I don't use the forum often, so I apologise if this is in the wrong place or if it's been suggested before.
An extremely high HDI is an interesting challenge, but I think that an extremely low HDI can be just as hard to achieve, and also deserves recognition. Of course 'inverse HDI' is a bit of a naff name, so maybe it can be called 'poverty' or something? I'm sure someone out there will be able to think of a better name.
