Fair Division 3

I was doing some computations on how far from envy free an equitable and efficient division can be with three people. As far as I can make out the worst case can give a second person (1+sqrt(5))/2 as much of the value by the first person's reckoning as he gets himself - i.e. he only gets the golden mean as much as the second person by his reckoning. I think 'the golden mean' must be one of the least suitable names for such a division!

Even so such an efficient and equitable division is I suppose what intelligent people should choose. One could try chopping down the value everyone got till it was envy-free and that might stop trouble in the real world, trying to do that though sounds terribly complicated and would just make the whole process seem silly. Not that that algorithm I set up was very applicable to the real world anyway as it is very prone to going wrong if anyone makes a mistake,