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Measuring Well-Being

A consequentialist theory of ethics requires that individual well-being be measurable, and furthermore that well-being be comparable between both individuals and species.

Table of Contents

I have argued elsewhere1 for the need for ethics to be based ultimately on the consequences of actions (i.e., that ethics should be, at least in part, consequentialist2), and furthermore that these consequences should be measured in terms of the well-being of individuals.  Having the ability to measure well-being is equivalent to possessing a metric by which well-being can indeed be measured.  For the unrealistic case of a completely isolated individual, all that is required of this metric is that it be an accurate measure of well-being for the individual himself.  In reality, however, ethical judgements must be made in the context of multiple individuals, and therefore this metric must not only be applicable to these individuals, but it must provide an accurate measure of the relative well-being of one individual vs. another.  This is known in philosophy and economics as the problem of interpersonal comparison of well-being3.  Furthermore, traditional welfare economics has concentrated only on human well-being.  However, many philosophers4 believe that any theory of ethics needs to take the well-being of non-human agents (e.g. animals) into account.  If this is true, then the well-being metric must also apply to all species of agent, and in particular, it must be inter-species comparable.

I have also argued that any metric of well-being should be completely objective.  Indeed, this is necessarily so if it is to be applicable to non-human agents who cannot report their current level of psychological well-being.  I propose here such a metric in a very schematic, speculative form.  While devising any such metric will inherently involve value judgements, there are certainly many details that must be worked out, and undoubtedly many improvements could be made to my proposal from a scientific standpoint alone, I believe that what I propose is the right approach to establishing such a metric.

I will begin by giving a very brief overview of the history of well-being measurement and its current state in modern philosophy and economics, and reiterate my argument for a fundamental change in the thinking with respect to such a metric.  I will then present the details of my proposal.

The History of Well-Being
Utilitarianism, the doctrine that ethics should be based on the overall sum of well-being, or utility, of individuals was first proposed in a comprehensive form in 1776 by Jeremy Bentham in the preface to his essay A Fragment on Government5, and in more detail in his book, The Principles of Morals and Legislation (1781), in particular Chapter I.  His student, John Stuart Mill, developed Bentham’s idea in his classic essay Utilitarianism6.  These and other philosophers of the day envisioned well-being as measurable in a cardinal sense, meaning that a value could be determined for a particular person’s level of well-being, based on a metric as describe above. 

However, around the turn of the 19th century, philosophers and economists began to question the use of cardinal utility as a measure of well-being7.  Levels of well-being are normally based on verbal reports from individuals, and this method of ascertaining these levels was called into question for two reasons.  One was that it was not felt that individuals could verbally provide a consistent and precise cardinal value of their current well-being.  Perhaps more importantly, however, verbal reports were considered non-objective: there was no way to confirm independently that the report from the individual was honest and accurate.

To address these problem, economist developed the theory of ordinal utility, in which all that was required was that individuals order a set of economic choices according to their personal preference.  Choices about which the individual was indifferent were considered to have equivalent utility.  The concept of ordinal utility could also be applied to society as a whole.  As long as all the different possible states of society could be ordered according to some collective preference, policy makers could then choose the most preferred policy as their goal.  By using ordinal utility or preferences, the difficulty in developing cardinal measure of well-being could be bypassed.

There are, however, two major problems with the use of ordinal utility in its own right.  The first is that ordinal preferences of individuals cannot necessarily be consistently aggregated into a collective ordering.  This fact was proven by Kenneth Arrow in his impossibility theorem8, and can be demonstrated by a simple example.  Assume that three people are deciding between three choices, A, B, and C.  Furthermore, assume that person #1 orders them A > B > C, that person #2’s order is B > C > A, and that person #3’s order is C > A > B.  There is no ordering of these three choices that satisfies all three people.  Furthermore, if a vote was taken on each pair of options, the result would be A > B, B > C, and C > A, which is clearly a contradiction.

The second problem is that a simple ordering gives no indication of how close two alternatives are considered to be to each other.  Suppose that option A was the most preferred option, but option B was very close behind in terms of cardinal utility.  Furthermore, suppose that option B was easy to achieve, while option A was much more difficult.  Then it might make more sense to select option B, as it is the better “value”.  Using simple ordinal utility would provide no basis for making such a decision.

An Objective Measure of Cardinal Well-Being
As mentioned in the Introduction, I believe that any measure of well-being should be objective.  In addition to avoiding the problems with self-reported utility raised by economists as described in the previous section, such a measure could in theory be extended to non-human agents, such as animals, and even plants or machines9.  This extension would be a prerequisite for any comprehensive consequentialist theory of ethics.

Furthermore, I believe that there is a physical as well as (for conscious species) a psychological component of well-being.  Let subscript i denote a particular species, and let j denote a particular individual.  Then the well-being of a particular individual could be given by:

WBij = Fi*fij * Mi*mij


Fi = the maximum level of physical well-being that can be obtained by an individual of species i
fij = the fraction of this maximum that is currently experienced by individual j (i.e., j’s current relative level of physical well-being)
Mi = the maximum level of psychological well-being that can be obtained by an individual of species i
mij = the fraction of this maximum that is currently experienced by individual j (i.e., j’s current relative level of psychological well-being)

I will now propose details on how the values for each of these factors might be objectively determined.  I will state up front once again that these proposals are very tentative, and could certainly be improved by experts in their respective scientific fields.  My purpose here is to raise the possibility that such values can in fact be measured10.

Maximum Level of Physical Well-Being
How might the maximum physical well-being of different species Fi be compared?  Obviously different species vary tremendously with respect to their relative size and complexity.  One might ask, for example, how to compare the well-being of a giant sequoia to that of a mass of (benign) bacteria of the same weight.  Arguments could be made on behalf of both.  In favor of the bacteria is the fact that such a mass would consist of a huge number of individuals, whereas the sequoia only constitutes a single individual.  In favor of the sequoia, however, is the fact that its trillions of cells constitute a much more complex system.

As a first approximation, I would opt for treating these two as roughly equal.  In particular, let Fi be equal to the number of cells in a typical organism of the species11.  Thus, since there are roughly 1016 cells in a giant sequoia, a single tree would be equivalent, in terms of maximum physical well-being, to 1016 individual bacteria12.

This metric obviously does not work for non-living entities, such as intelligent machines.  A possible equivalent measure for non-living things might be the number of independent parts.  Thus, a mechanical watch might be physically equivalent (in moral terms) to a 150-cell creature.

Measuring Individual Physical Well-Being
A current relative measure of physical well-being fij is essentially a measure of overall physical health.  It would be expedient for health care experts to devise such a metric13.  One possible method would be to determine life expectancy, which is done to a limited extent by actuaries for the purposes of issuing life insurance policies.  However, life expectancy is more of a measure of future risk than it is of current health.  I would instead expect to make use of the numerous physical tests that can be done to determine factors that contribute to overall health, such as many blood chemistry measurements, urine, stool & saliva chemistry, blood pressure & pulse rate, and eye & teeth exams. 

How might these various factors be consolidated into a single measure of overall health?  The most straightforward would be to normalize each value to a scale of 0 to 1, where 0 is fatal (or the worst possible value) and 1 is the best possible value.  The overall measure would then be simply the logarithmic mean of all of the different values.  Use of the logarithmic mean ensures that (unlike an arithmetic mean) if one value is particularly bad, this value makes a significant contribution to the overall assessment of health.  I would expect that all such measures would not be equally important, so experts might improve this simple formula by providing weighting values for each term in the overall score.

Obviously the set of contributing factors, as well as the normalization factors and weighting factors, if any, would vary from species to species.  Assessment of different species would have to be done by experts on each one.   One possible problem might be measurement of the well-being of non-living things.  However, there is no reason why the same general approach could not be followed, albeit in a much simpler vain.  For multiple species as well as non-living entities, the use of the same general guidelines, the fact that all values are normalized, and the fact that the extent of species differences are represented by Fi, will ensure that the results for widely varying species are compatible.

Maximum Level of Psychological Well-Being
The maximum level of psychological well-being, Mi, is the most difficult term in the overall well-being equation to determine empirically.  This factor would basically be a measure of intelligence or awareness of the species.  There are numerous problems that would make it difficult to come up with such a uniform measure.  One is that intelligence alone is a multidimensional subject that would be difficult to aggregate into a single metric even for an individual species14.  The vast differences between species make a uniform metric difficult to devise, as a metric created, for example, for mammals would yield an insignificant score for all much more primitive species.  Another problem would be the method of extending this metric to species that were not conscious at all.

These problems not withstanding, I believe that such a measure is possible.  Certainly value judgements by experts would be required, but aggregate measures of intelligence could be devised by weighting the various possible input parameters.  The vast differences in levels of intelligence could be handled by devising multiple measures of intelligence for different ranges, and then calibrating these different measures against each other in the areas in which they overlap, much as is done today to calibrate measures of distance in cosmology over vastly different ranges15

For species such as plants and protozoa that have no conscious experience, the value of this factor would simply be unity, or the lowest possible value among all species.  This would serve to reduce the overall contribution to well-being that is made by these species, which in my opinion makes sense.  Note that the complexity of plants would not contribute to this factor.  Despite the fact that a giant sequoia is a magnificently engineered system, that fact would not be relevant to a measure of psychological well-being.  Any such factor would have to be included in the maximum level of physical well-being.

Measuring Individual Psychological Well-Being
Measurement of individual psychological well-being mij would be performed in a manner similar to measurement of individual physical well-being.  However, rather than using a broad spectrum of physical indicators, only those objective indicators of psychological well-being would be used.  It would seem to me that these would constitute simply the concentration of neurotransmitters in the bloodstream or brain.  As with individual physical well-being, the measured indicators would differ from species to species, the contribution value from each indicator would need to be normalized to a scale of 0 to 1, and the overall level of individual well-being would the logarithmic mean of these values.  The value for unconscious agents would always be 1.  This would not results in a level of well-being for these agents that was high relative to other species, because their maximum level of psychological well-being Mi would be the minimum possible value, as described above.

Measurement of psychological well-being would suffer from two problems.  One would be the potential long-term sensitivity to levels of these indicator chemicals.  It is well known that the human body becomes adapted to (and dependent on) psychoactive drugs, which artificially alter the levels of these chemicals.  Therefore, rather than measuring absolute levels of these indicators, level differentials, or some kind of hybrid measure based on an empirical correlation might be required.  Unfortunately, this correlation would have to be ultimately based on reported psychological well-being.  However, the fact that reports from numerous subjects would be aggregated to create the correlation would reduce or eliminate the problems inherent in individual subjective reports.

Another problem that might be raised is whether or not artificially increased levels of neurotransmitters that enhance psychological well-being are really good for the individual.  Is it not better to achieve happiness for a reason, rather than to have it artificially generated by a drug?  I do not believe that this will be a serious problem for two reasons.  One is that in reality, as mentioned above, organisms tend to adapt to artificial levels of mood-altering drugs.  Thus, in the long run, not only do the drugs’ effects wear off, but afterwards the recipient is faced with the choice of either discontinuing the drug, and thus facing a severe drop if psychological (and possibly physical) well-being, or continuing the effort and cost of taking the drugs for no benefit.  Either way, the recipient’s well-being is lowered in the long run16.  The other reason is that even if the recipient chooses the latter path, or if the affects of the drug are long lasting, he still knows that his current psychological state is artificial, and that knowledge in itself will at least in part counteract the affects of the drug.  These reasons notwithstanding, there certainly may be cases in which a person is actually better off taking mood-altering drugs than he would have been without them.

Objections & Solutions
As mentioned above there are two main objections to any attempt to create a universal, objective measure of well-being.  The first is that all four parameters require value judgements.  This is particularly true for the maximum values Fi and Mi.  For example, the value of the maximum level of physical well-being Fi for living creatures could have been set equal to the total biomass of those creatures rather than cell count.  Neither did the value of Fi need to be a linear function of cell count.  A complexity factor could have been introduced to rank larger, more complex living things ahead of the same number of cells of simpler organisms, such as in the sequoia vs. bacteria example given above.  Also, it is certainly debatable whether or not non-living things should count at all, although I believe that the case for intelligent machines would be strong.

As also mentioned above, determining the maximum level of psychological well-being Mi would be even more difficult.  Value judgements would be required to determine the weights applied to the many factors that would go into devising a concept of intelligence that was broad enough to apply to all species.  Devising the relative measures would be more straightforward, as the list of contributing factors would be objective, however their relative weights, if any, would be based on subjective judgements.

The fact that value judgements are required in some or all of the factors in WBij would make any such metric necessarily ad hoc or arbitrary.  But any metric is better than none.  We can be confident that a metric devised by experts would be close to optimal (if optimality could be even defined in this case).  And more importantly, it would provide a consistent basis for making ethical decisions.

The second major problem would be the difficulty of determining accurate values for the numerous parameters that would contribute to fij and mij.  The maximums could be defined independently by experts on each species, and made available to everyone.  However, use of the individual values would be cumbersome since they would have to be remeasured in every situation in which an ethical decision needed to be made.  Short cuts could be used in this case that have been shown to correlate well with the more comprehensive measures, and for most situations we could revert to what we have always done, which is to make best-guess estimates based on our own intuitions and personal judgements.  This would still be an improvement over the status quo because we would still have Fi and Mi to guide us.

One of the biggest objections to any ethics that is even partially consequentialist is the need to measure and compare individual well-being.  This problem is compounded for those theories that apply to agents other than human beings17.  While like most theoretical issues in ethics, there is more than one such possible measure — ought cannot be derived from is — any measure would be better than none.  I have proposed an outline for such a measure, which could certainly be used by experts in the respective scientific fields to create a workable metric, that could in turn be chosen by consensus as the basis for all ethical decisions.

End Notes

  1. I discuss this primarily in my essay on Reductionist Naturalism in Ethics.  See also Ethical Theoretical Guidelines and A Theory of Ethics.
  2. See for example “Consequentialism”, Wikipedia, URL=<http://en.wikipedia.org/wiki/Consequentialism>.
  3. For a brief introduction to this problem see “Social choice theory”, Wikipedia, Interpersonal utility comparison, URL=<http://en.wikipedia.org/wiki/Social_choice_theory#Interpersonal_utility_comparison>.
  4. The pioneer in the application of ethics to animals is Peter Singer.  See is book Animal Liberation, Harper Collins, New York, NY, 1975.
  5. Available online at http://www.efm.bris.ac.uk/het/bentham/government.htm.
  6. Available online at http://www.gutenberg.org/catalog/world/readfile?fk_files=3418684.
  7. See “Cardinal utility”, Wikipedia, History, URL=<http://en.wikipedia.org/wiki/Cardinal_utility#History>.
  8. For more on Arrow’s theorem, see “Arrow’s impossibility theorem”, Wikipedia, URL=<http://en.wikipedia.org/wiki/Arrow_impossibility_theorem>.
  9. Daniel Dennett has argued that the philosophical concept of intentionality, the ability to have goals and desires, is just a matter of degree, and exists in small amounts in the most simple of mechanism.  He based this claim on the fact that these mechanism were designed with a purpose, and that they “want” to achieve that purpose.  See Dennett, Daniel C., The Intentional Stance, MIT Press, Cambridge, MA, 1987.
  10. I will also reiterate that the final method chosen to measure each of these factors will necessarily in themselves involve value judgements.  However, a particular method selected by experts and agreed to by consensus would be better than having no such metric at all.
  11. Strictly speaking, F could be a function of both the species and the individual, equal to the number of cells in the individual.  This would be preferable for species in which there was a great deal of variation of size.  I list F as a function of species here for simplicity.
  12. I can appreciate the validity of an argument in favor of giving greater weight to the sequoia in light of the fact that it is a more complex system.  Some kind of metric of complexity would need to be devised, and this would have to be added to the cell count metric.  With this additional factor, a strictly linear function of cell-count might not be necessary.
  13. Surprisingly, a cursory literature search has not turned up even an attempt at such a measure by health care researchers.  Numerous online surveys for individuals to determine their own level of health do exist, such as http://www.quibblo.com/quiz/_ig7/How-Healthy-Are-You, but these tend to vary tremendously in the questions that they ask and thus the inputs that they use to their overall health functions, and many only provide qualitative answers.
  14. For a list of factors currently being investigated with respect to animal intelligence, see “Animal intelligence”, Wikipedia, URL=<http://en.wikipedia.org/wiki/Animal_intelligence>.
  15. See for example, “Cosmic distance ladder”, Wikipedia, URL=<http://en.wikipedia.org/wiki/Cosmic_distance_ladder>.
  16. The long-term drop in well-being might be significant enough for the recipient’s Net Present Well-Being (a rigorous measure of current and future well-being) at the time that he first takes the drug to be lowered by that action.  For a definition of Net Present Well-Being, see my essay on Reductionist Naturalism in Ethics, in particular the section on An Isolated Individual.  For a fully rigorous definition, see my Formal Theory of Ethics.
  17. I believe that this is a requirement for any theory of ethics.  For more details see my essay on the Guidelines for Creating a Theory of Ethics.

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