This is the second part of the ‘From Neural Is to Moral Ought’ series of talks, which follows on from the ‘Ethics 101’ introduction which presented Utilitarianism:

  • As an exercise in optimization within the ‘Moral Landscape’ in order to achieve ‘the greatest happiness for the greatest number’.
  • As a moral theory not without significant problems, even if the above optimization could be achieved.

Here, I want to introduce a new moral theory which I will call ‘Prospectarianism’. This is not because I want to advocate it as a serious moral theory. I just want to use it as a stepping stone towards future arguments.

5. Utility Theory

The Benthamite Utilitarianism of summing usefulness to find a happier place in the ‘moral landscape’ was a significant influence on Utility Theory, within economics. ‘Utility’ is a measure of the usefulness of goods and services that may be traded which ultimately boils down to the price (in money terms) that  people are willing to pay for those goods and services. Whereas utilitarianism is normative, utility theory is supposed to be descriptive – using abstracted mathematical models that approximate to how people actually behave in choices that lead to trade. With marginal utility:

  • If A values X less than what he can sell X for then he will want to sell X.
  • If B values X more than what he can buy X for then he will want to buy X.
  • If both of the above occur, there can be a sale of X from A to B.

The mathematics of risk, gambling and lotteries was the inspiration for the foundation of economic theories in the 18th Century, calculating the ‘expected value’ of a particular scenario, to compare with alternatives:


The ‘expected value’ (E) is the mathematical average (mean) return on a gamble, by summing over all possibilities the payout (Ii) of each possibility, weighted by its probability (Pi).

But this created some problems. To circumvent these, Daniel Bernoulli introduced a ‘utility function’ to correct for the fact that:

“The determination of the value of an item must not be based on the price but rather on the utility it yields. … There is no doubt that a gain of a thousand ducats is more significant to the pauper than to a rich man though both gain the same amount.”

I think this Two Ronnies sketch illustrates the point…

Tramp #1: “You know, if I was as rich as Rockefeller, I’d be richer than Rockefeller.”

Tramp #2: “How’s that then?”

Tramp #1: “I’d do a bit of window cleaning on the side.”

The formula for ‘expected utility’ is then:


in which the payout is modified by the utility function, u(w). Bernoulli proposed:

u(w) = log(w)

for this.

Thus, we have a shift from:

‘expected value’ (known in the past as ‘mathematical expectation’)


‘expected utility’ (known in the past as ‘moral expectation’)

What is valued is return on investment, but how we use it in calculations is to modulate whatever is measured with the utility function. It was said that:

“mathematicians estimate money in proportion to its quantity”


“men of good sense [estimate money] in proportion to the usage that they may make of it.”

The economics theory is all about managing risk but what I want to discuss here is nothing to do with risk, uncertainties and probabilities. In the optimization of the ‘moral landscape’, I am continuing to ignore the rather significant practical difficulty that we cannot predict the future with any real certainty (I am still assuming I am Laplace’s Demon ). The principle here is one of science. Bernoulli introduced a function (the utility function) to modify a system that had some problems to create one that worked better. (Complexity was added, but the advantage of the better usefulness of the new theory outweighed the disadvantage of the added complications.)

6. Prospect Theory

Some 240 years after Bernoulli, Daniel Kahneman and Amos Tversky proposed a new improvement: ‘Prospect Theory’, with 2 non-linear functions, w() and u():


Note the deltas (‘Δ’) in the equation. Although the equations I have presented before now have calculated a total utility U, economists are only interested in changes in U – ‘marginal utility’. A change from U=2 to U=4 is the same as a change from U=4 to U=6 but it is meaningless to say that U=6 has three times the utility of U=2. The ‘reference point’ is arbitrary. Referring back to the landscape analogy (see the previous section: ‘The Moral Landscape’), we can choose to set the zero point for heights at any level, as long as that convention is accepted. In most cases, we happen to agree to use ‘mean sea level’ as the reference point rather than ‘height above the agreed centre of the Earth’ for example. In Prospect Theory, the reference point is effectively how things are now – the status quo.

The w() function operates on probabilities and accounts for the tendency to overreact to unlikely events. The v() function translates measurable quantities to an indicator of value in order to account for:

  • ‘loss aversion’: the tendency  of people to make decisions in which it is more important to avoid losses (ΔIi<0) than to make gains (ΔIi>0); in quantitative terms, this number comes out at around 2, as well as
  • diminishing marginal utility (‘a gain of a thousand ducats is more significant to the pauper than to a rich man’).

The S-shaped curve of the v() function is shown below.

Value function for Prospect Theory

Prospect Theory’s S-curve value function v()

The combined effect of these non-linearities can account for the observed behaviour of people that make them risk-averse in some scenarios and risk-seeking in others, for example:

  • A certainty of a gain is preferable to a chance of a gain.
  • A chance of a loss is preferable to a certainty of a loss.

Two scenarios that are actually the same will tend to be assessed differently, depending on whether the problem is presented in a positive (prospect of a gain) or a negative (prospect of a loss) manner:

  • I give you an 80% chance of winning $1000, or
  • I give you $1000 but you must then take a 20% risk of losing $1000.

This is what is called the ‘framing effect’ – the preference depends on how the question is framed.

So Prospect theory takes into account the ‘irrational’ behaviour of how Homo Sapiens individuals actually do behave instinctively – particularly when they rely on our intuition (‘gut feeling’) when making decisions of the sort that they have to deal with only infrequently in life (example: buying and/or selling a house) and the decision is made in relative isolation of other their other decisions.

In contrast, Utility theory is for explaining how a ‘homo economicus’ ideally should behave rationally. Note that people are more inclined to act this way (‘more rationally’) if they are asked to ‘act like a trader’ – i.e. for if they will be making decisions repeatedly’ (an example: commercially buying and selling properties within a large property portfolio), in which each decision is just one of many similar decisions and it is the overall effect of the many decisions that is important.

7. Proposing Prospectarianism

What if we take the descriptive Prospect Theory as an inspiration for a normative theory, without at this point asking for any justification in doing so?:

  • Prospectarianism is to Prospect Theory, as
  • Utilitarianism is to Utility Theory.

However, Prospectarianism will only adopt 1 of the 3 main ideas of Prospect Theory. For now, I will ignore the effect of the reference point (the deltas: ‘Δ’). And I will also continue to ignore aspects concerning risk/probability so Prospect Theory’s w() function will be discarded, leaving us just with the S-shaped curve of the v() function:

A tentative value function for Prospectarianism

A tentative Prospectarian S-curve value function v()

I will define this function here as:

v(x) = (1 – e-αx), for x ≥ 0


v(x) = n(e-αx– 1), for x ≤ 0


  • n defines how much more that pain is counted than pleasure. Let us start with n=2.
  • α is a factor that adjusts for however we are measuring the intensity of pleasure and pain into a personal (individual’s) utility factor (between –n and 1). For simplicity, assume α=1.

Consider the v() function as follows. The intensity of an individual’s pleasure or pain is what we value, but what we find most useful is to moderate this by the function v() when aggregating into an overall utility value for all people, for all time:


Utilitarianism is contained within the above formula but the S-curve is replaced by a linear function:

v(x) = x

Value function for Utilitarianism

The Utilitarian value function v()

This linear function results in Utilitarianism aggregating pleasure and pain by simple addition, resulting in absurd counter-examples discussed previously:

  • Parfit’s ‘Repugnant Conclusion’ of maximizing total utility, and
  • the opposite problem of maximizing average utility, thus rejecting below-average lives that are still ‘worth living’.
  • Nozick’s ‘Utility Monsters’ hoarding pleasure, and
  • the opposite problem of loading all the pain onto one individual for the benefit of many others, such as with the unfortunate hospital visitor who becomes a mere ‘collection of spare parts’ organ donor.

In contrast, Prospectarianism’s ‘moral value’ function v() has the potential to aggregate pleasure and pain so as to:

  1. Prioritize the minimization of pain over the maximization of pleasure, and
  2. Distribute pleasure and pain across individuals

8. Popper’s Pinprick

Let’s look at the first of these: the prioritizing of the minimization of pain over the maximization of pleasure. This is not new. Karl Popper proposed an extreme version of this in ‘The Open Society and Its Enemies’:

 “I believe that there is, from the ethical point of view, no symmetry between suffering and happiness, or between pain and pleasure. Both the greatest happiness principle of the Utilitarians and Kant’s principle ‘Promote other people’s happiness…’ seem to me (at least in their formulations) wrong on this point … In my opinion human suffering makes a direct moral appeal, namely the appeal for help, while there is no similar call to increase the happiness of a man who is doing well anyways.”

(Chapter 9, note 2, page 284)

Popper thus proposed what has became known as ‘Negative Utilitarianism’. This is effectively the same as proposing a value function of:

v(x) =0

for x>=0 and

v(x) =x

for x<0.

Value function for Negative Utilitarianism (red), superimposed on that of basic Utilitarianism (blue)

The Negative Utilitarianism value function v() (red), superimposed on that of basic Utilitarianism (blue)

Note: This issue of asymmetry between the positive (pleasure) and negative (pain) is similar to the asymmetry in epistemology that Popper is more famous for: that no number of confirmations will positively prove a truth claim whereas a single counter-example will disprove a claim.

A counter-argument to Popper’s proposal is the ‘pinprick argument’. Supposing there was a way to painlessly terminate life, any pain could be overcome simply by extermination of the sufferer! It would seem to

‘call for the destruction of the world even if only to avoid the pain of a single pinprick’!

The problem here is that there is no amount of happiness that would offset the slightest pain. In contrast, Prospectarianism would allow us to trade off pleasure and pain to the ration 1:n instead of 1:∞. (There is then ‘only’ the matter of deciding an appropriate value for n!)

9. Monsters and Lambs

Now I turn to the second aspect of Prospectarianism’s value function: the distribution of pleasure and pain across individuals.

The saturating feature of the Prospectarian value function

v(x)→1 as x→∞

will work against the transfer of hedons of pleasure from the many to a single ‘Utility Monster’. In fact, there is a strong mechanism for the redistribution of valuable resources. In the transfer of hedons from a single wealthy individual (in hedonistic terms) to many paupers, the exponential gain term in v(x) will outweigh the n-weighting of losses so that the collective paupers’ gain of v(x) will be more than the single person’s loss.

That leaves the Utilitarian problem of the hospital visitor, plundered for functioning body parts. As the antithesis of Nozick’s ‘Utility Monster’, the victim here is a ‘Utility Lamb’, sacrificed for the benefit of others. Prospectarian’s solution offers a mixed bag:

  • When trading between pleasure and pain, it is an improvement, since pain is counted n times more than pleasure. In the most simplistic of moral calculation, the sacrifice of an individual is justified if it saves n others. If you are unhappy with this with n=2 (from Kahneman and Tversky’s experiments with Prospect Theory), then increase n! What’s your price? If you deny you have one then you expose yourself to the counter-counter-example: you would not sacrifice a single individual to save the entire rest of society. This leads us on to…
  • When we look at just moving pain from one place to another, things are worse. The saturation of pain (v(x)→ –n as x→ -∞) advocates transferring pain to someone who already has more pain! Ultimately, all the pain of the world would be loaded onto a single individual! (This is a major problem which I will just ignore for the moment.) Not only do we seem to accept the sacrificing of an individual in some circumstance, we positively promote it!

10. Conclusion

I have proposed an improvement over Utilitarianism, something that is certainly not free of problems but one that does not suffer from many of problems than Utilitarianism does. It is a step in the right direction (although there may be some fundamental barriers ahead). The point here is that an improvement has been achieved by introducing some non-linearities into the basic Utilitarianism (with some control parameters to define the non-linearity, which need to be tweaked somehow). We could improve it further to avoid some remaining problems (an obvious one being the removal of the saturation of pain in the value function) but that is beyond the scope of the point here and would move us away from the close analogy with Prospect Theory.

We have gone:

  • from Utilitarianism (a normative, linear proposition)
  • via Prospect Theory (a descriptive, non-linear proposition)
  • to Prospectarianism (a normative, non-linear proposition)

without at this point making any justification about switching between ‘is’ and ‘ought’.

In the next part, I continue this interplay between the normative and the descriptive (with emphasis on the ‘play’) and between the linear and non-linear by looking at something quite different.

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2 Responses to Prospectarianism

  1. Wyrd Smythe says:

    I’m going to have to re-read this a couple times before I can claim to be keeping up, but I was really struck by the idea of asymmetry between misery and happiness. That had never occurred to me, but it “clicks” immediately as an accurate assessment!

  2. Pingback: Moral Equalization | Headbirths

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