This is just my thoughts on how the factors came to be. I might be close or I might be way out in left field.
Since a perfect score of all 9's yields a score of 180, I think this part was intentional, although I can't think of any reason it was chosen. So if you take 180 and divide by 5 (number of scores counted out of 6), you get 36.
Now make the assumption that the original idea was that taste was to be twice as important as tenderness, which in turn was to be twice as important as appearance. In effect, you get the 4, 2, 1 numbers others have described. Solve (4x + 2x + 1x) * 9 = 36 where x is the weighted value of appearance and you get x = 0.5714.
So the appearance weighted value of 1x = 0.5714
If you go back to your assumption that the tenderness is worth twice as much as appearance, you get 2x = 2 * 0.5714 = 1.1428, or the weighted value of tenderness
Now although the value of 1x is determined to be 0.5714, it actually has some additional digits beyond that. Therefore, to solve back to the original equation we have to rearrange it a little bit. Solve (y + 1.1428 + 0.5714) * 9 = 36 where y would be the weighted average of taste and you get y = 2.2858
So the taste weighted value of y = 2.2858
I think that makes sense. Appearance is 0.5714, tenderness is 1.1428 and taste if 2.2858. Isn't algebra wonderful! :-D:-D
I think the original premise that the coefficients are random is not accurate, but I could be wrong.
To remove the 0.0002 difference in scores the whole fractions (36/63), (72/63) and (144/63) would have to be used.
Hope this makes sense.
