"X times as many as" or "X times more than"

A recent article from the OpenSecrets.org website bears the headline “Dark Money Spending Three Times More Than at Same Time in 2012 Cycle, CRP Testifies” (April 30, 2014). A graph in the actual CRP document (“Exhibit 2,” on page 9 of the submitted testimony) identifies the relevant figures as being slightly more than $4 million in 2012 (“to date”) and slightly more than $12 million in 2014 (“to date”). Clearly the headline writer considers “three times more than” to be synonymous with “three times as much as.” The main text of the testimony (on page 3) evinces a similar understanding in describing the difference between the two figures:

As of April 29 in the current cycle, despite this being a midterm election, spending by nondisclosing groups is nearly three times higher than it was at the same point in 2012, totaling $12.3 million compared to $4.4 million in the same point in 2012.

It seems to me that many writers and speakers of English are inclined to use "X times more than" and "X times as much as" interchangeably and to interpret them as being equivalent. But in a paper titled “Common Errors in Forming Arithmetic Comparisons,” Professor Milo Schield of Augsburg College in Minneapolis, Minnesota, treats this understanding as a common error:

Confusing ‘times as much’ with ‘times more than’. If B is three times as much as A, then B is two times more than A — not three times more than A. The essential feature is the difference is between ‘as much as’ and ‘more than’. ‘As much as’ indicates a ratio; ‘more than’ indicates a difference. ‘More than’ means ‘added to the base’. This essential difference is ignored by those who say that ‘times’ is dominant so that ‘three times as much’ is really the same as ‘three times more than’.

Of course, the fact that “more than” indicates a difference doesn’t alter the fact that “times more than” indicates a ratio of a certain kind. The real question is whether people understand the ratio implied by “times more than” to compare the entire amount of the larger quantity to the smaller quantity or whether they understand it to compare only the difference between the larger and smaller quantities to the smaller quantity.

Historically, at least one fairly early text supports Professor Schield’s distinction. From a 1657 translation of Voltaire’s The General History and State of Europe, Part V:

The farmers of those alienated duties plundered the people of four times more than their demand amounted to ; and when at length the general depredation obliged Henry IV, to give the intire administration of the finances to the duke de Sully, this able and upright minister found that in the year 1596, they raised about a hundred and fifty millions of livres on the people, to bring about thirty into the Exchequer.

In this example, Voltaire observes that 150 million is four times more than 30 million, though it is also clearly five times as much as 30 million.

In my view, if substantial numbers of English speakers and readers have conflicting understandings of the two terms—some taking the position that “X times as much as” and “X times more than” refer to equivalent ratios, and others adopting Professor Schield's view that the two ratios involved differ fundamentally—a writer who doesn’t want to be misunderstood by some significant portion of readers might do well to avoid ever using the potentially ambiguous phrase “X times more than,” especially since any such ratio is easy to recast (and recalculate, if necessary) as an unambiguous “X times as much as” ratio.