“The most good for the most people” is the most common everyday description of Utilitarianism. If you want to think long-term then its “The most good for the most people across the most time”

I’d like to take the broader view which simply suggests that “possible worlds” (worlds we can imagine) can be assigned a single (non-unique) summary value.  This allows them to be compared and ordered for utility/good.

My approach will be fraught and won’t be unique, but it will be structured which, in general, makes for good conversation.

Because I don’t want to  focus in on whether happiness/ actualization/number of bunnies or any other specific approach to moral evaluation is the ‘right’ one, I’m simply going to call my function f. The big bonus is that this system will be general enough to apply to assessing the future from multiple perspectives like knowledge, confidence etc and not just good/utility.

f is a function which takes any possible world and assigns it (rather cleverly or maybe magically) a utility (‘goodness value’)  between 0 and 1. Worlds with rating 1 are perfect, worlds with rating 0 are useless and I’d rather be in a 0.8 than a 0.5 if f (for example) rated “worlds I’d rather be in”.

Promising to think long term, we don’t want to act like we can evaluate a world in isolation. We need to importantly look at all of  a single world’s possible futures and their likelihoods. To do this, here’s a diagram of a start world S from which a number of possible worlds can be reached in the next instant.

The idea is that we use f as well as the probability of each of these worlds to work out the expected utility value (E) we will achieve from the successors of S.  Now you might say “this isn’t an issue of probability, it’s an issue of choice” but say that S is a world just a short way into the future from right now and you’ll start to see that even if you yourself could decide everything at S you yourself right now wouldn’t be certain about which choice you would make in the near future. In other words, we can factor in all and any desires to choose any particular world into the probabilities that they will be chosen. The need to do this is even greater when it comes to dealing with the world as a whole (rather than just yourself) and the fact that laws of nature, everyone’s desires and random chance all affect the outcomes.

The method of arriving at the expected utility E is broadly :

E(X)=SUM(X->r=1..N) of (Prob(X->r)*f(r))

….this will assign E(X)=0..1, a calculation of the expected utility of the next world considering the possible of choices.

That is to say that you look at the product of every immediately reachable possible world’s utility  and the probability of that world occurring.

So to really do the trick we need to be able to not just deal with possible worlds in isolation, but “possible world chains” of an arbitrary possible world X and it’s entire possible futures:

The method of combination needs to be such that to evaluate g you evaluate the instantaneous good at world X then combine it with all its successors and their successors etc each multiplied by the probabilities of them occurring. g is therefore a recursive function, but one that can be caused to stabilize if you apply certain limits on how important the future is compared to now.

As an equation:

Try 1: Get the isolated value of the instantaneous world:-

g(X)=f(X)

Try 2: Rate the instantaneous importance of now against immediate future importance:-

g(X)=f(X)*(importance) + (1-importance)*E(X)

Step 3: adapt E to be for all futures rather than just immediate ones:

g(X)=f(X)*(importance) + (1-importance)*SUM(X->r=1..N) of g(r)*Prob(r)

In practice you need to work out importance as a discount function and it should be more than 0.5 for the current world being more important than the combination of all future ones otherwise your search for g(X) may well go on forever. An alternative is to use a heuristic approximation (ie. guessing technique) that looks at a small sample of future possible worlds and estimates their utility and their likelihoods, ignoring the unknown ones.  Doing this well involves techniques I will describe in another post.

In my next basis post I hope to take this model and create specific labels for specific types of worlds with specific configurations of futures. For example a “calamity” might be “a choice where all accessible future worlds  are worse than the current one”. In a final post I will look at strategies for using this approach to optomise in earnest.

For more on discount functions see Kenneth Arrow’s excellent paper where he applies them to Global Warming

For a rather good formal summary see Kripke Structures which were the major influence in writing this.

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But statements like “Everyone knows X and everyone knows that everyone knows X” start to make it much harder

This happens to be the strong version of ‘group knowledge’ of X:

‘I know that nobody thinks that everyone knows X” is harder still. If you aren’t convinced, just try building up to your own limit. The point isn’t that it’s hard to do, it’s that it’s hard to communicate.

If the top sentences were to be written in a more formal notation (where all the references are clear)  it would be something like:

1: “London is a city”:   is_a(London,City)

2: “I know London is a city”:  Know[I, is_a(London,City)]

3: “I know that you think that London is a city”: Knows[I, Think[you, is_a(London,City)]]

I tend to label 1, 2 and 3 as ‘first’, ‘second’ and ‘third order statements’ respectively. This is because the first one is simply a statement, the second is a statement about a statement and the third is a statement about a statement about a statement etc.

The complexity builds up pretty quickly even when all the markers are present. The problem is that there are so many social abstracts that depend on second and third order concepts like “what people believe that  most people believe” and “what people believe that almost everyone thinks”

Here are just a few examples:

Most racists in the BNP believe that most BNP members could tell ‘white’ from ‘non-white’ [second order]

Does everyone think that everyone thinks that ‘the Tories’ will win the next election? [third order]

Does everyone believe that everyone knows that the value of Jewelry is based only on other people over-valuing it ? [third order] {This nearly made a famous British Jewler go bust}

Christians believe that God exists [second order]

Christians believe that they know God exists (because God tells them so) [third order]

Scientists know that they don’t know God exists (because their methods cannot test him) [third order]

How do scientists know that they can’t know God Exists? (because God is unfalsifiable) [third order]

At the very least I hope you can agree they are a mouthful, where the question “Do people have ‘Group Knowledge’ of the fact Jewelry is overpriced?” is less so.

Politicians try to imply statements in the third and fourth (comment highlighted) orders all the time and many such statements are genuine open questions. As we explore increasingly sophisticated ideas in the social graph we need to popularize terms like ‘Group Knowledge’ and create new ones for similar phenomena so we can have a richer debate about the mechanics of politics, economics and society.

MIT’s Stephen Pinker explains why this all matters and how it relates to indirect speech acts (like offering bribes) in one of his fantatstic ted talks:

For a much more academic treatment on Group Knowledge see Group knowledge and group rationality: a judgment aggregation perspective  C List – Episteme, 2005 – Edinburgh Univ Press

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So ‘Slavery’:

GNU foundation founder and general ‘Free as in Freedom’ guy Richard Stallman declared:

“If all you can do in your current occupation is make slaves of people then GO DO SOMETHING ELSE!”

in his 2008 lecture at Manchester University.  This got me thinking: ‘Why do comfortable middle class people with comfortable lives and very little correlation between getting new stuff and feeling happier, bother taking things from people who do actually want them?’ i.e Why do comfortable people drive hard bargains or get involved in selling customers things that the customers don’t want?

To frame this a bit more formally:  With the decreasing marginal utility of wealth, how does effecting a non-pareto trade benefit those who have more than enough?’

So breaking this down into premises [and out of economics jargon]:

A Pareto trade [technically 'pareto-efficient trade'] is one where an exchange benefits both parties, it is the trade of a surplus for a surplus. I have too much timber but need some cloth, you have too much cloth but need some timber -if we trade it will benefit us both. Things only get a little more complicated when you talk about how much timber for how much cloth, but the principle stays the same -it’s win win.

A Non-pareto trade is therefore one where someone loses out

[a much more formal definition]

The diminishing marginal utility of wealth is a desciption of how $1 extra is much less useful to a billionaire than it is to a Ugandan Farmer. Similarly 1 extra dollar is more useful to a millionaire than to a billionaire, but is still worth much more to the Ugandan Farmer.

[more]

So, you would imagine that: As the incentive to gain extra money decreases, so does the incentive to take other people’s money.

This is probably broadly true even  now: Someone who needs money to feed their family is far more likely to steal criminally than someone who has a stable source of income greater than her requirements. However, I notice a lot of comfortable middle class people get involved in marketing products they don’t really believe in. That is to say they think that either the customer or society or both will be worse off for responding to the marketing messages. In other words, they believe they are effecting non-pareto trades with their customers or encouraging them to become involved in them elsewhere.

Now, I see this all the time and it’s not just marketing, it’s people in investment banking, people in telesales, journalists as well as a whole range of less often criticized fields. My deep-set feeling is avoid it!  Particularly if your life is comfortable, you are much more likely to see a good return through making society better than by exploiting individuals. I hope to go into how later on, but at the very least helping yourself will not help you much.

While Slavery is a dramatic and politically loaded term for this [and is very much Stallman's rather than mine], it gets the message across. When you make non-pareto trades with people you essentially make use of them beyond what is good or rightful. You might think that more stuff is always good, but after you are comfortable you will find that the comfort does not increase and the cost to the other person does not make a meaningful contribution. It is fundamentally an issue of the exploitation of someone else for your needless gain, a mild form of slavery.

Taken all together this binds society up in knots of manipulation where everyone is serving some desires that exploit them and there is little coherence in motivation. So it is incumbent on us to avoid slavery. This means avoiding enslaving others, avoiding becoming a slave and avoiding helping people make slaves of others. Genuine freedom of choice for people is desirable to us all and if we ever deviate from fostering that, there should be clear and valid goals associated.

In later posts I hope to consider how corporations legal obligations to their shareholders and to ‘growth’ as well as competition more broadly incentivise people to make non-pareto trades. For now it is enough to say that no matter what grand organizing systems we live in, the baseline will be true: ‘Once you have enough to be comfortable, every trade you do should be a win win. If you win and the other person loses, you lose too.

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