Posted by: dacalu | 8 March 2012

Complex Utility Functions

Last night, I wrote about my most basic utility function – optimizing relationships between agents or, in Christian-speak, promoting love between souls.  That makes for a very simple function in what turns out to be a very complex world.  Most of us, myself included, have multivariate functions.  We don’t have a single scale on which we judge preferences;  rather we have multiple, sometimes competing preferences.

So let me start by saying that I think the most rational utility functions will have a very small number of base preferences, with other preferences being derivative.  More simply put, I want some things for their own sake.  Other things I want because they provide something else.  I may want a brownie for instance.  It’s possible that I have a base preference for brownies, but it’s more likely that I value pleasure – which I know comes from eating fat, sugar, and chocolate – or that I value general well being and know my blood sugar is low.

This may seem a trivial case, as very few people would claim a base preference for brownies, but other preferences may be less clear cut.  I have spoken this week about questions of love or obedience.  Some Christians think love is important, but only because God commands it.  Others think that obedience is primarily a result of our love for God.  (See “Love or Obedience” from 15 Jan 2011.)  Both utility functions lead Christians to choose both love for and obedience to God.  At a simple level, they make the same predictions.  Once we start looking at other behaviors, though, we will see that it matters which one is more important.  What if our understanding of love and obedience conflict – as is often the case in morality?  It matters which of the two is primary, which one is the base utility function and which is derivative.

This distinction becomes particularly important when we start talking about moral justifications and moral arguments.  Because our utility functions are so complex, we are almost always speaking about derivative utility.  I buy her flowers because I love her.  I don’t run the stop sign because it is against the law.  I give him food because he’s hungry.  In all of these cases one preference depends upon another.  When someone asks us to justify an action (or a preference) we can respond by reducing it to another preference, generally one we believe is held in common with the questioner.

Why are you choosing the purple one?   It’s cheaper.

Why didn’t you smack him?  It didn’t seem worth the trouble.

Why do you give 10% of your income to the church?  Because it is my duty.

Most of the time we really do share the lower lever utility function and the answers makes sense.  Increasingly, however, as we live in a more and more pluralistic world, we encounter people who have different preferences, different orders of preferences, and different base assumptions.  Miscommunication happens when we are mistaken about the utility functions of others.

Two people can take the exact same action, but for different reasons.

Others will take different actions for different reasons.  If they are both derivative reasons and they share base preferences, then a debate between them will be nothing more than a discussion of moral reasoning.  They start with the same premises and  data, logic, and rhetoric alone can determine who is correct.

On the other hand, two people may take different actions, each of which rests on different utility functions.  For these people, the first step will be to identify where their functions differ.  Perhaps they both have the same base function – love or obedience or happiness, but the intermediate stages differ.  We both want the pleasure of a good meal, but I think that involves quantity and you think it involves quality.  In this case, the problem devolves to the previous question.  We can still resolve the problem with data, logic, and rhetoric.  We will, however, have to do some careful communication first.

Finally, and luckily infrequently, we will run into cases where base utility functions differ radically.  In this case, no amount of data or logic will compel one party to change.  A base utility function must be axiomatic – by definition – because it cannot be defended in terms of any lower lever preference.  In this case it’s important to identify the difference and accept the fundamental divide.

The worst antagonism can result when people mistake what level they are arguing on.  Frequently one person will assume the other is arguing in bad faith (ignoring evidence, failing to see logic, or using bad rhetoric) when they have failed to identify the depth of the disagreement.

Similarly, we can become very unhappy very quickly when we have competing preferences and have not identified where the competition lies.  Only that level of self awareness will allow you to resolve the internal conflict.

This is not to say that no avenues exist to change base preferences.  They do, but that will be a subject for tomorrow.

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