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<div>Martin Bailey suggested "<span class="correction" id="">maximise</span> the probability of <span class="correction" id="">minimising</span> harm" as the <br>
method to combine utility functions into a single social decision.<br>
<br>
For something like this to wo<span class="correction" id="">rk</span>, there would need to be a reference point as <br>
the question then becomes, "<span class="correction" id="">minimise</span> harm relative to what?".<br>
<br>
Anyway, back to Pareto:<br>
<br>
<pre><tt><tt>(Par) The "Pareto" principle:<br>
If <span class="correction" id="">ui</span>(x)>=<span class="correction" id="">ui</span>(y) for all i, then <span class="correction" id="">xSy</span>.<br>
</tt></tt></pre>If you have have a currency this can be used to compare 2 utility functions.<br>
<br>
A currency in this context is something the everyone has an unlimited supply of <br>
and which they always consider having more of it being better (all else being equal).<br>
This obviously is somewhat of a contradiction. However, when comparing small<br>
changes, it is reasonable.<br>
<br>
Also, it should also be finely divisible.<br>
<br>
<pre><tt><tt><tt><tt>(Currency) <span class="correction" id="">Ui</span>(x and c(z)) > <span class="correction" id="">Ui</span>(x) for all x, i and z>0<br>
<br>
</tt></tt></tt></tt><font face="Verdana, Arial, Helvetica, sans-serif"><font face="Verdana, Arial, Helvetica, sans-serif">The reverse is also true, by definition. It means that c is a currency if everyone values <br>
having more of it. (z is the number of units).<br>
<br>
State "x and c(z)" is state x where the only difference is that the person has z units <br>
of the currency more</font>.<br>
<br>
<span style="font-family: "Verdana";"></span></font><br>
<tt><tt><tt><tt>(<span class="correction" id="">Kaldor-Hicks</span>) The "<span class="correction" id="">Kaldor-Hicks</span>" principle:<br>
If <br>
<span class="correction" id="">ui</span>(x and c(<span class="correction" id="">yi</span>) >= </tt></tt></tt></tt><tt><tt><tt><tt><tt><tt><tt><tt><span class="correction" id="">ui</span>(x and c(<span class="correction" id="">yi</span>) for all i</tt></tt></tt></tt></tt></tt></tt></tt><tt><tt><tt><tt> <br>
AND<br>
sum(<span class="correction" id="">yi</span>) >= 0<br>
for some set y then <span class="correction" id="">xSy</span>.</tt></tt></tt></tt>
</pre>
</div>
<div>This basically says that an outcome is better for society if the costs are less than<br>
the benefits. If a change does $100 of damage to 100 people and provides $10 of<br>
benefit to 1 million people, then it is worth doing. Under Kaldor-Hicks, the payment<br>
doesn't actually happen.<br>
<br>
If people had unlimited money, it is possible to convert it to <span class="correction" id="">pareto</span> efficiency by <br>
actually doing the transfer payments. Since the sum of yi is positive, the total<br>
amount people are willing to pay to obtain the change exceeds the total amount <br>
people want to allow the change. This means that money can be moved from<br>
one group to the other with some to spare.<br>
<br>
Another alternative is to take it in small st<span class="correction" id="">eps</span>. If <br>
<br>
<span class="correction" id="">aSz</span> under <span class="correction" id="">Kaldor-Hicks</span><br>
<br>
then there will be a set of states a', b, c ... and z such that<br>
<br>
(a')<span class="correction" id="">Sb</span> and <span class="correction" id="">bSc</span> and <span class="correction" id="">cSd</span> .... and <span class="correction" id="">xSy</span> and <span class="correction" id="">ySz</span>.<br>
<br>
If z is the current state, then this provides a method for getting from z to a'.<br>
<br>
The ideal would be to find the chain that <span class="correction" id="">minimises</span> the currency transfer for each person.<br>
<br>
This min could be <br>
- <span class="correction" id="">minimise</span> the max payment required by any one person<br>
- <span class="correction" id="">minimise</span> the max payment as a proportion of wealth required<br>
or some other system.<br>
<br>
Everyone will agree than a' is an improvement over z and the only difference between <br>
a and a' is the amount of money in everyone's bank account. <br>
<br>
One other thing about choosing the best option from a social utility point of view is<br>
taking into account how the rule will affect future actions. Taking something from<br>
someone to give to another may result in an improvement in the utility sum, but <br>
there could be long term utility problems.<br>
<br>
If the person who loses his loaves of bread is a baker, the supply of bread may <br>
decline because the baker, who "has more bread than he needs" always ends<br>
up having them allocated to someone else.<br>
<br>
</div>
<div style="clear: both;">Raphf<span class="correction" id="">rk</span><br>
--------------------<br>
Interesting site<br>
"what if anyone could modify the laws"<br>
<br>
<span class="correction" id="">www</span>.<span class="correction" id="">wikocracy</span>.com</div>
<div> </div>
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