Using non-contiguous cartograms?

Question

The non-contiguous cartogram seems to solve a lot of the area distortions seen with traditional cartograms, while preserving the ability to identify areas by their shape lost with Dorling or Demers cartograms.

However, I can see how there might be problems related to the size of objects. Are there any practical guidelines on when the ability to comprehend these cartograms breaks down, either by:

• The ratio of the smallest to the largest value, or
• The ratio of the smallest original area to the largest (e.g. in a map of US states, the viewer might have difficulty figuring out whether the values were encoded in the object size or rather in the object's size relative to its original size)

Or both?

Example cartogram with small states having large values:

Example cartogram with not much variation between values represented:

Answer 1

Borden Dent's excellent book Cartography: Thematic Map Design (I've got the 5th ed.) has a chapter on cartograms, in which he lists three potential problem areas with cartogram design:

1. shape recognition (less of an issue with non-contiguous cartograms, since each unit is distinct)
2. estimation of area magnitude (this is the problem you've identified: scaling the areas)
3. conflicts with the map reader's mental image of the area (confusion due to major distortion)

Regarding the area estimation problem, Dent does not provide any specific scaling ratio guidelines, but he does suggest certain design decisions to facilitate clear comparison:

1. "the shapes of the enumeration units should be irregular polygons (not amorphous shapes)" (the shape recognition problem with Dorling/Demers cartograms)
2. "at least one square legend symbol should be used at the lower end of the data range. It is best to provide three squares in the legend, one at the low end, one at the middle, and one at the high end of the data range."

The "square legend symbol" is illustrated in this version of the map you posted:

Dent cites his 1975 paper "Communication Aspects of Value-by-Area Cartograms" (from American Cartographer) in support of these assertions, but unfortunately I cannot locate an accessible copy online. Note that the chapter does end with a list of about 30 references which may be of interest if you really want to dig in to the history of the cartogram.