“When am I going to use math in real life?”

It is tempting to answer, “Never!” However, in truth leaders in all sorts of fields use mathematics to understand and thereby control the world. Their knowledge builds their power.

For an example of the practical power of math, let’s turn to the recently adjourned 127th Maine State Legislature.

Lately, complaints about the partisanship in the legislature seem to be everywhere. A July 19 story by the Associated Press describes “partisan animosity” in Augusta. As reported this spring, “partisan battles” drove Rep. Stanley Short out of the Democratic Party.

Are these anecdotal stories confirmed by a check of all 844 roll calls on bills voted on by 186 legislators this year?

Just a little math can answer that question. Partisanship happens when members of the same party take the same actions. A special kind of Pearson correlation called “phi” measures partisanship mathematically:

Phi = ((n1*n2) – (n3*n4)) / X
n1 = # Republican legislators voting yes on a bill
n2 = # non-Republican legislators voting no on a bill
n3 = # non-Republican legislators voting yes on a bill
n4 = # Republican legislators voting no on a bill
X = the square root of the product of the number of people answering each possible combination of each question.

X sounds complicated, but it’s just a technique to make the answer vary between +1 and -1; we can ignore it here.

Instead, let’s think about the other, simpler measurements.

When will phi be really large in magnitude? When either n1 and n2 are large and n3 and n4 are small (producing a large positive phi), or when n3 and n4 are large but n1 and n2 are small (producing a large negative phi). This happens when many Republicans vote one way on a bill and many non-Republicans vote the other way. A large positive or large negative phi indicates large partisanship.

When will phi be small in magnitude, hovering around zero? When n1 and n2 are about the same size as n3 and n4. That happens when some Republicans vote yes but some other Republicans vote no, and when some non-Republicans vote yes but some other non-Republicans vote no. A phi close to zero indicates non-partisanship.

These graphs report phi calculations for each of this year’s roll call votes on bills:





This year’s legislature is not overwhelmed by partisanship after all:

• Few votes on bills were completely partisan (phi = exactly +1 or -1).

• Some votes were mostly partisan (phi = +/- .75 to .99), but many votes were completely non-partisan (phi = 0, usually a unanimous vote) or mostly non-partisan (phi = +/- .01 to .24).

• The partisan trend is greater in the House than in the Senate (with a large spike at Phi = 0).

In short, while partisanship is visible in some votes, partisanship is rarely as extreme as it could be, and non-partisan action is also common. Cooperation in the Legislature can be found, and math helps us look.