Most people intuitively understand what "half" and "two times" look like. For example if I display a medium pizza and say that I will give you half of the pizza then most people would be able to immediately picture how much I am giving you. If I instead display a small pizza and say that the medium pizza is twice as large then most people would be able to immediately picture how large the medium pizza is.
Likewise I think most people understand one quarter intuitively as well. If I display a large pizza and say that I will give you quarter of the pizza then most people would be able to immediately picture how much I am giving you. They would think of cutting the pizza in half and then in half again. However if instead I display a small pizza and say that the large pizza is four times as large - well given a bit of time - I believe that most people would be able to figure out how large the large pizza is - but the image might not be quite as immediate.
But what would happen if I show you a small pizza and say that the super-deluxe pan pizza is twenty five times as large. I would be surprised if many people (outside the pizza making world) could immediately picture how large that is. They would know that the super-deluxe pan pizza is much larger than the small pizza but how much larger? I might go back to how I learned to multiply. Twenty five is five times five. So if I make five rows of five small pizzas that would approximately equate to the size of a super-deluxe pan pizza. But obviously this takes a bit of thinking.
The above examples illustrate Daniel Kahneman's System 1 & System 2 processes. Kahneman argues that there are two modes of thinking. System 1 is fast and automatic, based on relating new information to old learned situations. System 2 is slow and requires analytic thought. One half, two times, one quarter are System 1 ....larger numbers require System 2. However I contend that when most people hear someone quote a large number X they do not immediately revert to System 2 and try to figure out what the true scale of that number is - rather they stay with System 1 and just accept that number X is large and relate large to what they think of as large.
For example most children know that a million is a large number, and billion is a large number, and a trillion is an even larger number. And we would hope that most high school students can figure out that one billion is 1000 times one million. And that one trillion is 1000 times as large as one billion - as well as 1,000,000 times as large a as one million. But when brought up in casual conversation I believe that most people will revert to System 1 and just know that one trillion is a big number.
Where am I going with this? I started thinking about this after hearing the Gov. Romney's comment about cutting funds for PBS and the Corporation for Public Broadcasting (CPB) so we won't need to borrow money from China to fund our deficit. As many pundits have pointed out afterwards that cutting funding for CPB would only be a drop in the bucket toward closing our budget deficit much less get anywhere near to funding a 20% across the board tax cut. But our reversion to System 1 thinking leads us to gloss over the magnitudes of the numbers and instead just think large.
The actual numbers. In 2012 Congress appropriated 445 million USD to CPB. The 2012 federal budget had predicted receipts of 2.469 trillion USD and predicted expenditures of 3.796 trillion USD leading to a predicted deficit of 1.327 trillion USD. Obviously 1.327 trillion is a larger number than 445 million - but ....
Imagine instead that Congress was spending 100 billion USD on CPB appropriations. Then cutting CPB funding and twelve other programs like it could close the budget deficit. Obviously 100 billion is a small number relative to 1.327 trillion, but stated in this way it is not a ridiculous suggestion. But Congress is actually only spending 445 million USD on CPB. How does 445 million that compare to 1.327 trillion? Here is where our System 1 thinking starts foundering. 1.327 trillion, 100 billion, 445 million - these are all big numbers. We know that 1.327 is the biggest but how much bigger is it?
Sure we can all do the math. 1,327,000,000,000 / 445,000,000 = 2,982. So if we defund CPB and find another 2,981 budget items of the same size to defund then we could close the budget deficit. If you also want to fund a 20% tax cut that would require finding an additional (20% * 2.469 trillion / 445 million = ) 1,078 CPB sized budget items or 4,059 budget items in total to defund. Once again 2,982 and 1,078 and 4,059 are large numbers and our System 1 again starts foundering.
Let's help our System 1 thinking put this in context...In order to close the deficit and fund a 20% across the board tax cut we would need to cut federal government spending by ((1.327 trillion USD +20%*2.469 trillion USD ) / 314 million persons = ) 5,755 USD for every person in US. Cutting funding to CPB would account for (445 million USD / 314 million persons = ) 1.41 USD of those spending cuts. So we need to cut 5,755 USD for every person in US and Gov. Romney suggested $1.41 in cuts per person.
To be fair...I assumed a 20% across the board revenue cut. If you want to instead assume it is a 20% across the board income tax cut then we would need to cut federal government spending by ((1.327 trillion USD + 20%*1.165 trillion USD ) / 314 million persons = ) 4,968 USD per person. Or if you want to assume that we just cover the deficit and forget the tax cuts then we would need to cut federal government spending by just (1.327 trillion USD / 314 million persons = ) 4,226 USD per person....of which Gov. Romney has suggested $1.41 in cuts per person. So obviously that makes it a lot more manageable.
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