"Most Admired"—Interpreting Statistics

I recently came across a post online by someone who argued that the stories about Obama's loss of popularity must be bogus, since a poll had shown him to be the most admired man (and Hillary Clinton the most admired woman) in the country. I pointed out in a comment that "most admired" might mean admired by ten percent of the population if nobody else got above nine.

It turns out that I was correct, although the number is a little higher than my example.

The open-ended poll released Monday found 16 percent of people named Obama as the most-admired man, while 15 percent named Clinton as the most-admired woman. Both scores, however, have dropped significantly since 2012.  

In 2012, 30 percent of people named Obama as the most-admired man, while 21 percent named Clinton the most-admired woman. 

(From The Hill)

One implication is that the post's argument was strikingly wrong, since Obama's popularity, by this measure, is only half what it was a year ago. The more interesting point is the risk of arguing from factoids without thinking carefully about what they actually mean.