of several parameters and are of a nature that can be defined as a decision tree. For example, one is making the gun control law. Some of the parameters might be the type of gun. (Is this a BB-gun, an antique gun, a non-functional gun, an assault gun, a pistol, etc?) Is the weopon concealed? And there are the characteristics of the owner of the possessor. Are they mentally ill, convicted of a crime, have an order of protection against them, etc. Was the person's life threatened? Does the person job need it, e. g. security guard. And lastly, what is the place: a school, bar, a place where beer is sold such as some supermarkets.

The answer could be a simple boolean, "permitted" or "not permitted" Or we could get a classification such that the possession might be a misdemeanor or a felony. Many states have categories for felonies. For example, in the State of New York, a class A felonly, the term is life imprisonment, for class B, the term for a class B felony does not exceed twenty-five years, etc. (There are other special rules for dispositions, such as those who have prior convictions or are youthful offendors.) Then the bulk of the penal code defines offenses to be a class D felony, a class B felony, etc.

A possible decision tree

Gun Type	Location	Age	Personal Status	Penalty, if any
antique				No Offense
BB Gun				N Offense
Pistol		15-20		A Class Misdemeanour
Pistol		20-30		B Class Felony
Pistol		30-50		Felony
Pistol		50-70		A Class Misdemeanour
Rifle	Bar			Class B Felony
Rifle	Schol			Class C Felony
Rifle	Place where Beer is Sold			Class A Misdemeanour
Rifle	other			No Offensse
Assualt				Class B felony
Rifle	Other		mentally ill	Class D Felonly
Rifle	Other		Convicted of a Felony	Class C Felony
Rifle	Other		Other	Class B Misdemeanor

An ID3 algorithm would take a series of examples such as the one in the table above. It would create a decision tree that would give the same answers as the examples. It needs to pick which parameter to use for the root node--in the above tree, it was Gun Type. It picks one that divides a lot of examples between thee categories. Often the formula from information theory is used. In the above example, the tree was precisely determined from the input data. That is not always true. In a diagnosis application, there would likely be lines that contradict each other. Or there would might be several lines with very similar attributes. All might have the same classification or penalty, except one. Is that due to a real difference, or just a random error?

A	B	C	D	Result
1	2	3	44	ii
1	2	4	44	ii
1	2	5	44	ii
1	2	3	45	ii
1	2	4	45	ii
1	2	5	45	ii
1	2	3	46	ii
1	2	4	46	ii
1	2	5	46	iii

There is a danger of overfitting when there are lots of examples. Thus, a pruning process removes those divisions that don't have much information gain.

Mr. Yeluri set up an example to illustrate these ideas. Since it is long, I put it at the end in an appendix.

In participatory democracy, we do it a little bit differently. For each node in the tree, the users vote on what the next parameter should be. Thus, at the start the individuals would vote on which of the above questions regarding place, type of gun and person should be asked first. Then, the group for each resulting category would be classified again. The individuals can vote to decide for any node when it comes up to classify it once and for all. E. G., if the category of assault weopon shows up, individuals might vote to always ban it and for the category of BB-gun, they may vote not to consider any other factors and always permit it. This is a leaf node and the people will then vote on the classification from the possibilities available.

We established the following terminology, for the input to our experiment:

title

a thing on which one chooses, like gun type

attribute

one of the possibilities for a title thus gun type could be antique, bb, assualt, rifle, assault or shot gun

node

this corresponds to series of pairs of parameter and type.

for example, the voting might bring us to making a decision on what to do with those caught with an antique guns, a history of mental illness, and who are sixteen to twenty years old. This is a list of title (nature of gun) and type, antique, mental illness status, and type of history of mental ilness and age, which is divided into types or ranges. this is defined as

of root node

age top of the tree which coresponds to no titles and parameters selected so far.

The voters first vote on which title to choose as the root parameter. Then, they vote for each attribute of that title, how next to classify it. as ech of thse achieve quorum, each of these nodes becomes accessible, that is, the voters might vote on what title to use for gun-type= antique, choosing from the remaining titles of personal status, age range, location. then, they vote on what title to use for gun-type="bb" gun-type="pistol" gun-type="rifle" gun-hattype="assault." Each creates a new node which is marked accessible; and individuals vote for each in turn. One of Masters students, Mr. Chaitanya Yeluri, just implemented this. More details are in his masters project.

After the root node, the users can assign a penalty. Observe in the figure that we immidetely assign "no offense" to those possessing antique guns. on the other hand, there arthree levels until we get to gun type ="rifle",m location="other" and "mental health status" = "felony conviction." at each node, the users have the option to "vote now" and if that gets more votes than any title, the users vote on a penalty for same.

How would we apply this to tax law? The ID3 algorithm is not designed to deal with cases that produce a continuous function, like the amount of tax that the taxpayer should payer. (Note, ID3 is used when there are input parameters that are numeric. The algorithm sorts the examples in numeric order of the parameter. It then finds the decision pont that gives the greatest information theory gain.)

Thus, for a tax system by ID3, at each leaf node, there would per be a formula. The titles in a tax problem might be various income ranghe atues, the number of children, marital status. And then the users might vote for those unmarried head-of-household with three children and in the range $20,000 to $40,000 to make the tax = $500.00 + 0.10*(Income - $20,000). That is $500.00 on the first $20,000 plus ten percent of the remaining income. They might put other components of the formulae in for the amount of state tax they paid, the mortgage interest, etc.

Reference

, Quinlan Ross, Programs for Machine Learning, Morgan Kaufman, San Mateo CA 1993

Appendix, The Information Theory Formula

We have three titles, A, B and C. The possible choices, or parameters for each of these are:

A	F, G, H
B	I, J, K
C	M, N, P

Assume the input examples are:

A	B	C	Classification Yes /No
F	I	M	N
F	I	N	Y
F	I	P	N
G	I	M	N
G	I	P	Y
G	I	M	N
G	I	P	Y
G	I	N	Y
G	J	M	Y
G	J	P	Y
F	J	M	N
F	J	N	Y
F	J	P	Y
H	I	N	N
H	I	N	N
H	J	N	N
H	I	P	Y
H	J	M	Y
H	J	N	N
H	J	P	Y
H	K	M	N
H	K	N	Y
H	K	P	Y
F	K	M	N
F	K	N	Y
F	K	P	Y

The information content of the entire sest is 0.3149. We try classifying it on the basis of A, and we get an information content 1.3328. And it happens by coincidence that if we tried B for the root node, we also get 1.3228. (The three nodes for a would have been:

A	B	C	Classification Yes /No
F	I	M	N
F	I	N	Y
F	I	P	N
F	J	M	N
F	J	N	Y
F	J	P	Y
F	K	M	N
F	K	N	Y
F	K	P	Y

giving an information content of 4/9 log ₂ 4/9 + 5/9 log ₂ 5/9.

A	B	C	Classification Yes /No
G	I	M	N
G	I	P	Y
G	I	N	Y
G	J	M	Y
G	I	M	N
G	I	P	Y
G	J	P	Y

giving an information content of 5/7 log ₂ 5/7 + 2/7 log ₂ 2/7.

A	B	C	Classification Yes /No
H	I	M	N
H	I	N	N
H	J	N	N
H	I	P	Y
H	J	M	Y
H	J	N	N
H	J	P	Y
H	K	M	N
H	K	N	Y
H	K	P	Y

giving on an information content of: 5/10 log ₂ (5/10) + 5/10 log ₂ (5/10) .

By comparison, the sample sets for classifying by C are:

C="M"

A	B	C	Classification Yes /No
F	I	M	N
G	I	M	N
G	J	M	Y
F	J	M	N
H	I	M	N
H	I	N	N
H	J	M	Y
H	K	M	N
F	K	M	N
G	I	M	N

And, if we tried to split this by A, we would have:

A	B	C	Classification Yes /No
F	I	M	N
F	J	M	N
F	K	M	N

A	B	C	Classification Yes /No
G	I	M	N
G	J	M	Y
G	I	M	N

A	B	C	Classification Yes /No
H	J	M	Y
H	K	M	N

giving a total information content of 0.6438. If we split C="N" by B

A	B	C	Classification Yes /No
F	I	N	Y
G	I	N	Y
F	J	N	Y
H	I	N	N
H	J	N	N
H	K	N	Y
F	K	N	Y

Then, there are two possibilities breaking it down by A

A	B	C	Classification Yes /No
F	I	N	Y
F	J	N	Y
F	K	N	Y

A	B	C	Classification Yes /No
G	I	N	Y

A	B	C	Classification Yes /No
H	I	N	N
H	J	N	N
H	K	N	Y

This gives us an information value of 1.5579.

Or we can split it by B, giving us:

A	B	C	Classification Yes /No
F	I	N	Y
G	I	N	Y
G	I	M	N
H	I	N	N

A	B	C	Classification Yes /No
F	J	N	Y
G	J	P	Y
H	J	N	N

A	B	C	Classification Yes /No
H	K	N	Y
F	K	N	Y

This gives us an information value of 1.6253.

The resulting tree chosen would be given by the below:

Patient Copyas and Encouraging Efficiency.

Patients who have to pay more for the doctor do visit the doctor less! They also end up in the hospital more.

So much for using patient copays to reduce patient costs.

See our four-part participatory democracy framework to reform health care. The last part is the doctors are paid on the basis of the service they provide, after they provide it.

Corporate Democracy a Cure for Political Contributions

A cure for corporate political contributions is to requrire them to be approved by shareholders-- Britain does this. And, of course, shareholder approval has also been suggested for approving executive compensation.

But proposed here in a share economy, and where sortition juries of share holders approve all expenditures. This helps prevent slippery definitions from allowing perks to go through. It does not single out speech for special attention will probably upset first-amendment purists. It simply says that a randomly-selected set of jurors, weighted by the number of shares they own, must approve each and every expenditure. This would do wonders for many accounting controls!

Senate Fillibuster and conversion to a Referendum Requirement

On the Media had a show about the fillibuster. The media simply treats the fact that sixty votes are necessary to stop a fillibuster in the Senate as a given. Legislation needs sixty percent to pass the Senate--of course, this is not in the Constitution, it is simply a rule of the Senate, which can be changed. (Each house may determine the Rules of its Proceedings", Article One Section Five)

But the answer is not to get rid of the fillibuster. it is simply to say that fourty percent of one house or the other can propose a referendum. I proposed this in the second sentence of my second post in this blog. Note, that if there are several related proposals they would be resolved by approval voting.

And Congress can do this, I believe, without a Constitutional Amendment--although that would make it bullet proof. The United Supreme Court has required that Congress provide some standards in delgation of powers. And in Clinton versus City of new York, the Supreme Court stopped a line-item veto to the President. The question is whether this proposal, a delgation back tot he people is an unconstitutional delegation of powers. I would argue that there is a very definite standard, simply counting the number of votes of the populace.

Solve the Campaign Finance Problem by Getting Rid of the Campaign

Probably all the readers have heard that the American Supreme Court has ruled that corporations can campaign for or against candidates for election, but they still cannot contribute directly. Both Daniel Shor, senior columnist of NPR and the President of the United States, Barak Obama, have said this undoes a century of campaign reform.

I propose several reforms of the campaign, not the financing of itself. Many of these, although dramatic in effect, can be done without a Constitutional Amendment. (Although I see no reason not to attempt an amendment of the Constitution.)

1. Allow a random selection of individuals to do the voting for office holders. This would be large enough to avoid brib4ery and to provide a random sample. But it would be small enough that a candidate for congress, senate, governor, etc. could contact all of them at reasonable cost. Possibly they could even visit with all of them at reasonable cost. (If we assume a group of one thousand voters making the decision, at 200 hours per month, a congress person candidate could visit with each of them for one month in a five month campaign.) Article One, Section Four of the United States Constitution provides that "Congress may at any time by law make or alter Regulation determine the Time, place or manner of holding the elections for senantors and representatives." So this can be done by Congress, or even in a specific state.
2. Of course an alternative is to simply randomly select the House of Representatives
3. Or, perhaps we could have three houses, the first two being our house and senate and the third being chosen by sortition
4. But perhaps, the most radical idea is to have two elections, the first in each state would decide how to decide. The second would be the actual election for whatever percentage the voters in that state decide should be elected and not chosen by sortition.

Individuals would vote what percentage of their state delegation would

1. be elected in the conventional manner, from geographically-based districts
2. elected at large
3. chosen by sortition as described by one above. That is modest-size randomly-selected groups would elect the representatives as described above.
4. selected randomly

Particularly, for small states, Conress would have to increase the number of representatives. Our Constitution allows Congress to have one representative per thirty thousand population. Wyoming, our smallest state by population, has 544,270 population and would choose eighteen people. This would be a reasonable number, allowing a few to be selected by each of the above such mechanisms, based upon the votes of the population.

But California would send a whopping 1192 representatives instead of the 53 they now do. (Many people would consider this unwieldy.) The solution would be to allow a single CongressPerson to represent many districts if they can achieve the popularity. Thus, the larger state delegations would consist of a few popular mega-congress persons that would have have tens or hundreds of votes out of a total delegation of a thousand individuals. The popular congress persons would be pretty much guaranteed being returned to Congress. They would campaign to get more votes. There would also be those representing what most would be considered fringe ideas or groups and a few new people starting out, getting 30,000 or 90,000 votes in their first campaign and hoping that leads to being a mega-congressperson one day.

This would also encourage more competition for safe seats. Each mega-representative could increase their number of votes by getting a few more votes than they did last time. Safe seats are a problem in many countries and voters don't have an opportunity to have a meaningful voice. For our readers who are United States voters, imagine being one of the twenty percent republicans in certain urban congressional districts that have voted democratic for many years. Major Owens in New York's Eleventh congressional District, my mother's old district, won relection with over eighty five percent in every election from 1998 to 2006. But the problem is not confined to the United States. Canada has safe seats with 75% for the incumbent and Australia has a safe seat with the incumbent getting 67.7% voter and the rival getting 12.5% of the vote.)

In the same participatory democracy spirit, we can allow the states to determine the minimum size for a representative. There would be a trade-off. On one hand a state would allow minority viewpoints to be heard and new candidates to make a start by getting 30,000 votes and a seat in the House of Representatives. On the other hand, such a state would probably have a few embarassments. If Texas, New York and California all allowed representatives who would be seated with merely 30,000 votes, I am sure one of them would seat a Congressperson from the Nazi party.

I will discuss Proportional Representation in another post.

referndum determining tax rates

Oregon is having a referendum on a tax targeting those earning over $125,000.00 in taxable income and another tax on corporations. Polls show they will win but the margins are going down.

I have a thoughtful Thursday post queued for January 28th on using ID3 to select among other things a tax code. And I discuss applying genetic algorithms to determing tax codes and budgets.

I believe that voters should vote on a regular basis, not from time to time via referndum, on the rates for each tax bracket and for, at least the major classes of taxes (property, corporation, individual, sales and excise taxes.) The votes of rates should be combined by median. (median has a role in median income.)

Executive Bonuses and Compensation

NPR had a good discusion of executive compensation particularly those at investment banks such as Goldman Sachs, particularly from the point of view of stock holders.

Relatedly, the AARP Bulletin in its Jan Feb 2010 issue ( Volume 51 Number One Page Six)said:

In 2008, the top five hundred S&P companies put
44.5 billion into stok grants and options for their top execf
39.5 billion to pension funds
Financial service companies the ratio was $2.30 to top executive stock options to employee fund contrivutions.

Boards of Directors are not necessarily aligned wit the long-term share holder--some are paid by management. (One interviewee referred to this as an oligarchy that has hijacked the statement.) We have propsed two solutions here:

1. Sortition democracy where the stock holders can approve financial decisions directly. Every payout (including executive) is approved by a sortition jury of the share holders. Thus, if A is a pension holder or 401B holder in Company X, then there is a probability proportional to the number of share sthey indirectly own that they would be asked to sit on a sortition jury.
2. Executives should not be able to spend the money in their bonus until quite some time after the executive had joined the firm and become a senior executive. That way one can know the long-term results of the payment.

The Icelandic president refused to sign a bill to pay back a bailout from England and Netherlands. He received a petition signed by a quarter of the population. There will be a referendum. There is a question whether it is necessary to just to agree to pay the bill so that it can move on and so it maintains its economic reputation.

People say that Iceland should go away from "neoliberal greed" to its Nordic values. Some question whether a compromise wioth what was originally negotiated at the time of the bailout will avoid the referendum.

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)

Excise Taxes and Fees versus general Taxation

At the beginning of the year, NPR has a good summary of States choosing specific taxes versus a general tax increase like a n increase sales tax across the board or a property tax increase. Of course, the alternative is a unique tax for each item, determined by sortition jury. This was the first posting I made to this blog.

Data-Driven Administration

NPR had a great presentation summarizing Obama's use of performance-base decision-making and the pro's and problems with this technique. I believe a combination of numbers and anecdotes will provide the best input to a participatory democracy sortition jury making decision on individual performance and on voters.