Good morning.
- Military adventurism and consequences.
- A forgotten tragedy. Oh, and update your feed reader, Richard moved.
- Move along, no religious content here, Jews beaten by “North African youths.”
- Future and matrimony.
- Ooookay.
- China.
- Indulgences, Eastern style … dogma. A prior not unrelated post here.
- City design for those banking on predicting a future increase in mean solar output.
- Needing a little intellectual defenestration.
- Happy happy.
- Aha!
- Miyazaki and love conquers all.
- Resolved. Use the word “brainstorm” in the future.
- Connecting Canada to Obama via liberal tendancies. A stretch or no?
- Apparently math is a lost art to some.
- Two posts on love, #1 and #2.
On the MPG article: I don’t think it’s an issue of math. The problem is that the question is being asked wrong. It isn’t being posed as a question of how well a person can make an estimate of two percentages. It’s being posed as “which is better” and any fool can see that 50 is better than 20, so it doesn’t matter if you start with 10 or 34 or anything else.
Kyle,
The point is the relationship is not linear and people, being often innumerate make the following error. If you compare an improvement of 10mpg to 20 mpg, that is less than the improvement of 50mpg to 150mpg. For a 300 mile trip, the first car buns 30 gallons, the second, 15. The second two burn 6 and 2 respectively. They expect (apparently) a linear relationship to be maintained and the difference of 10mpg to yield less gas savings than the 100mpg difference between 50 and 150.
If one used a metric of gallons per hundred miles, the first would be 30, the second, 15, the third 6 and the final one 2. That, according to the article gives a better picture (to as I claim the innumerate) about expectations of mileage and gas consumption.
I understood the point, and they are right in saying that, if the question people are asking is “how much gas can I save on my [fixed distance] journey?” then the ratings ought to be listed in gallons per mile rather than the other way around, because doing conversions like that, on the fly, is something of a whamdinger. But gallons per mile isn’t any more linear than miles per gallon, and people would give similarly wrong answers if they were asked (in europe maybe) to compare cars listed in l/km and asked which pair would result in an improved distance on a given tank of gas.
My point was that a casual polling situation is not an appropriate time to be asking math questions, especially questions that involve converting familiar ratios to unfamiliar ones which have not actually been predefined. Most people have been preconditioned to think about math only in certain environments or in response to certain kinds of questions. I could almost guarantee that those expectations were specifically played against in Larick and Soll’s experiments, so it’s not surprising that their participants came up with mathematically unsound answers. Participants would have automatically translated their questions into the most reasonable non-math equivalent: which improvement is better?
Imagine the MPG figures were dollar amounts. Would you rather I gave you $10 and you converted it to $20, or would you rather I gave you $34 and you converted it to $50? Since the initial funds aren’t even coming out of your pocket in the first place, it doesn’t matter which is actually a higher percent of return. All we have to look at is the final dollar amount.