[EM] When and how can we speak of "individual utility" and "social utility"?

[raphfrk at netscape.net]

 Martin Bailey suggested "maximise the probability of minimising harm" as the 
 method to combine utility functions into a single social decision.
 
 For something like this to work, there would need to be a reference point as 
 the question then becomes, "minimise harm relative to what?".
 
 Anyway, back to Pareto:
 
 (Par) The "Pareto" principle:

      If  ui(x)>=ui(y)  for all i, then  xSy.

If you have have a currency this can be used to compare 2 utility functions.
 
 A currency in this context is something the everyone has an unlimited supply of 
 and which they always consider having more of it being better (all else being equal).
 This obviously is somewhat of a contradiction. However, when comparing small
 changes, it is reasonable.
 
 Also, it should also be finely divisible.
 
 (Currency)  Ui(x and c(z)) > Ui(x) for all x, i and z>0



The reverse is also true, by definition.  It means that c is a currency if everyone values 

having more of it.  (z is the number of units).



State "x and c(z)" is state x where the only difference is that the person has z units 

of the currency more.





(Kaldor-Hicks) The "Kaldor-Hicks" principle:

      If  

         ui(x and c(yi) >= ui(x and c(yi) for all i 

            AND

         sum(yi) >= 0

      for some set y then xSy.
  This basically says that an outcome is better for society if the costs are less than
 the benefits. If a change does $100 of damage to 100 people and provides $10 of
 benefit to 1 million people, then it is worth doing. Under Kaldor-Hicks, the payment
 doesn't actually happen.
 
 If people had unlimited money, it is possible to convert it to pareto efficiency by 
 actually doing the transfer payments. Since the sum of yi is positive, the total
 amount people are willing to pay to obtain the change exceeds the total amount 
 people want to allow the change. This means that money can be moved from
 one group to the other with some to spare.
 
 Another alternative is to take it in small steps. If 
 
 aSz under Kaldor-Hicks
 
 then there will be a set of states a', b, c ... and z such that
 
 (a')Sb and bSc and cSd .... and xSy and ySz.
 
 If z is the current state, then this provides a method for getting from z to a'.
 
 The ideal would be to find the chain that minimises the currency transfer for each person.
 
 This min could be 
 - minimise the max payment required by any one person
 - minimise the max payment as a proportion of wealth required
 or some other system.
 
 Everyone will agree than a' is an improvement over z and the only difference between 
 a and a' is the amount of money in everyone's bank account. 
 
 One other thing about choosing the best option from a social utility point of view is
 taking into account how the rule will affect future actions. Taking something from
 someone to give to another may result in an improvement in the utility sum, but 
 there could be long term utility problems.
 
 If the person who loses his loaves of bread is a baker, the supply of bread may 
 decline because the baker, who "has more bread than he needs" always ends
 up having them allocated to someone else.
 
  Raphfrk
 --------------------
 Interesting site
 "what if anyone could modify the laws"
 
 www.wikocracy.com   
   
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