# Public Direction

## Budget Calculation

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How exactly does the budget distribution formula work? Can I see a simple example?

Funds are distributed to departments based both on voter ratings and on the overall size of the department. A department's average rating is multiplied by its proportion of the total budget to determine its component score. A department's component score is then divided by the sum of all component scores to determine its new percentage of the total budget.

The example below shows the process, with a departmental averaged raw score of 5, previous year's budget of 6%, and sum of component scores as 4.92.

(5) * (6%) = .3
(.3) / (4.92) = 6.1%

In this example, the budget for the department is raised from 6% to 6.1%. The change in percent of a department's budget from one year to the next will not be extraordinary. Each year's votes are valued against budget percentages from the previous year to balance public opinion against the realities of existing structures.

How are my adjusted ratings found in Steps 2 and 3 in the ratings calculator spreadsheet?

The Step 2 ratings can be seen as a halfway point - they are representative of the distribution of funds when money has been removed from the budget. The Step 3 ratings are representative of the distribution of funds once the money has been put back in.

Think back to the equation that uses your original ratings, from Step 1, to find the new budget percentages (a description and example of the original equation can be found in the question preceding this one). Keeping that original idea in mind, you can see that the adjusted ratings are calculated in a similar manner.

First, two specific values are found. The maximum rating that the user awarded to any department in Step 1 is noted. Then every department's Step 2 budget is divided by its 2010 budget. This change in percentage is compared against all other departments, and the maximum percentage change is noted.

If a department's individual percentage change equals the maximum percentage change, the maximum rating is multiplied by that department's 2010 percentage of the budget. This value is then divided by the department's Step 2 percentage of the budget. The resulting number may be referred to as the sum.

Calculation #1:

(Max User Rating * 2010 % of Budget) / Step 2 % of Budget = Sum

The sum is then multiplied by each department's Step 2 percentage of the budget. This value is then divided by each department's 2010 budget percentage. This final equation yields the department's adjusted rating.

Calculation #2:

(Sum * Step 2 % of Budget) / 2010 % of Budget = Adjusted Rating

This process is used in both Steps 2 and 3. The rationale behind these equations is in how they relate to the Step 1 calculation. In Step 1, ratings are calculated against their original percentage of the budget. In Steps 2 and 3, ratings are calculated against their adjusted percentage of the budget.

In Calculation #1: The sum is the largest number that can be found when the maximum rating is calculated against the budget values of department who registered as having the maximum percentage change. The sum is a sort of placeholder which is representative of the largest user rating.

In Calculation #2: The adjusted rating simply reverses the process of the first calculation. It takes the sum and finds out what rating is comparable to it. The rating can be no higher than maximum rating awarded in Step 1.

Are my ratings rounded in the ratings calculator? What impact does this have on the budget that is displayed?

In the ratings calculator your ratings are all rounded in the display, but the calculations use the non-rounded numbers.

As a result, the monetary values that are displayed in the spreadsheet may not be exactly proportional to the ratings that are displayed. This means that, when your ratings are submitted to Public Direction, the monetary values associated with those numbers may not be the same as the spreadsheet suggests.

The fact that those numbers may not match is a necessary consequence of the rounding. In order to ensure a 100 percent match the numbers sent to Public Direction would need to include many decimal places. This issue is also compounded by the fact that our website rounds and then stores values with only one decimal place.

We strive for both accuracy and usability. Limiting the ratings to one decimal place does have some minor consequences, but it also has the strengths of being simple and easy to use.

Why is the pending budget weighed against each department's budget percentage from the previous year?

There are two main reasons that this is so. First, stability is necessary for the government to run effectively and efficiently. Weighing the pending budget against the previous year's budget keeps monetary fluctuation to a manageable level.

Second, necessity of funds is a large part of what makes one department larger or smaller than any other department. As a short example, the State Department does not necessarily need funds from the Justice Department, and vice versa. Each federal department has specific responsibilities and they are able to fulfill their obligations by using their portion of the budget.

This way, Public Direction allows a large department and a small department that the public considers equally important to gradually become the same size over a number of years.

What percentage is the initial distribution of funds weighed against?

Each department currently receives a percentage of the federal budget. This percentage is the number that will be used to calculate the distribution of funds in the first year that Public Direction is used.

Is it easier to lose or gain funds? Is it different for large and small departments?

The proportions of departments depend on the relative size of each department and on the ratings each receives. First, let's consider how quickly a department can grow or shrink.

As a percentage, large departments see much smaller changes than small departments. Imagine two departments share a budget where one is twice the size of the other. If the larger department increases in size, from two to four times greater than the smaller department, and then from four to eight times greater, it will grow by 16.7%, then 9%. The smaller department will shrink by 40%, then 45%.

You can see these changes in the example below, where the two departments share a budget of approximately \$100. The value of \$80 is 16.7% greater than \$66.66, and the value of \$88.89 is 9% greater than \$80.

 Large dept. Small dept. \$66.66 \$33.33 \$80.00 \$20.00 \$88.89 \$11.11

Changes in the larger department will continue to shrink and changes in the smaller department will continue to grow. The same amount of money makes a much bigger difference to smaller departments than larger ones.

Now we can look at how the ratings come into play. Consider again two departments, this time where one is 10x the size of the other. If the smaller department gets double the rating of the 10x department, the larger budget will be reduced to only 5x. Alternatively, if the 10x department gets double the rating then the 10x department's budget will increase to 20x.

 Large dept. Small dept. Large dept. Small dept. Rating: 2 4 4 2 Original budget: \$60.00 [10x] \$6.00 \$60.00 [10x] \$6.00 New rated budget: \$55.00 [5x] \$11.00 \$62.86 [20x] \$3.14 Budget change %: -8.33% 83.33% 4.76% -47.62%

If you compare the budget change percentages above it is easy to see that the smaller department creates larger change. When the small department gets a rating of a 2 it loses 47.62% of its budget. But when the large department receives that same rating it is only reduced by 8.33%.

In our ratings calculators, Steps 2 and 3 are very important because they let you adjust your ratings by directly changing monetary values. This allows you to make sure that your rated budgetary changes make sense.

What change in budget percentage can be expected for each department in a given year?

We ran several different voting simulations to generate an educated guess. The spreadsheets found here show the results of several different scenarios.

If votes are closely centered around 5 for every department, you can expect the rise or fall of a single department's budget to be about 7 percent. Votes centered around a smaller number, say 1 or 2, will create greater change. Votes centered around a larger number, say 8 or 9, will create less change. We have a seperate FAQ exploring this phenomenon. In any case, if voters award universally high or low scores to a department, a larger gain or loss would be achieved.

Our Test Run, the result of the participants who submitted votes through September 11, 2010, shows that their favor will create an average change in the range of -8 to 30 percent.

There are several budget years listed in the Summary Tables (FY2011). Which one is used in the Public Direction calculations?

The 2009 listing is used. It is the most accurate because the years following 2009 are either estimates or projections.

Why is the National Infrastructure Bank, Climate Policy (Clean Energy Technologies), and TARP program not calculated by Public Direction?

The list of federal agencies in the Updated Summary Tables (FY2010) does contain the National Infrastructure Bank and Climate Policy (Clean Energy Technologies). These were not included because they will not begin until the 2010 year, or later.

This document also lists the TARP program in the mandatory spending. It is not included in Public Direction because the spending that takes place for this program is, for the most part, only dedicated to the single year of 2009. Projections indicate that the spending will dramatically decrease in 2010 and that it will be discontinued by 2018.

I received the message, "Macros are disabled," when I tried to use the ratings calculator. Now I can't copy my ratings.

There are several elements in the calculator that will not operate correctly if macros are disabled. They are needed for the scrollbars to adjust your ratings and for the buttons that will copy your ratings.

In Microsoft Excel 2003 you can turn on macros by going to Tools - Macro - Security... If you choose the Medium setting you will be able to choose whether or not to run a macro when you open Excel. You must restart the program before the settings will take effect.

In Step 3 of the ratings calculator, why is there a '% Change' column?

This column displays the percentage change from the 2010 budget to your new rated budget. A 100 percent change means that the new budget for that department is the same as the 2010 budget. A figure lower than 100% is a loss of money, and a figure higher than 100% is an increase of money.

The numbers will display normally when the change is below 100%, in bold text when between 100 and 199%, in red text when between 200 and 499%, and in italics and dark red text when above 500%. These changes are to alert you when the budget of any one department has increased by a substantial amount.

This is an important idea to keep in mind because it can be very easy to add a large amount of money to a small department. For instance, you may think nothing of adding 5 percent of the budget surplus to a small department. But it is possible that the 5 percent could equal upward of 25 percent of a small department's initial budget. Adding such a large amount will have the effect of applying a great importance to that one department. Its rating may be changed to a very high number, such as an 8 or 9, and all the other departments could easily drop to very small numbers, like a .3 or .5. The proportions between the departments would still reflect your views concerning monetary distribution. However, they may cease to reflect your views about how high you would like to rate a department.

Yes, the proportions between the departments' ratings are what counts when they are calculated. But other factors may come into play after all the rating is said and done. It is the view of Public Direction that each department should see their overall rating for each given year. If it is low, this may signify that the public is unhappy with them. If it is high, it may signify that the public is pleased. It is desirable for all concerned to let you rate how you feel and not to let a computer program decide how your ratings should be represented. We hope that you will account for these various issues when you are filling in your ratings.

The message '#DIV/0!' is displayed in various steps of the ratings calculator. What does this mean?

Thanks for making us think harder about our coding. The updated sheets, as of December 24, 2010, should not do that anymore.