AUTOMATIC EFFECTS CAUSE DEFICIT SPENDING

People rant and rave that the Congress can't keep the budget balanced. They blame political interests for causing the deficit. There is another force at work here. It is an unseen force, straight from the world of probability mathematics:

ITEM-BY-ITEM SPENDING

Assume a 9-member city council, where each councilman gets an equal vote. Let there be $100,000 available to be spent, and suppose there are enough small programs vying for that money that they total $120,000. Also assume that each councilman analyzes the available budget items before the meetings, and randomly decides what items to vote for and against. Let's look at a typical budget process, and what goes wrong:

• Each councilman gets a list of these spending items. From the list, the councilman picks a list of favored items totaling $100,000 (a balanced budget).
• Each councilman votes for the items on his/her own list of favored items, and against the items not on his list.
• Each budget item comes up for a separate vote.
• Since only 5/6 of the items can be funded, the probability that any councilman votes for any one item is 5/6.
• More than 5/6 of the items pass, creating deficit spending.

How can this be? The answer is that the probability of an item passing is NOT 5/6.

Here is an analysis of the probability of a budget item passing the council. Since each councilman chooses randomly, the probability an item passes is found using the Binomial Distribution on a simple majority vote:

SUM [C(9,x) * (5/6)^x * (1/6)^(9-x), for x = 5 to 9] = .99065.

Google the Binomial Distribution to understand this probability function.

Use the mean of a Binomial Distribution to find the number of items that pass. Multiplying the budget by the probability of passing approximates this. If each item has a .99065 probability of passing, then the budget will be overspent, because $120,000 times .99065 is $118,878, or $18,878 over budget.

Another way to see this is to look at the votes in a table: Green values are within budget. Red values are over budget:

Even though each councilman planned for and voted for a balanced budget, the government overspent. Hence, these conjectures follow:

ALL of these conjectures assume a simple majority vote is taken on each budget item in sequence:

• SPENDING CONJECTURE #1

  If the amount of proposed spending is between 1 and 2 times the available revenue, and if all legislators plan all votes in advance for a balanced budget, then deficit spending will occur.

  Notice here that the probability of a "yes" vote is between .5 and 1.

• SPENDING CONJECTURE #2

  If the amount of proposed spending is between 1 and 2 times the available revenue, then the first items voted on have a higher probability of passing, if all legislators change votes to ensure a balanced budget.

  Note that as the budget fills up, the probability of "yes" votes goes down.

• SPENDING CONJECTURE #3

  When the amount of proposed spending is between 1 and 2 times the available revenue, the proportion of the budget overspent increases as the number of legislators increases.

  The Binomial Distribution becomes less varied as the number of trials increases.

• SPENDING CONJECTURE #4

  When the amount of proposed spending is over twice the available revenue, almost no spending will occur, if all legislators plan all votes in advance for a balanced budget.

  Notice here that the probability of a "yes" vote is between 0 and .5. (Of course, this works only until they notice that this happened.)

• SPENDING CONJECTURE #5

  When the amount of proposed spending is over twice the available revenue, the last items voted on have a higher probability of passing, if all legislators change votes to ensure a balanced budget.

  Note that as the budget does not fill up, the probability of a "yes" vote goes up.

• SPENDING CONJECTURE #6

  When the amount of proposed spending is less than the available revenue, all legislators will add projects to the budget until the amount of proposed spending is more than the available revenue.

  Here, the probability of a "yes" vote is exactly 1.

• SPENDING CONJECTURE #7

  When a bicameral (two house) legislature votes on each spending item separately, the probability the item is included in the budget is the product of the probabilities of the item passing each house.

  This is the original intent of the US Constitution.

  In the above example, if both houses have 9 members, then each house will have a probability of passing the item of .99065. So both houses together will have a probability of passing the item of:

  .99065 * .99065 = .9813874225

  This is better, but still way too high.

OMNIBUS BUDGET BILL SPENDING

If an omnibus spending bill is prepared in advance by a committee, the same conjectures apply, but the probability of overspending is even greater in a bicameral legislature.

Assume the same conditions as above, that the two houses have 9 members each, and that each legislator again makes up his list of items to vote for in advance. Then the probability a legislator favors a particular spending item is again 5/6, and the probability that the lower house favors an item is:

SUM [C(9,x) * (5/6)^x * (1/6)^(9-x), for x = 5 to 9] = .99065.

So the probability that the lower house does NOT favor the item is .00935
(The probability of failure is 1 minus the probability of success.)

The probability that the upper house favors the item is also:

SUM [C(9,x) * (5/6)^x * (1/6)^(9-x), for x = 5 to 9] = .99065.

Again, the probability that the upper house does NOT favor the item is .00935

With an omnibus budget bill, BOTH houses must vote to AMEND the bill to remove the item, before it can be removed. This does NOT agree with the method prescribed in the Constitution. Only once outcome, instead of three, removes the bill. So the probability of removing a spending item is even lower:

.00935 * .00935 = .0000874225

The probability of the item passing is therefore:

1 - .0000874225 = .9999125775

This is even worse than any of the cases above.

• SPENDING CONJECTURE #8

  An omnibus spending bill in a monocameral (single house) legislature has the same spending probabilities that voting on individual spending items has.

  The only real difference is that the house votes to remove an item rather than to add it.

• SPENDING CONJECTURE #9

  When a bicameral (two house) legislature votes on spending through an omnibus spending bill each spending item has a smaller chance of being removed.

  Here the probability of removing the bill is lower, being the product of the probabilities of the item removal passing each house. This is definitely cheating the original intent of the US Constitution.

The omnibus spending bill violates constitutional intent.

First, the case of the constitutional method. Assume the following:

1. A bicameral legislature with each house larger than 40 members (so the normal distribution applies).
2. The bill is for an individual spending item.
3. Each legislator, and the executive, flips a coin to decide how to vote (an even chance of voting for or against).

Then the probability that the bill passes is shown by the following table:

With a probability of .12625 using the constitutional method, legislators have to really want to spend the money to spend it.

If the President always passes the budget, the problem simplifies to:

With a probability of .25 legislators still have to really want to spend the money to be able to spend it.

Now, the case of the omnibus budget bill method. Assume the following:

1. A bicameral legislature with each house larger than 40 members (so the normal distribution applies).
2. The vote is on removing an item from the omnibus budget bill.
3. Each legislator flips a coin to decide how to vote (an even chance of voting for or against).
4. It is assumed that the executive signs the resulting budget bill, so no veto override is needed.

Then the probability that the money is spent on the item is shown by the following table:

With the .75 probability of spending with the omnibus budget method, legislators must really want to not spend the money to not spend it.

• SPENDING CONJECTURE #10

  An omnibus spending bill by itself causes overspending.

  The omnibus spending method is a sneaky way to bypass constitutional limitations on spending. It gives the committee writing the bill the power to overspend.

This entire section shows that no legislature can control spending by itself, without special processes to prevent spending into debt.

SOLUTIONS

Now that we know the problem exists, what can be done about it? We know that, to get a balanced budget, these things must be avoided:

1. Avoid sequential voting on budget items.
2. Legislators must not stick to plans made in advance, unless a system to prevent overspending is in place.
3. Simple majority votes do not work without a system to prevent overspending.
4. Omnibus spending bills must be avoided.

Here are some suggestions on what to do, with good and bad points of each:

• INDEPENDENT VOTING METHODS

  Use the Independent Voting System, a fair election method, with budget ballots in the legislature. Put ALL budget items on this ballot. The vote on all items must be simultaneous. Each legislator marks a ballot, putting YES, ABSTAIN, or NO for each budget item. Each ballot is signed by its legislator, and is kept secret until the vote is completed. Then the vote is tallied, and the votes cast by each legislator are released to the press. The score for each budget item is its YES tally minus its NO tally.

  Then use at least one of the following methods:

  1. INDEPENDENT VOTING WITH REDUCTION FACTOR:
     1. Take all of the budget items with positive scores.
     2. If this results in a deficit, divide the revenue available by the total amount of spending approved by the ballot, giving the Reduction Factor. If there is no deficit, the Reduction Factor is 1.
     3. Multiply each item's original amount by the Reduction Factor, reducing all items proportionally.
     • Advantage: All favored items are approved.
     • Disadvantage: All items have reduced funding if a deficit would occur.
  2. HIGHEST INDEPENDENT VOTES:
     1. Sort the budget items according to score.
     2. Taking the highest scores first, go down the sorted list, adding in each item, until the next item either has a negative score, or would cause a deficit.
     • Advantage: All approved items are fully funded.
     • Disadvantage: Items favored by a majority are sometimes not approved.

• ADDITIONAL METHODS

  The following methods can add insurance that a deficit will not occur:

  1. LOSS OF SALARY:
     1. Make legislators lose all of their pay if there is a deficit.
     2. This makes them watch the amount already appropriated.
     • Advantage: They will actively work for a balanced budget.
     • Disadvantage is that items presented first will have a higher chance of being passed, compared to items presented later, unless some kind of balancing process is used.
  2. TAX USE RESTRICTION:
     1. Restrict use of tax revenue to only necessary items.
     2. Fair Taxation reduces the chance that a deficit budget will be approved.
     • Advantage: Other sources of funding must be found for unnecessary government spending. I suggest little cans at supermarket checkout stands, user fees, or donations.
     • Advantage: This goes a long way to cutting out "taxic waste."
     • Disadvantage: Some idiots think funding for the arts, sports, night basketball, entertainment, parades, and professional sports domes are "necessary."
  3. SPECIAL DEALS UNCONSTITUTIONAL:
     1. Make it unconstitutional for governments to offer special debt-finance deals that are illegal for private business to offer.
     2. Government has to pay just as much to borrow money as private individuals do.
     • Advantage: It makes debt harder to finance.
     • Disadvantage: It does nothing to prevent heedless legislators from voting for a debt that can't be financed.
  4. LINE-ITEM VETO
     1. Give the executive a line-item veto.
     2. If the legislature overspends, it gives the executive the power to decide which items to veto.
     • Advantage: The executive has the power to balance the budget.
     • Disadvantage: It does nothing to prevent the executive from allowing debt.
     • Disadvantage: The executive gets too much power.
     • Disadvantage: The legislature can override the vetoes.

Using these measures can once again get our government spending under control.

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