Interesting thoughts on the mathematics of polling

John Allen Paulos in the New York Times:

John_Allen_PaulosOne way to get a clearer picture of an electorate’s preferences is to ask prospective voters to rank the candidates and not merely say which one is their first choice. Who is their second choice, third, fourth, fifth? Doing this allows us to get a better overall view of their appeal or lack thereof. It also makes clear that “Who’s ahead?” is not by any means a question with a single, simple answer.

Let’s imagine that likely Republican voters were asked to rank Herman Cain, Newt Gingrich, Ron Paul, Rick Perry, and Mitt Romney (Michele Bachmann, Jon Huntsman and Rick Santorum, please accept my apologies). This is for illustration only, although it’s not that far off the mark, so let’s further imagine:

that 36.3% of them favored Romney to Gingrich to Paul to Cain to Perry;

and 27.3% of them favored Cain to Paul to Gingrich to Perry to Romney;

and 18.2% of them favored Perry to Paul to Gingrich to Cain to Romney;

and 9.1% of them favored Gingrich to Perry to Cain to Paul to Romney;

and 9.1% of them favored Paul to Gingrich to Perry to Romney to Cain.

Romney is clearly preferred by the highest percentage of voters so using the conventional method of plurality, Romney, the most conventional candidate, is the clear leader.

But impressed that the second highest percentage of voters prefer him (“Wow! 27.3% is almost exactly the sum of my 9-9-9 plan”), Cain might well argue that a runoff between him and Romney is appropriate. In such a runoff, the numbers above suggest that Cain would win since 54.6% all of the voters polled ranked him higher than Romney.

More here.