## Saturday, May 22, 2010

### A Question of Math and Ethics

Theoretically, what is the difference between 99% and 100%?

I was listing an item on eBay yesterday and took note of the fact that I still have a customer satisfaction rating of 100%. I am approaching 300 feedback comments, so the 100% is something I'm proud of. It has been something I have worked for, even having to really negotiate with some not-so-nice people I've done business with. That 100% rating makes my auctions more successful, as it shows that I am a trustworthy eBayer.

But I was thinking about the numbers today. If I had one negative feedback comment out of 290, would my rating still be 100%? When you calculate 289 out of 290, the math comes to 99.67555% positive transactions. Is this close enough?

In so many other applications, we round up. If a student has earned a 84.994%, it may be recorded as an 85. At what point, however, can a person round up when the next whole number gives a different result? If a student has earned an 89.96 in a class where 89 earns a 'B,' but 90 earns an 'A,' should the teacher round up then? Has the student reached a 90, an 'A?' No. Is it close enough?

This brings me to my question regarding the ultimate difference: Is it ethical to ever round up from 99% to 100%? In the eBay situation, 99.6755 is probably still recorded as a 99, but I'm not sure. What if it were closer yet? What if I had 990 feedback comments instead of 290 and had only one black mark on my record? Mathematically, I would be at a 99.8999899%. Would it be rounded up? I don't know. A rating of 100% implies that every transaction has been positive. Can 100% ever be achieved without perfection? Can it be earned only mathematically, but not ethically? Is this a point where the science of mathematics meets philosophy and becomes subjective, rather than precise?

I suppose I should get out more. My poor kids have me for a teacher.