I've been trying to work out a way of computing area for a two-dimensional median voter model I've been working on. A, B, and C are political parties that can choose where they want to be on the political spectrum (left/right, authoritarian/libertarian). Each party wants to maximise the area of the graph that they gain within the bounds of the political spectrum in order to maximise the number of voters they get (assuming political preference is uniformly distributed across the spectrum):
Points can be moved around and cannot completely overlap. I want to know if there is an expression I can use to find the area of the zone closest to A / closest to B / closest to C thereby finding who wins purely based off
- the coordinates of each party and
- the size of the political spectrum box.
So far all I have been able to do is graph it out using perpendicular bisectors, but nothing further.
Any help would be appreciated :D