Voters will start speaking their minds shortly in caucuses and primaries across America. Among the many issues one weighs when voting is a pragmatic one: which candidate is best positioned to win the general election? The answer to that question is complex. For simplicity, we decided to look at the results of national head-to-head polls between the two leading Democrat presidential candidates versus the five leading Republican presidential candidates.

This data was obtained January 28, 2016 from Huffington Post Pollster, which tracks a more comprehensive set of polls than does Real Clear Politics. We chose "More smoothing" to remove noise; we removed polls based on live phone interviews, which seem to be less reliable than other forms of polling, according to a study by Morning Consult; and we removed polls of all adults, focusing on polls of likely voters and registered voters alone. The numbers in the table represent the comparative percent advantage of the Democrat candidate over the Republican candidate.

On average, the Democrats have a 2-3 percent advantage over Republicans. This varies by candidate. The obvious outlier is the Carson-Sanders match-up. This is probably an artifact of the fact that only one poll made it through our filters, so the point estimate is probably unreliable.

On average, there is little difference between the performance of the two Democrat candidates. The Republican candidates are ordered in the table in order of increasing strength. Trump has the best average performance against the Democrat field. In turn, Clinton has a better chance of beating Trump than does Sanders. See the chart below.

A linear model of the above data suggests that Trump is the strongest Republican presidential candidate, while there is not much substantial difference between the Democrat candidates; see below.

We begin with the candidate power rankings. However, we change the vertical scale compared to last time we discussed the subject; now it measures distance between logits rather than between the raw poll numbers.

Only 4 candidates are above water: Trump, Clinton, Cruz, and Rubio. Sanders, Carson, and Bush are close to break-even. It is hard to consider the other candidates as viable. (Gov. Gilmore is not shown on this graph; he would appear down at negative infinity.)

We consider whether Zipf's law, or some power law, as discussed in an earlier post, could apply to the odds ratios for the candidates in their respective races.

The fit is fairly good in each party, and becomes even better when the trailing candidates (O'Malley, Santorum) are removed.

The expected performance of the leading candidate is given below.

If Zipf's law holds for odds ratios in a 2-person race, the leader should poll about 58.6%. In a 3-person race, it's 46.8%; in a 4-person race, it's 40.9%; and in a 5-person race, it's 37.2%.

Lastly, we analyze the distribution of the 22 national polls in the Republican presidential race conducted entirely during December. We focus only on the 6 top candidates. A biplot is shown below.

There are several interesting items to observe. One is that Trump is the only candidate who has negative correlations with each of the other 5 (the correlation matrix shows this), suggesting Trump is rather distinctive in the race. Another is the appearance of two axes dominating the picture: a Trump-Rubio axis (outsider vs. establishment?) and a Cruz-Carson axis (choices for social conservatives?). We also can perceive poll 21 as a distinctive outlier.

The Democrat presidential race does not offer much in the way of statistical challenges. It has become essentially a 2-person race, for the moment. If that should change, we will analyze it.