Equality of Utility II

Some time ago we investigated the equality of benefits. Roughly speaking let us consider degenerate real world actions into discretely selectable choices of action a\in A given individual x, who has observable features f(x) and protected feature p(x). Suppose the company has to choose among a set of actions to take a \in A. What is a workable definite of fairness or equality in such a decision making effort with respect to protected properties p?

Let god bestow us, a neutral third party, with a utility functor u whose evaluation on the individual u(x) results in a function u(x)(a) is the utility of company taking action a to individual x, u(x)(b) is the utility to individual x of company taking action b.
Let f be the decision process of company g, g(x) is the decision company makes, some a for the individual x. Then the right thing to do
g(f(x)) = argmax_{a\in A}(u(x)(a)) = g(f(x), p(x))
Simple, we do as god says, act as if we have the knowledge of an oracle–even when knowing some discriminable information that we then chose to ignore.

This is not as easy as it looks in a formula. Think of a person with a clown nose and one without, your behavior will likely be very different between those two persons, even if you decide that a clown nose has absolutely nothing to do with the task at hand.

Additionally, the nature of our imperfection dictates that our systems that we build are imperfect. What if we cannot achieve God’s will? What if we fail to do the virtuous even when we know what the right thing to do is?

What could a neutral thirdparty reasonably demand of a faulty company? One suggested approach is to establish probabilistic equality among protected classes. Suppose there are some number of classes, m\in M which corresponds to values of p(x), between which we must protect their utility. (So for example M could be cartesian product of age, sex, race, birthplace, religion and political party)

E(u(x)(g(f(a)))| m) = c\ \forall m\in M

That the customer utility for each class is identically some value c. This is a simplification as there are other classes of equivalence in stochastic variables.

Note this framework has some slight benefit over traditional machine learning framework evaluating equality on confusion matrix of classifier performance g. There two most inspiring examples that I suffer from:

Situation 1: I noticed that my coworker was getting Tesla car advertisements while I do not receive one. Even though my utility in not receiving the advertisement was a negligibly loss–because I cannot afford a tesla, I still feel angry. I may even be tempted to find a protected attribute of mine to claim that tesla discriminated against me in its advertisement campaign: What! they think mid-aged Asian man can’t have a midlife crisis or can’t afford to splurge on a Tesla? In this case a true negative for prediction regarding response/conversion through a Tesla car Ad but offensive enough to cause problems. In retrospect this would have had positive utility for me, when I reached out to Tesla I learned more about how the car would work for me. But the decision seem to produce a negative sentiment from its subject.(The company has, since my drafting of this blog entry, sent me repeated invitation to test drive the S, perhaps due to recent but small increase in my disposable cash, which I may consider calling upon by taking the offer to test drive, at a suitable time. this is just an example)

Situation 2: I am offended when I do receive an advertisement for STD testing, and in particular for hepatitis family of diseases. For gods sake, there’s a Asian Liver Center at Stanford whose purpose for establishment is to check me for hepatitis or other Liver problems present in Asian livers. In this case, god bless me, that I am free of hepatitis and other liver problems of any kind, and that this is a false positive in advertising. I am offended. And in reality one may argue that the benefit of this advertisement, to me, to increase my chances of early detection is positive–E(u(huan)g(f(huan)))>0 I still feel offended. This case is a false positive to advertisement conversion. It is a positive utility to have shown it to me. And yet it produced negative sentiment.

Situation 3: I just received a piece of snail mail from a Redwood City mortuary advertising their service to Mr. And Mrs. Chang. I am terrified. I feel this is a death threat of some form. Putting the idea of me dying in Redwood City in my head. The letter has hand addressed envelope. This is a false positive for advertising relevance(I did not die, not yet any ways, and I am not planning on dying) it has zero utility for me, and I am definitely feeling very negative sentiment.

These are but several of many possible situations where the company could do the right thing in front of God, and in front of the board, by still be erring and thereby producing very negative sentiment. At risk of running out of numbers to enumerate all of them, I have not numbered all the types starting at 1.

To summarize, there are several factors that ultimately factor into a company’s decision making process, nonexclusively they are:

  • The E.u.g.f for x, whether it is defensible in front of an oracle, God, or court of law;
  • how will any action make the subject individual feel, the sentiment it produces, irrespective of objective utility;
  • is utility function universally accepted;
  • and finally the company’s bottom line.

With these considerations in mind, we can now continue with our exploration of fairness.

Wikipedia Dependency

I find that I can spend a lot of money on a book on a subject but wiki still makes the subject most clear in far far shorter time.
This is becoming a problem. I am less and less able to read longer expositions. Less patience and probably reduced mental capacity to hold longer strands of thoughts. As a species, wiki-style knowledge transfer improves our knowledge sharing, as a person this drastically reduces my own distinctiveness and competitiveness. I may, in fact, be organizing my thoughts as wiki articles. I can say every thing I know in a few minutes, and they are all incredibly clear and right.
I am frustrated with everything else: people speak in imprecise and unedited ways–I can’t stand it, need to ask for clarificationnof every thing! Books do not have introductory paragraph that actually introduces the ensuing content of discussion–what will I be spending next few hours on? Idk! TV will conveniently cut away when vital information should naturally be revealed–and there should be a infographic explaining the relationship between all the characters!!! I can’t stand not knowing the definition of everything–all of which is only available through a link on wiki.
In the future, where we actually do depend on wiki for knowledge, how should it maintained? Admittedly the current management has done well, but when all of humanity shifts to depending on wiki for up to 50% or even 80% of the facts they depend on, there should probably be more thoughts on how it should be maintained.
Not to be worrying about malicious or political edits that the website can have. And further, not worrying about psychological and evolutionary impacts when everyone has access to high quality information. Not considering the possible problems associated with monopolistic situations such as Wikipedia.
If it becomes a public utility, should it not be regulated as public utility. Granted the foundation is an American incorporated organization it already comes with a lot of American values: non-discrimination, nonprofit, apolitical, etc–it is already regulated.
But that regulation is not sufficient for a public utility that a large proportion of the population depends on in a way vey much like how they depend on roads, electricity, water, the weather report, etc. some guarantee of universality must be made to ensure every human has access to knowledge. Some higher level of backup and guarantee of reliable availability in times of crisis. Stated another way, this is mainly to say that more financial resources and more social procedures to safeguard the utility(usefulness, universality and availability) and righteousness(adherence to American values) of Wikipedia and related internet establishments. I’d love for a portion of my taxes to pay for its upkeep, if there comes a time that government regulation are so strong that it becomes part of the government  operations(e.g. USPS, military, intelligence, education, roads, etc), when that is established.
In the same breath, we should say that human knowledge loves freedom. If there is any person in the world who knows of freedom, and who values freedom, and who insists on freedom, that person is with high likelihood a knowledgeable one. Knowledge will resist restriction to the extent of self-destruction. If we do impose any additional restriction not yet ingrown organically, it may be ruined. 
Must tread carefully.

Must think more on the matter.

Equality of Benefit

I’ve been involved in a lot of discussion around bias, equality and fairness regarding algorithmic decision making. Without going into excessive amount of background and detail the gist of my believe at the current moment is that equality of utility is the safest thing for companies to aspire to.

What is equality of utility? Let’s degenerate into binary decision making: given individual x, who has observable features f(x) and protected feature p(x). Suppose the company has to choose among two actions to take {a,b}. What is a workable definite of fairness or equality in such a decision making effort with respect to protected properties p?

Let god bestow us, a neutral third party, with a utility functor u whose evaluation on the individual u(x) results in a function u(x)(a) is the utility of company taking action a to individual x, u(x)(b) is the utility to individual x of company taking action b.

Let g be the decision process of company, g(•) is the decision company makes either a or b for the situation. Then the right thing to do

g(f(x)) = argmax_{i\in{a,b}}(u(x)(i)) = g(f(x), p(x))

Simple, we do as god says is best for the customer, act as if we have the knowledge of an oracle–even when we know of some reason for discrimination.