# Alan Carter on the Complexity of Value

It’s always good news when someone else develops an idea independently from you. It's a sign you might be onto something. Which is why I was excited to discover that [Alan Carter](http://en.wikipedia.org/wiki/Alan_Carter_%28philosopher%29), Professor Emeritus of the University of Glasgow’s Department of Philosophy, has developed the concept of [Complexity of Value](http://wiki.lesswrong.com/wiki/Complexity_of_value) independent of Less Wrong.

As far as I can tell Less Wrong does not know of Carter, the only references to his existence I could find on LW and OB were written by me. Whether Carter knows of LW or OB is harder to tell, but the only possible link I could find online was that he has criticized the views of [Michael Huemer](http://www.colorado.edu/philosophy/fac_huemer.shtml), who knows Bryan Caplan, who knows Robin Hanson. This makes it all the more interesting that Carter has developed views on value and morality very similar to ones commonly espoused on Less Wrong.

The Complexity of Value is one of the more important concepts in Less Wrong. It has been elaborated on its [wiki page](http://wiki.lesswrong.com/wiki/Complexity_of_value), as well as [some](/lw/ld/the_hidden_complexity_of_wishes/) [classic](/lw/l3/thou_art_godshatter/) [posts](/lw/lb/not_for_the_sake_of_happiness_alone/) by Eliezer. Carter has developed the same concept in numerous papers, although he usually refers to it as “a plurality of values” or “multidimensional axiology of value.” I will focus the discussion on [working papers](http://glasgow.academia.edu/AlanCarter/Papers) Carter has on the University of Glasgow’s website, as they can be linked to directly without having to deal with a pay wall.  In particular I will focus on his paper "[A Plurality of Values](http://glasgow.academia.edu/AlanCarter/Papers/86004/A_plurality_of_values)."

Carter begins the paper by arguing:

> Wouldn’t it be nice if we were to discover that the physical universe was reducible to only one kind of fundamental entity? ... Wouldn’t it be nice, too, if we were to discover that the moral universe was reducible to only one kind of valuable entity—or one core value, for short? And wouldn’t it be nice if we discovered that all moral injunctions could be derived from one simple principle concerning the one core value, with the simplest and most natural thought being that we should maximize it? There would be an elegance, simplicity and tremendous justificatory power displayed by the normative theory that incorporated the one simple principle. The answers to all moral questions would, in theory at least, be both determinate and determinable. It is hardly surprising, therefore, that many moral philosophers should prefer to identify, and have thus sought, the one simple principle that would, hopefully, ground morality.

> And it is hardly surprising that many moral philosophers, in seeking the one simple principle, should have presumed, explicitly or tacitly, that morality must ultimately be grounded upon the maximization of a solitary core value, such as quantity of happiness or equality, say. Now, the assumption—what I shall call the presumption of value-monism—that here is to be identified a single core axiological value that will ultimately ground all of our correct moral decisions has played a critical role in the development of ethical theory, for it clearly affects our responses to certain thought-experiments, and, in particular, our responses concerning how our normative theories should be revised or concerning which ones ought to be rejected.

Most members of this community will immediately recognize the similarities between these paragraphs and Eliezer’s essay “[Fake Utility Functions](/lw/lq/fake_utility_functions/).” The presumption of value monism sounds quite similar to Eliezer’s description of “someone who has discovered the One Great Moral Principle, of which all other values are a mere derivative consequence.” Carter's opinion of such people is quite similar to Eliezer's.

While Eliezer discovered the existence of the Complexity of Value by working on Friendly AI, Carter discovered it by studying some of the thornier problems in ethics, such as the [Mere Addition Paradox](http://en.wikipedia.org/wiki/Mere_addition_paradox) and what Carter calls the Problem of the Ecstatic Psychopath. Many Less Wrong readers will be familiar with these problems; they have been discussed numerous times in the community.

For those who aren’t, in brief the Mere Addition Paradox states that if one sets maximizing [total](http://en.wikipedia.org/wiki/Average_utilitarianism) wellbeing as the standard of value then one is led to what is commonly called the [Repugnant Conclusion](http://en.wikipedia.org/wiki/Mere_addition_paradox#The_Repugnant_Conclusion), the belief that a huge population of people with lives barely worth living is better than a somewhat smaller population of people with extremely worthwhile lives. The Problem of the Ecstatic Psychopath is the inverse of this, it states that, if one takes [average](http://en.wikipedia.org/wiki/Average_utilitarianism) levels of well-being as the standard of value, that a population of one immortal ecstatic psychopath with a nonsentient machine to care for all their needs is better than a population of trillions of very happy and satisfied, but not ecstatic people.

Carter describes both of these problems in his paper and draws an insightful conclusion:

> In short, surely the most plausible reason for the counter-intuitive nature of any mooted moral requirement to bring about, directly or indirectly, the world of the ecstatic psychopath is that either a large total quantity of happiness or a large number of worthwhile lives is of value; and surely the most plausible reason for the counter-intuitive nature of any mooted injunction to bring about, directly or indirectly, the world of the Repugnant Conclusion is that a high level of average happiness is also of value.
> 
> How is it that we fail to notice something so obvious? I submit: because we are inclined to dismiss summarily any value that fails to satisfy our desire for the one core value—in other words, because of the presumption of value-monism.

Once Carter has established the faults of value monism he introduces [value pluralism](http://en.wikipedia.org/wiki/Moral_pluralism) to replace it.^1^  He introduces two values to start with, “number of worthwhile lives” and “the level of average happiness,” which both contribute to “overall value.”  However,  _their contributions have diminishing returns,^2^ so a large population with low average happiness and a tiny population with extremely high average happiness are both  worse than a moderately sized population with moderately high average happiness. _

This is a fairly unique use of the idea of the complexity of value, as far as I know.  I’ve read a great deal of Less Wrong’s [discussion](/lw/17h/the_lifespan_dilemma/) [of](/lw/14s/the_difficulties_of_potential_people_and_decision/) [the](/lw/14z/a_normative_rule_for_decisionchanging_metrics/) Mere Addition Paradox, and most attempts to resolve it have consisted of either trying to reformulate Average Utilitarianism so that it does not lead to the Problem of the Ecstatic Psychopath, or redefining what "a life barely worth living" means upwards so that it is much less horrible than one would initially think.  The idea of agreeing that increasing total wellbeing is important, but not the be all and end all of morality, did not seem to come up, although if it did and I missed it I'd be very happy if someone posted a link to that thread.

Carter’s resolution of the Mere Addition Paradox makes a great deal of sense, as it manages to avoid every single repugnant and counterintuitive conclusion that Total and Average Utilitarianism draw by themselves while still being completely logically consistent.  In fact, I think that most people who reject the Repugnant Conclusion will realize that this was their [True Rejection](/lw/wj/is_that_your_true_rejection/) all along.  I am tempted to say that Carter has discovered Theory X, the hypothetical theory of population ethics [Derek Parfit](http://en.wikipedia.org/wiki/Derek_Parfit) believed could accurately describe the ethics of creating more people without implying any horrifying conclusions.

Carter does not stop there, however, he then moves to the problem of what he calls “pleasure wizards” (many readers may be more familiar with the term “[utility monster](http://en.wikipedia.org/wiki/Utility_monster)”).  The pleasure wizard can convert resources into utility much more efficiently than a normal person, and hence it can be argued that it deserves more resources.  Carter points out that:

> …such pleasure-wizards, to put it bluntly, do not exist... But their opposites do. And the opposites of pleasure-wizards—namely, those who are unusually inefficient at converting resources into happiness—suffice to ruin the utilitarian’s egalitarian pretensions. Consider, for example, those who suffer from, what are currently, incurable diseases. … an increase in their happiness would require that a huge proportion of society’s resources be diverted towards finding a cure for their rare condition. Any attempt at a genuine equality of happiness would drag everyone down to the level of these unfortunates. Thus, the total amount of happiness is maximized by diverting resources away from those who are unusually inefficient at converting resources into happiness. In other words, if the goal is, solely, to maximize the total amount of happiness, then giving anything at all to such people and spending anything on cures for their illnesses is a waste of valuable resources. Hence, given the actual existence of such unfortunates, the maximization of happiness requires a considerable inequality in its distribution.

Carter argues that, while most people don’t think all of society’s resources should be diverted to help the very ill, the idea that they should not be helped at all also seems wrong.  He also points out that to a true utilitarian the nonexistence of pleasure wizards should be a tragedy:

> So, the consistent utilitarian should greatly regret the non-existence of pleasure-wizards; and the utilitarian should do so even when the existence of extreme pleasure-wizards would morally require everyone else to be no more than barely happy.

Yet, this is not how utilitarians behave, he argues, rather:

> As I have yet to meet a utilitarian, and certainly not a monistic one, who admits to thinking that the world would be a better place if it contained an extreme pleasure-wizard living alongside a very large population all at that level of happiness where their lives were just barely worth living…But if they do not  bemoan the lack of pleasure-wizards, then they must surely value equality directly, even if they hide that fact from themselves. And this suggests that the smile of contentment on the faces of utilitarians after they have deployed diminishing marginal utility in an attempt to show that their normative theory is not incompatible with egalitarianism has more to do with their valuing of equality than they are prepared to admit.

Carter resolves the problem of "pleasure wizard" by suggesting equality as an end in itself as a third contributing value towards overall value.  Pleasure wizards should not get all the resources because equality is valuable for its own sake, not just because of diminishing marginal utility.  As with average happiness and total worthwhile lives, equality is balanced against other values, rather than dominating them.   It may often be ethical for a society to sacrifice some amount of equality to increase the total and average wellbeing. 

Carter then briefly states that, though he only discusses three in this paper, there are many other dimensions of value that could be added.  It might even be possible to add some form of deontological rules or virtue ethics to the complexity of value, although  they would be traded off against consequentialist considerations.  He concludes the paper by reiterating that:

> Thus, in avoiding the Repugnant Conclusion, the Problem of the Ecstatic Psychopath and the problems posed by pleasure-wizards, as well as the problems posed by any unmitigated demand to level down, we appear to have identified an axiology that is far more consistent with our considered moral judgments than any entailing these counter-intuitive implications.

Carter has numerous other papers discussing the concept in more detail, but “A Plurality of Values” is the most thorough.  Other good ones include “[How to solve two addition paradoxes and avoid the Repugnant Conclusion](http://glasgow.academia.edu/AlanCarter/Papers/158176/How_to_solve_two_addition_paradoxes_and_avoid_the_Repugnant_Conclusion),” which more directly engages the Mere Addition Paradox and some of its defenders like [Michael Huemer](http://spot.colorado.edu/~huemer/); "[Scrooge and the Pleasure Witch](http://glasgow.academia.edu/AlanCarter/Papers/661104/Scrooge_and_the_Pleasure_Witch)," which discusses pleasure wizards and equality in more detail; and “[A pre-emptive response to some possible objections to a multidimensional axiology with variable contributory values](http://glasgow.academia.edu/AlanCarter/Papers/158273/A_pre-emptive_response_to_some_possible_objections_to_a_multidimensional_axiology_with_variable_contributory_values),” which is exactly what it says on the tin.

On closer inspection it was not hard to see why Carter had developed theories so close to those of Eliezer and other members of Less Wrong and SIAI communities. In many ways their two tasks are similar. Eliezer and the SIAI are trying to devise a theory of general ethics that cannot be twisted into something horrible by a rules-lawyering Unfriendly AI, while Carter is trying to devise a theory of population ethics that cannot be twisted into something horrible by rules-lawyering humans. The worlds of the Repugnant Conclusion and the Ecstatic Psychopath are just the sort of places a poorly programmed AI with artificially simple values would create.

I was very pleased to see an important Less Wrong concept had a defender in mainstream academia.  I was also pleased to see that Carter had not just been content to develop the concept of the Complexity of Value.    He was also able to employ in the concept in new way, successfully resolving one of the major quandaries of modern philosophy.

**Footnotes**

^1^I do not mean to imply Carter developed this theory out of thin air of course. [Value pluralism](http://plato.stanford.edu/entries/value-pluralism/#ValConRatReg) has had many prominent advocates over the years, such as [Isaiah Berlin](http://en.wikipedia.org/wiki/Isaiah_Berlin) and [Judith Jarvis Thomson](http://en.wikipedia.org/wiki/Judith_Jarvis_Thomson).

^2^[Theodore Sider](http://en.wikipedia.org/wiki/Theodore_Sider) proposed a theory called "[geometrism](https://docs.google.com/viewer?a=v&q=cache:1JN1p5bFPT0J:tedsider.org/papers/theory_X.pdf+derek+parfit+theory+x&hl=en&gl=us&pid=bl&srcid=ADGEESgNDbO4KV0bKbHMkELB_O64FNRdz20r0R3FcmmpthKaTaJBCSiHAFBtEKA2egIqeJ6KXnoCNrVZfnUNhtjrEL-amgKW8mzBTewBhlT0IbbFRtNgPlgU3vGM7TvxK0K3OJphy6LD&sig=AHIEtbSw_UJVTARTkVcfgVDzxX2G-tN65Q)" in 1991 that also focused on diminishing returns, but geometrism is still a monist theory, it had geometric diminishing returns for the people in the scenario, rather than the values creating the people was trying to fulfill.

**Edited -** To remove a reference to Aumann's Agreement Theorem that the commenters convinced me was unnecessary and inaccurate.