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 wonder about these things.

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


Anonymous said...

Your "ponderment" reminds me of how I feel about prices usually being shown just a penny or two short of the more realistic dollar amount, and gas prices always shown with "9" following the listed prices. My dad always said the "9" meant that the listed price was actually for 9/10 of a gallon, rather than a full gallon. Others think that the "9" indicated 9/10 of a cent on top of the listed price.

No matter how you look at it, this has always bugged me because it just seems to have deceptive intent. So, with matters of price, I always tend to round up by the penny or two to the more realistic view of the price.

All that to say, if I saw a 99% rating, I would view it as 100%!

Mister Ed T said...

My son once passed a course with a 50% for half of his mark and 49% for the other half, made 49.5%, rounded up to 50% and a passing grade. The mathematical question is degree of accuracy, or line of separation. In my thinking, 89.999% is still less than 90%. Its a little bit like the kids in grade school who thought them came in second because the first two kids were tied for first. No! Ze was the third person to cross the finish line.