"Why do you think some people argue that it is important to use 'equal area' maps, with correct relative sizes of countries, even if the shapes are untrue?"
This would be an argument against Mercator projection maps, which make Greenland look bigger than Brazil, for example. Such maps make the areas of regions near the poles much too large.
It is better to get the relative areas right and distort the shapes a little
"It is better to get the relative areas right and distort the shapes a little"
Yes, but- why is this better? It is better for navigation? Is it easier to mark down statistics on?
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