The Mathematization of Morality?
Any Anus likes a good seat. Some call this “being grounded,” which is why many of the posts here emerge from conversations with friends or from other social settings. What better way to stay grounded in the world of ideas than to have the home field advantage; things usually come out so much better that way, and when they do, they mean something more than a floater in the empty bowl of “Dear Medium Page.”
In any case, this one comes from a conversation at second-hand, meaning the ideas of someone else were conveyed in a conversion, which got this Anus thinking because it reminded him — albeit belatedly and after the fact — of something he’d read a long time ago. The general topic was a ‘mathematical approach to morality.’ It’s not entirely clear whether this is the application of mathematics to moral decision making or whether it’s an attempt to give morality a mathematical structure. Since the two relate, however, and since both stand to be interesting, both get considered here.
On the face of it, one will surely object — morality reduced to mathematics! No way. Morality given a mathematical form… Why? Mathematical reasoning applied to moral reasoning…well, most suck a both, but there is game theory and some economists, so maybe…
Prima facie objections aside, the topic deserves serious consideration because no less a figure than John C. Harsanyi has offered a mathematical approach to “Morality and Social Welfare,” and if a Nobel Prize doesn’t earn one some deference on any idea, no matter how outlandish sounding on its face, what does!
In any case, Harsanyi’s approach is utilitarian, meaning he gives mathematical form to a utilitarian version of morality, taken to be “social welfare.” In one respect, this is understandable, as economists love utility functions, and what goes better with a utility function than a utilitarian moral scheme.
Yet, therein lies the rub: right away the mathematical approach to morality, aka a “critical rule utilitarianism” for Harsanyi, runs into a snag — it has to pick one moral system among others, usually the one that affords mathematical formalization; then it ignores the others while acting as though the selected version of “morality” is morality as such, and that moral reasoning with its mathematizable structure takes place within that framework.
However, there are at least three broad classes of moral systems — and the Anus says “at least “ three because these general classifications subsume a host of more individual approaches. They are, loosely speaking, utilitarian, deontological, and virtue ethics.
As far as the Anus knows, only the first has had attempts at mathematical formalization, and for good reason: it virtually defies imagination how one would frame a “duty function” or a “virtue function” to correspond to a “utility function.” That is, one does get ‘a measure of utility’ from many different things. To some extent, this measure can be weighted, ranked, and quantified (usually with a proxy that reveals a preferential ordering, like money spent). But how on earth would one weigh, rank, and quantify “virtues,” much less competing virtues, or “duties,” much less competing duties?
Unlike the utility one gets from the outcomes from having made a choice, and unlike the orderable preferences one starts with, before making choices, obedience to duty and the exercise of virtue defy ‘quantification’ in the way ‘utility’ can be approximately quantified. This is probably why utility functions abound in economics: consumption reveals preferences; consumables cost money; time and money resources are limited; therefore, specifiable choices within a formal framework obtain, given a reasonable or otherwise viable set of stipulations.
One can even — if bold — posit a ‘social welfare function’ that maximizes average aggregate utility, as Harsanyi does, without sounding like a kook.
All this so long as one delimits morality as such into “utilitarianism.”
Nevertheless, as soon as one does this, one hits the de facto reef of ethics and jurisprudence, as practiced in our fair land, which most assuredly does not maximize average aggregate utility. Nor is the law and the ethics of daily decision making predominantly — much less exclusively — utilitarian either. In fact, it’s unlikely any law or right submits to this schema, nor should it — i.e., it’s called a “Bill of Rights” for a reason, not a “Bill of Aggregate Utility Maximization.”
In any case, our political and legal structure is centered on avoiding the simple ‘tyranny of the majority’ that maximizing average aggregate utility entails, so while wonderful as an academic exercise, the mathematization of morality through the vehicle of “critical rule utilitarianism” is just that — an academic exercise. It has no useful application.
That is, none above and beyond what one might encounter in an ethics class, which pits the classical arguments both for and against utilitarian, deontological, and virtue ethics against one another — arguments stretching back millennia in some cases, with no resolution to date (at least none that’s universally agreed upon). Either way, instead of forcing students to pick one framework, as any mathematization would, most are encouraged to learn how to use these general classes of moral framing as tools and guides, applying them when and where they make the most sense, after learning to see the difference.
In short, for the pursuit of justice and the good — which always entails asking “what is justice?” and “what is good?”, both being indeterminate beforehand — an ecumenical approach to moral decision making is pragmatically preferable to putting all one’s eggs into one ethical basket, then forcing all possible situations into that limiting framework. By doing the latter, one may get a determinable meaning for “justice” or “good”, for all cases, beforehand, but this will happen at the cost of actually achieving either as often as one would like.
This idea of competing frameworks for moral decision making, with each acting as a tool and a guide in the pursuit of the otherwise indeterminable “good” and “just,” opens the second path to the mathematization of morality — mathematizing moral decision making, as opposed to mathematizing morality as such. Here, moral decision making can be seen as a subset of decision making in general, and decision making as such has most certainly been fruitfully mathematized. Understood in this way, a mathematical approach to morality gets a prima facie nod in its favor, since it stands to reason that a subset of a mathematizable topic would itself be mathematizable.
What might be involved in such an approach? What would need to be added to a ‘mathematization of moral decision making,’ above and beyond the mathematics of decision making per se? Is moral decision making qualitatively different than decision making generally conceived, and therefore quantitatively different as well?
Most assuredly so, as a simple illustration reveals.
Consider the Drosophila of game theory, the Prisoner’s Dilemma. It would be hard to overstate the research tradition it has spawned. In any case, the hallmark feature of the Prisoner’s Dilemma is that it’s a structured interaction according to rules with determinate, specifiable outcomes. This could, in fact, be a general definition of the types of decision-making subject to mathematization, a la “game theory:” whatever the venue, game theory is applicable to any situation where rules structure interactions with specifiable outcomes, given a set of reasonable (and in some cases, less than reasonable) stipulations. Most structured interactions like these can be readily quantified; hence the overwhelming importance of game theory in economics.
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However, is moral decision making akin to economic decision making? Can the tools of decision making in general — to be sure, as noted above, a specific kind of decision making — be applied to moral decision making?
Before answering this question, it is instructive to look at Harsanyi’s (inadequate) model for moral decision making in “Morality and Social Welfare” — to wit, “the disregard of one’s personal identity.”
For Harsanyi, by disregarding one’s personal identity, one becomes like a judge at the Olympics or an umpire in a baseball game, though in this case, the application is much broader; it applies to any case where one must abstract oneself out of a situation to which the judgment applies. Note right at the outset that this is quintessentially utilitarian, as it is meant to exclude self-interest from consideration of the greater, common, public interest.
However, note this is as well: it is nearly opposite to the deontological maxim, which calls for acting as though one’s own action is such that it could become a universal law, i.e., act in such a way that it could apply to everyone.
So, right away, the arbitrary selection of one moral framework at the expense of others rears its head at the heart of the moral decision-making scheme. It appears that the first step of mathematization requires this selection, making it less about moral decision-making as such and more about one’s preferred framework for it.
In any case, the utilitarian maxim fails in another way as well: being an impartial judge by no means captures the scope of utilitarian reasoning either. If it did, a woman would not be able to judge whether abortion is right or wrong for the greatest good for the greatest number, since as a woman, abortion applies to her. Similarly, one could not speak against murder, since obviously one puts oneself in the class of those not arbitrarily killed.
In short, while there is every reason to demand that judges, juries, and umpires set aside their personal stake in the decisions they are called to make, there is no reason on earth to demand this as the quintessence of moral decision making as such— unless one is in the position to arbitrate between two parties with their own interests, separate from one’s own.
This situation, while common enough, far from eclipses moral decision making as a whole, even in a utilitarian scheme. It can be an important part, to be sure, but as a basis for mathematization (as it is for Harsanyi), it only captures a fraction of what it needs to capture, to serve as a basis for a full “mathematization of moral decision making.”
Where does this leave us? What can be said of the mathematization of morality, as it might apply to either a moral framework as such or the decision making within it?
To be sure, more could be said about moral decision making, since if one sets out to mathematize utilitarian, deontological, or virtue ethics, different decision-making frameworks will follow, each with its own stipulations. However, as just seen, the principle stipulation of the easiest — and perhaps the only — framework subject to mathematizatical approximation fails to encompass moral decisions in the necessarily broad sense, and even the famous additions by Amartya Sen, who questions maximizing utility against realizing capabilities, don’t offset this limitation.
So, what can be concluded?
First, how about that morality as such is too indeterminate, too situational-specific, and to relative to endure mathematization. For two and a half millennia, philosophers, saints, and everyone in between have argued over the definitions of “justice as such” or the “good as such.” Mathematization, however, requires determinate answers to those questions, applicable to any and all situations. Providing them, however, means one casts into “mathematical morality” one’s personal choice, just given formal form, for there can be no universal mathematization of what by its nature defies universality [1].
Second, even mathematizing moral decision making requires asserting one moral framework among others as the proper framework — full stop. To date, the efforts to do this with utilitarianism — so far, the only one subject to the tools of economics and mathematicians — have fallen short. On top of this, utilitarianism itself falls short as the moral framework, for obvious reasons now rehearsed in almost every introductory ethics course one might take— the arguments are that old.
So why even persist in mathematically representing what is inherently unrepresentable in ordinary language?
The Anus thinks the efforts of brilliant men like Harsanyi and Sen (and all those who would follow them) illustrate quite well the unfortunate proverb about hammers and nails: achieve enough success with the hammer and everything starts to look like a nail.
To that point, the Anus is reminded of a recent case of just how insular academic success can get. A former student of a colleague just presented a research poster showing that facial expressions reveal more about inner emotional states than measures of cardiovascular activity. Seriously. Who knew? Only a lab devoted to heart rate or heart rate variability as the physiological variable of interest in human emotion, attention, and behavior could possibly think this is news.
Likewise with the mathematization of morality: so much success has followed mathematization in so many fields that an insular attitude about its universal applicability has taken shape, and something like “morality” becomes its next target. However, just about everyone without mathematical training (rightly) intuits that morality is no more mathematizable than love, truth, and beauty — and we’re better off for it.
While the Anus is ecumenical and dislikes academic boundaries, sometimes the tools deployed in one area are unsuitable for use in another, and using mathematics to better understand or otherwise capture “morality” is one of those cases.
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[1] Imagine an algebra that applies only to a subset of the real numbers, not all numbers as such. That algebras apply to ‘objects as such’ and not just “numbers” only strengthens this point…
