This is not so much a “Soap Box” as it is a reflection on the concept of “thinking like a lawyer.” This evokes the phrase heard by every law student that in Law School “You teach yourself the law, we teach you how to think like a lawyer.” In truth, “thinking like a lawyer” is really nothing more (or less) than thinking critically about any topic. It’s looking at the situation, identifying the facts you need to know, the terminology what you need to define, and the strengths and weaknesses of one position as well as the strengths and weaknesses of its opposite. It also requires an understanding of human nature, of the need for order out of chaos, the desire for a story.

The following example deals with an area about as foreign to the law as rutabaga farming is to rocket science — math (or maths, as the British would say). It shows, however, how a subject that is foreign to the law can be addressed with critical legal thought — albeit in a fashion that would probably make a mathematician’s head explode. So view this not only as an example of how a simple question — in this case, “what is meant by a percentage?” — can be not so simple to answer if you “think like a lawyer” about it, but also an example of how “a little knowledge is a dangerous thing,” because none of what follows is based in more than a rudimentary understanding of the deeper mathematical concepts (and with full awareness of the logical fallacies that result for ignoring these concepts). And for any mathematician who happens to come across this post and desires to print it out, mark it up in red ink, scan it and post it as a comment, please understand that this is exactly how you (and doctors and engineers and other “really smart people”) sound to lawyers when you try to explain the law to us. In other words, I know that the following discussion is not mathematically accurate in every respect, and it is not intended to be. It’s to show why the correct legal answer to any question is “it depends.”

What is a percentage? For most lay people, it’s the representation by a number of the fraction out of the whole that something represents. Half a pie is 50% of a pie. But is that really how percentages work? If I cut the 50% of the pie in two equal portions, does each portion represent 50% of the original half of the pie or 25% of the whole pie that I never had? What if the baker used a frame to bake a pie in only half the pie pan (such a utensil actually exists)? Is the result 50% of a pie or 100% of a pie? If I promise to pay your 50% of my earnings, is that 50% of all I earn, or 50% of all I net? So before we answer “what is a percentage,” we need to understand not just what percentages are and if percentages change by context.

For comparisons, it is possible to have an unlimited percentage and even a negative percentage — but changes in relative positions do not always result in changes of percentages. Example, if I have one dollar and you have two, your net worth is 200% of mine, and if I then become indebted to you for $2, your net worth goes up 200% ($2 of assets plus $2 receivables), while mine drops by -200% (from $1 of assets to -$1 of net assets less payables). If I pay you the dollar I have, the net change in both positions is 0% — I am still worth -$1 and you are still worth $4. If I acquire another dollar, my net worth is now $0, but the change in my net worth is -100%, not 100%, while your net worth remains the same. If I again give you the dollar I acquired, the net change in positions again remains unchanged.

But as a unit of measurement, you can never have less than 0% of something or more than 100% of something. In the above example, there are four physical dollars. At the start you have 66.6% of the dollars and I have 33.3%. When I pay you the $1, you have 100% and I have 0%. When I acquire the fourth dollar, I now have 25% of the dollars and you have 75%. Then I pay you again and we revert to 0% and 100%. If you then acquire a fifth dollar from someone else, you have 125% more dollars than before, but the fifth dollar represents only 20% of your net worth, and you still have only 100% of all the dollars between the two of us. The increase in quantity changes the relative percentage that each unit has as part of the whole but does not result in a change in the measurement of the division of quantity. If you then (in violation of federal law — so do not try this at home) use one of the dollars to light a cigar, you have reduced your quantity of dollars by 25%and your net worth by 20%, but you still have 100% of the dollars remaining.

So what is a percentage? It depends.