The earliest cartograms -- maps whose boundaries are distorted to reflect a set of data other than area -- began appearing in the late 19th century. This 1921 cartogram by General Electric is the earliest example -- OK, the only example -- I've found in the Minneapolis Tribune archives:

No, Dear Reader, This Is Not a Cubist Map!
It Shows Where Electricity Is Used in the U.S.

This odd map of the United States may seem at first glance to be a cubist artist’s conception of the familiar geographical outlines of our country, but it has a strictly utilitarian purpose. It is known as the map of the “electrical United States” and pictures graphically the number of household users of electricity in each state.
A glance at this map will also show which state boasts the largest number of household electrical consumers and how other states compare in number of users. How each state ranks may be judged by its size as shown on the map, which was prepared by the General Electric company, Schenectady, N.Y., from data compiled through a national survey made by the commercial service section of its publication bureau.
New York ranks first, having an electrical population (served by central stations) of 8,620,700, or 78.7 per cent of its actual population. The second largest state is Pennsylvania, with an electrical population of 6,330,000, or 68.8 per cent of the actual population; third, Illinois, with 5,150,000, or 79.8 per cent; fourth, Massachusetts, with 4,030,000 or 97,8 per cent; fifth, Ohio, with 3,550,000, or 66.1 per cent, and sixth, California, with 2,827,000, or 86.5 per cent.
At the bottom of the list is Nevada, squeezed into a tiny circumference on the map, because it has only 66,300 persons served by central power stations, which, however, is 54.3 per cent of its actual population.
The most nearly electrified state is the District of Columbia, where 430,000 out of a population of 437,000 are served by electricity. This is a percentage of 98.2. The next best showing is made by Rhode Island, where 98 per cent of the people are served by central stations.
The electrical population of the United States is 62,023,400, out of an actual population (last previous census) of 108,148,000, a percentage of 57.3.