I was reading an argument happening in the comments of an article about Light Table switching to open source. The argument was about freedom in relation to software, and it went basically something like this:
People who use OSX are less free [than Linux users], because they don't have the freedom to modify their OS source code.
No, they have the exact same freedom. People who use OSX and people who use Linux both have the freedom to modify the source code of Linux.
I'm not entirely sure, but this conversation reminded me immediately of arguing about a tree falling and making a sound when nobody's around to hear.
The first persons statement uses a variable in the place that the second persons statement uses a constant.
X's freedom is [partially] a function of [X's OS].
vs
X's freedom is [partially] a function of OS_List. (where OS_List is just a list of the OSs that he could in principle modify, regardless of if he wants to or is using any of those OSs)
(Obviously OS_List is a variable as well, but with respect to each person it's relatively unchanging).
I've seen this crop up in various conversations before - one person arguing using a variable where another person is using a constant (if that's the right way to describe it).
How does one diagnose the problem with this argument, if there is a problem? Is it a similar problem to the Tree in the Forest problem? Is there a standard rationalist way to dissolve the dispute so that both parties can leave not only agreeing, but also having a high probability of being correct when they leave?
Normalize the results - put each person on a 0-1 scale, where 0 is them being unable to do anything at all that they want to, and 1 is them being able to do everything they want to. Don't bother with dot products, just take the mean(probably the geometric mean, to preserve minority rights).
Sure, each element of the usefulness matrix is between 0 and 1. You need the freedom vector to quantify how valuable each freedom is in general before scaling it by the usefulness of it to each individual. Feel free to explicitly write out your expression for the overall freedom and try it out on some simple examples.