West: Of our company's three quality control inspectors, Haynes is clearly the worst.
West's Conclusion
Haynes is the worst of our three quality control inspectors.
West's Evidence
Half of the appliances that were returned to us last year for being defective were inspected by Haynes.
Young's Response
Yeah, but Haynes does way more than half of the appliances.
Evaluate
This is a response that's talking about proportionality.
All other things being equal, if all three quality control inspectors were equally good at their jobs, then they would each be responsible for 33.3% of the items returned because of defects. They would always be tied in terms of, .
However, let's say they are equally good, but Haynes inspects 50% of the items, Rocco does 25%, and T-Bone does 25%. If it turns out that Haynes is , is it fair for Rocco and T-bone to tease him?
No, because of course Haynes will have the most items returned. He's inspected twice as many items as those rascals, so he has way more items out there in the world, with his name on it as the quality control inspector.
If Haynes inspects 50% of the items, and he's equally good as the other two, then we would expect 50% of the returned items to be from Haynes.
If someone does better than their percent, it shows they're better than average.
If Rocco inspects 25% of the items but is only responsible for 20% of the returned items, that means that Rocco is outperforming others.
Goal
Young responds by Introducing a New Consideration, i.e. bringing up important information that makes us see the first person's evidence in a different light.
When we were assuming the work was divided 1/3, 1/3, 1/3 among the three inspectors, we would have assumed that each inspector would have inspected 1/3 of the items that got returned.
Since Haynes inspected 1/2 of the items returned, he looks like he's doing worse than his fair share. But Young is saying, actually he's doing better than his fair share.
He inspects like more than 65% of these items, and he's only responsible for 50% of the returned items.