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Below is a famous map produced by the Facebook team, which shows the connections between their users. Where there are multiple overlapping features, the lines show more brightly, giving a clear indication of feature density.

enter image description here

How can this effect be emulated in ArcMap? For example, is it possible to show individual features with a set transparency, and stack these features with the transparency values accumulating to show where multiple features coincide?

The standard > Display > Transparency option applies to the whole layer equally.

The Facebook example uses light features on a dark background, but I'm also interested in dark features on a light background.

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Although some ArcGIS for Desktop answers have been provided at Making map where overlapping symbols increase Opacity?, I do not think there is a good solution for doing this in ArcMap.

I think this would be a good candidate for ArcGIS Ideas if you need it in ArcMap, but it looks like the functionality you are after may already be in ArcGIS Pro - see the ArcGIS blog post Increase your transparency with ArcGIS Pro.

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