numbers and percentages chapter

[alberto]

Good afternoon its alberto question please to Dave or Jon: Logical reasoning question respectfully:
On chapter 17 :Numbers and Percentages, the example given on page 581(not going to rewrite) about waste management companies and the plastic issues and other waste or garbage the increase and decrease factor: I am asking I was not sure and the right answer was: D. which made sense, is it okay for me to use :Assumption Negation to arrive at that answer sense it is a reverse weakener, I recall in one of the PodCast that this method can be used only if down to 2 answers and not sure of which answeris correct but use it judiciously because does not work all the time? Am I correct or wrong here, to use Assumption Negation in these abstract problems? Thank you.

[Zach Foreman]

Alberto,
This is a pretty typical example of the fallacy of switching from percentages to numbers. Recall that one cannot make inferences from rising/falling percentages to rising/falling numbers or the reverse.

The premise talks about an increasing percentage, but the conclusion says that attempts to decrease plastic waste are failing, which is talking about an absolute amount.

Whenever this happens, you need to consider how it is possible for a percentage to rise but the absolute number to fall. Let's put some numbers in:

Last Year This Year
Plastic as Percent of total waste: 30%. 50%
Tons of plastic waste 150 tons 140 tons
Tons of non-plastic. 500 tons. 140 tons

So, how can this happen? Well, if the non-plastic waste falls faster than the plastic, then the percentage of plastic waste increases even as the total amount of plastic decreases. ALWAYS LOOK FOR THIS when you see the percent/amount switch!

As for using the assumption negation technique in weakeners, it can work but I see no advantage. The real power of the ANT is that when you negate an assumption (because it is necessary to the argument), you attack/undermine/weaken the conclusion. But just because you weaken the conclusion, it doesn't mean that negate an assumption (that's a MR). Again, it can work but I certainly wouldn't do it here as the prephrase of "percentage/absolute number confusion" is the key.