1. Ignorance

Perhaps the most widely accepted explanation of what makes a choice hard is that we are ignorant or uncertain of the normative or nonnormative factors that are relevant to making the choice. After all, what matters in a hard choice is typically complex and multidimensional, and so how can we, limited creatures that we are, determine which alternative we should choose? At the very least, given our epistemic limitations, our judgment about the relative value of the alternatives is subject to a margin of error.

There are, however, two reasons to doubt that our cognitive limitations are what make hard choices hard.

The first thing to note is that some choices are ones over which we have first-personal authority. Suppose you are offered lemon sorbet or apple pie for dessert. What matters to the choice between them is which tastes better to you right now. ‘Tastiness to you right now’ is, arguably, something over which you have first-personal authority; your judgment, assuming you are functioning normally, determines the truth of the matter, give or take a margin of error. You are, as someone once put it, ‘The Decider’.

Tasting the sorbet and pie in turn, you might judge that neither tastes better to you right now. After all, they taste very different, and while both would be delicious, they would be delicious in rather different ways. By your lights, the tart, cool, refreshing taste of the lemon sorbet is neither better nor worse in tastiness than the sweet, warm, comforting taste of the apple pie.

Do they taste equally good? There is an experiment you can perform to settle the matter. You add a dollop of whipped cream to the pie. So now, by your lights, the pie tastes a bit better than it did before. (If the improvement is so slight that it falls within the margin of error, make it bigger—two dollops and an extra pinch of cinnamon—so that the pie is now definitely improved in tastiness by your lights.) The pie-with-whipped-cream tastes better to you right now than the pie without.

But now, tasting the pie-with-whipped-cream and the lemon sorbet in turn, you might judge that, even with the improvement in the pie, neither tastes better to you. Thus, you must rationally conclude of the original pie and lemon sorbet that they are not equally tasty to you. For if they were equally tasty, an improvement in one of them would require you rationally to judge that the improved item tastes better. Since it is perfectly rational to judge of the pie-with-whipped-cream and the lemon sorbet that neither tastes better to you, it follows that none of the three usual comparative relations, ‘better than’, ‘worse than’, and ‘equally good’, holds between them.

I have elsewhere called this the ‘Small Improvement Argument’.Footnote ¹ Since we need to fix the respect in terms of which comparisons of the merits of alternatives is made, we relativize judgments to what I have called a ‘covering consideration’, here abbreviated as ‘V’, which gives what matters to the comparison.

The Small Improvement Argument

1. 1. A is neither better nor worse than B with respect to V.

2. 2. A+ is better than A with respect to V.

3. 3. A+ is not better than B with respect to V.

4. 4. A and B are not equally good with respect to V. (From 1, 2, 3, and the principle of the Substitutability of Equality, according to which if two items are equally good with respect to V, one can always be substituted for the other in comparisons with respect to V. Applying this principle, if A and B were equally good, then substituting A for B in premise 2 would yield the contradictory of premise 3. Therefore A and B are not equally good.) Therefore,

5. 5. A is not better than, worse than, or equally as good as B with respect to V. (From 1 and 4).

Whenever the premises of the Small Improvement Argument hold—and there is empirical work suggesting that people actually make such judgments (Messerli and Reuter Reference Messerli and Reuter2016)—reasons ‘run out’, but not epistemically. The problem is not lack of information—you have all the information you need to judge tastiness to you—but a structural feature concerning how the alternatives relate to one another.

It might be pointed out that choices between desserts are not terribly important, but that hard choices typically are. So how does appeal to such cases help us understand hard choices? One thing to note is that we have first-personal authority over some important hard choices. If you have a medical condition whose amelioration requires you to choose between severe pain for a week or a medium-grade headache for a year, which should you choose? You have first-personal authority over which hurts more by your lights, and you could rationally judge that neither is better with respect to being less painful, and yet the options are not equally painful. Again, the choice may be hard, but not hard epistemically. The point here is that once we allow that choices over which we have first-personal authority can be hard, not because we lack information but because of how the alternatives relate, we open the door to thinking that this structural feature holds also in other cases.

It is easy to think that hard choices are hard because we do not—and perhaps cannot—know everything relevant to the choice. But is knowledge the standard our judgments should meet? Although we may never know whether our normative judgments are correct, we can be practically certain that they are. Practical certainty, not knowledge, is the correct standard for deciding what to do. And we can achieve practical certainty, in at least some cases, that of two options, one is neither better nor worse than the other, and nor are the options equally good.

Suppose you are on your way to work when you find yourself wondering whether you turned off the kitchen lights. You are now faced with a practical problem: should you go back and check whether you did? What matters in the choice, suppose, are the costs to your utility bill, your contribution to global warming, and not being late for your morning meeting. You might be pretty sure that you flicked the switch to ‘off’, and your level of certainty—or credence—might make it irrational for you to go back given what matters in the choice. If so, you are practically certain that you turned off the lights. Practical certainty about a proposition is a function of your level of confidence—or degree of belief—and of what matters in the choice or comparison of the alternatives. If you are uncertain whether you left your infant in the car in the parking lot with the windows rolled up, the level of confidence needed to achieve practical certainty is higher since what matters is of greater significance (cf. Stanley Reference Stanley2005).

Just as you can be practically certain that you turned off the lights, you can be practically certain that neither of two alternatives is better than the other and that they are not equally good. Of course, the higher the stakes, the harder it is to achieve practical certainty. This allows us to conclude that in at least some hard choices, even ones over which we do not have first-personal authority, the problem is not lack of information but the fact that none of the usual trichotomy of relations holds for the alternatives. And if this is what is going on in some hard cases, we might extrapolate to other hard cases, including those in which it seems that the problem is epistemic.

The lesson here is that it can be something about the way the alternatives relate to one another and not something about us that explains the hardness of a hard choice. Again, this is not to say that in hard choices we are not ignorant or uncertain; chances are, we are. But we should not assume that this ignorance or uncertainty is what makes the choice hard. I suggest that in searching for an explanation of hard choices, we turn away from ourselves as choice makers to the choice itself. What makes a choice hard is a structural feature of the choice situation. Or so I now want to argue.

2. Incommensurability

Maybe a choice is hard because the alternatives or the values they bear are incommensurable. As it turns out, there is a decisive reason to reject this explanation. But first we need to understand what incommensurability is and why it might be thought to explain hard choices.

Two items—values, goods, etc.—are incommensurable with respect to V just in case there is no common unit by which they can be measured with respect to V (see Chang Reference Chang and La Follette2009b and Reference Chang2014). In modern parlance, items are incommensurable with respect to V if their values cannot be represented cardinally, for instance, by a ratio scale such as meters or an interval scale such as Celsius, in V-ness. Put measure-theoretically, there is no function unique up to linear or affine transformations that represents their respective V-ness.

If there is no cardinal scale of, say, goodness as a career, by which two values, such as intellectual satisfaction and financial security, can be measured, there are no interval or ratio differences between those values. And thus we cannot say that the intellectual satisfaction you might get by being a philosopher is 1.18 times as great as or 10 flourishons greater than the financial security you would have achieved by being a lawyer. Because we cannot put each career on a single scale of units of the relevant value, it seems that we cannot choose between them. After all, it might be thought, being rational is a matter of maximizing units of value. On this view, reasons run out in the sense that there is no unit by which the underlying values or the corresponding strengths of reasons can be measured.

Incommensurability is usually defended by pointing out that some values—and thus the goods that bear them, such as human life, free speech rights, and love relationships—have a special ‘status’ or are ‘sacred’ and thus cannot be put on the same scale as commodity values, such as pleasure and economic efficiency (e.g., Anderson Reference Anderson1993; Radin Reference Radin1996; Lukes Reference Lukes and Chang1997; Nussbaum Reference Nussbaum1986 and Reference Nussbaum1990). Indeed, if all values were ultimately commodity values measurable by a market price, then many of our most cherished and fundamental attitudes would require radical revision. If, for example, the contribution of having children to the good life can be measured by the same unit that measures the contribution of a beach vacation, then the difference in your attitudes toward your children and toward having to forgo a holiday in the Maldives should be a matter of degree—the loss of dear Suzy is worth twenty such vacations while troublesome Johnny is worth only ten. Moreover, incommensurability plausibly holds even between two quite similar values. It is hard to believe, for example, that there is some unit of gustatory pleasure by which apple-pie-with-whipped-cream is .8 times as great as or 1.43 units more pleasurable than apple pie without.

Note that widespread incommensurability forces us to recast our understanding of standard models of rational choice, such as expected utility theory, cost-benefit analysis, QALY-based models for health care rationing, and so on, as, at best, inaccurate and, at worst, fundamentally misguided representations of the value of alternatives. Indeed, widespread incommensurability suggests that we need nonstandard, alternative models of rational choice (Chang Reference Chang2002a; Hare Reference Hare2010; Schoenfield Reference Schoenfield2014).

The key point for our purposes is that incommensurability does not entail incomparability. Even if there is no unit by which we can measure the contribution to your well-being of apple pie as opposed to a lifetime achievement, it is clear that the latter is better than the former. For one thing, we can have merely ordinal comparability between incommensurable items—we can rank order them. For another, we can have ‘imprecise’ cardinality among incommensurable items. Although there is no unit that measures the value of two items, perhaps there are fuzzy units or an indeterminate range of precise units by which the value of items can be measured, what Derek Parfit calls ‘imprecise comparability’ (Parfit Reference Parfit2016; see also Hsieh Reference Hsieh2005; Sinnott-Armstrong Reference Sinnott-Armstrong1988: 66–67; Hurka Reference Hurka1993: 87; for a discussion of Parfit's imprecise comparability, see Chang Reference Chang2016b). Since it is compatible with alternatives being incommensurable that one of them is better than the other with respect to V, the choice between incommensurables could be easy: choose the better alternative. Thus, incommensurability is not what makes a choice hard.

3. Incomparability

This brings us to a third explanation of hard choices: incomparability. Perhaps choices are hard because the alternatives cannot be compared with respect to what matters in the choice. On this view, the reasons run out in that there are no all-things-considered reasons for choosing either of the alternatives. This explanation of hard choices looks promising. After all, if the alternatives—or reasons for and against choosing them—cannot be normatively ranked, then how could we rationally choose between them?

Let us assume for the sake of argument that there is incomparability (although establishing incomparability is rather more difficult than one might think, see, e.g., Chang Reference Chang and Chang1997; Broome Reference Broome and Chang1997). Two items are incomparable with respect to V just in case no ‘basic’ relation—the relations that exhaust the conceptual space of comparability between two items (typically ‘better than’, ‘worse than’, and ‘equally good’)—holds with respect to V. Is incomparability what makes a choice hard?

There are three arguments that, taken together, suggest that we should reject this explanation. They all depend on a further but I think relatively uncontroversial assumption about hard choices, namely, that choice in hard choices can be made rationally, that is, as an exercise of rational agency. It is, after all, plausible that paradigmatically hard choices between careers, places to live, whether to have a family, and so on, occur within the life of rational agents and are appropriately responded to with an exercise of rational agency. If hard choices fall within the scope of practical reason, there are good reasons to doubt that incomparability among the alternatives is what makes them hard.

The first argument trades on what seems to be a relatively common feature of hard choices. Despite the hardness of a hard choice, sometimes an agent concludes that she has most reason to choose one option over the other. Let us suppose that this conclusion can be rational. The question is how could it be rational if the alternatives are incomparable? How could it be rational to conclude between incomparables that one has most reason to choose the one alternative over the other? Indeed, how can it be rational to choose between incomparables?

Joseph Raz (Reference Raz and Chang1997), a leading incomparabilist who is aware of the problem, argues that it can be rational to choose among incomparables. Suppose, Raz says, that you could have either a pear or a banana for dessert and that they are incomparable. According to Raz, the reasons you have for choosing one or the other do not include the fact that you want the pear, assuming for the sake of argument that you do. Your wanting the pear is not a reason that contributes to the conclusion that the pear and banana are incomparable because the fact that you want something is not a reason to have it, Raz argues. However, since the pear and banana are incomparable, Raz says, your wanting the pear ‘rationalizes’ your choosing the pear and is a reason to choose it. So your choice of the pear is rational.

But how can it be? Suppose that wanting the pear is relevant to the question of which dessert is rational to choose in the first place, either because your wanting it is itself a reason to choose it (pace Raz) or because it is a subjective condition on the value-based reason you have to choose it, for example, that you would enjoy having it. If wanting the pear can make choosing it rational, then why not think from the outset that the pear is better than the banana rather than incomparable with it? Put another way, wanting the pear can rationalize choosing the pear only by double counting a consideration—that you want the pear—that has already been taken into account in the conclusion that the items are incomparable. But why should you double count the fact that you want the pear rather than the fact that the banana will help remedy your potassium deficiency?

In the alternative, if wanting the pear is not already relevant to determining which you should choose in the first place, then making it relevant changes the choice situation. The choice situation you started with was, by hypothesis, one in which what you wanted was not relevant to which you should choose, and in that choice situation the alternatives are incomparable. Now you could always switch to a different choice situation in which what you want matters to which you should choose. In that choice situation, having the pear is better and you have most reason to choose it. This maneuver, however, does not establish that there can be rational choice between incomparables.Footnote ²

In short, incomparabilists cannot make sense of the relatively common fact that sometimes in a hard choice the agent rationally concludes that she has most reason to choose one rather than the other of the alternatives. Either she must double count some factors, or she must change the choice situation so that it is no longer one among incomparables.

A second reason to doubt that incomparability makes choices hard has to do with the attractiveness of maintaining an isomorphism between evaluative relations, on the one hand, and practical responses, on the other. For example, when one alternative is better, it is rational to choose it. And if it is worse, it is rational to choose the better option. And when the alternatives are equally good, it is rationally permissible to flip a coin between them. Evaluative relations correspond in a one-to-one way with distinctive rational responses.

Now when alternatives do not stand in any evaluative relation with respect to V, they are incomparable. What is the appropriate practical response to a choice between incomparables? Sometimes, there is no rational response in a choice situation. Think of the existentialists, like Sartre (Reference Sartre1947 [2007]), who deny that there are any reasons or values prior to choice and that all choices are an exercise, not of rational agency, but of a sui generis existential agency. When Sartre's young man contemplates whether to join the Free French or stay home to prevent his mother from losing another son to the war, there are, Sartre maintains, no reasons or values in favor of going one way rather than another. It seems natural to say in such cases that the alternatives are incomparable. And so whatever the young man decides to do, he decides not as a rational agent, being guided by reasons, but as an existential agent who chooses in a nihilist world devoid of normativity. The incomparability of alternatives corresponds to choice outside the scope of rational agency.

When we select among incomparables, we plump; that is, we arbitrarily select an alternative—arbitrarily in the sense of not being guided by reasons—not qua rational agent but qua some distinctive sui generis agency, such as existential agency. Plumping should be distinguished from another kind of arbitrary selection, picking. Picking is the arbitrary selection of an alternative—arbitrary in the sense of not being guided by reasons—qua rational agent. As Edna Ullman-Margalit and Sydney Morgenbesser (Reference Ullman-Margalit and Morgenbesser1977) suggested long ago, when alternatives are equally good, a rational agent picks an alternative because the reasons fail to determine which alternative one should choose. But in the case of equality, there is an all-things-considered conclusion concerning how the alternatives normatively relate—they are equally good. When items are incomparable, by contrast, there is no all-things-considered conclusion—there is only the failure of such a conclusion. The appropriate practical response in such cases—plumping—is an arational response.

We might describe an isomorphism between evaluative relations and practical responses as follows:

(For those skittish about linking values with reasons, we can just as easily understand A and B not as alternatives but as relevant reasons for choosing an alternative and V as ‘the strength of reasons given what matters in the choice’).

Since there are two ways we can arbitrarily select an alternative, one within the scope of our rational agency and one without, it is natural to understand the case of equality as corresponding to the former and the case of incomparability as corresponding to the latter. Hard choices—paradigmatic ones between careers, places to live, people to marry, and so on—are choices we face in the course of the exercise of our rational agency and to which we respond as rational agents. If this is right, incomparability is not a good fit for how the alternatives relate in such cases.

There is a final reason to doubt that incomparability makes choices hard. When alternatives are incomparable, there is no overall assessment of their relative evaluative standing—no conclusion of practical reason about how they normatively relate with respect to V. By what else can the rationality of choice between two alternatives be determined if not either by the evaluative relations among the alternatives or by the normative relations among the reasons for and against them with respect to what matters in the choice?

Any temptation to think that rational choice is possible between incomparables might be due to a confusion. If A and B are incomparable, then neither is worse than the other. Now it is a plausible principle of practical reason that a choice is rational so long as the option chosen is not worse than the alternative. But we should distinguish being ‘not worse’ as it might figure in a principle of practical reason from being ‘not worse’ as it might obtain when practical reason does not get a toehold, when being ‘not worse’ is not a conclusion of practical reason but rather the result of the failure of practical reason to deliver a conclusion. Rational choice is possible in the former case but why should we think it is possible in the latter? (For further argument, see Chang Reference Chang, Lord and Maguire2016a).

Within the context of practical reason, the claim that A is not worse than B is equivalent to the claim that A is better, or equal, or stands in some other relation to B. There is some basic relation that holds between A and B, and thus there is a corresponding conclusion of practical reason about how one should rationally respond. But outside the context of practical reason, the claim that A is not worse than B may entail the claim that A and B are incomparable, that is, that there is no basic relation that holds between A and B with respect to what matters in the choice between them. It is easy to slide from one situation to the other and consequently to think, mistakenly, that it is sufficient for the possibility of rational choice that one item be not worse than the other.

4. Parity

If the arguments above are correct, what makes a choice hard is not our ignorance, the incommensurability of values at stake, or the incomparability of the alternatives or of the reasons for and against them. How then should we understand hard choices?

I propose that what makes a choice hard is a structural feature of the choice, and in particular, the way in which the alternatives relate to one another with respect to V. In a hard choice, neither alternative is better than the other, nor are they equally good. And yet they are comparable. They are on a par.

Parity is a fourth possible basic way comparable items can relate beyond the standard trichotomy of being better than, worse than, and equally good. There are four and not simply three relations that exhaust the conceptual space of comparability between two items. We should reject what I have called ‘The Trichotomy Thesis’, the claim that if two items are comparable with respect to some V, one must be better than the other, worse than it, or the two must be equally good with respect to V (Chang Reference Chang2002b).

Parity may seem puzzling. How can two things be compared without one being better, worse, or equal to the other? After all, Lady Justice, with her balance scale, weighs alternatives with respect to justice by more, less, and equal. How could two alternatives be on a par with respect to justice?

We can give a diagnosis of the puzzlement and then offer a way of understanding value that makes parity not only possible but also, I think, plausible.

First, the diagnosis. Parity will seem puzzling to those who simply assume that values have the same trichotomous structure as quantities like length, weight, and volume and so can be related only by the evaluative equivalents of ‘more’ (‘better’), ‘less’ (‘worse’), or ‘equal’ (‘equally good’). While a balance scale may be the correct model for comparing quantities, why should we think that a model appropriate for comparing weights is appropriate for comparing values such as justice, love, and beauty? Indeed, on its face, the assumption is absurd; given that values are so different from mere quantities—most notably because they have qualitative aspects—what reason is there to think values have the same trichotomous structure as nonevaluative quantities?

I suggest that we understand the structure of values, and by extension of normativity in general, by taking as foundational the idea of an evaluative difference (Chang Reference Chang2002a).Footnote ³ The way values can relate items, then, can be understood in terms of the kinds of evaluative differences that can hold between them.

There are two kinds of broad answer to the question, ‘What is the evaluative difference between A and B with respect to V?’ One answer is ‘Nothing’, and in that case A and B are incomparable. Another answer is ‘Something’, and in that case the items are comparable. If there is some evaluative difference, it will have various features—it might be a zero difference, for example. A zero difference is a kind of difference and is distinct from there being no difference at all. (There is a third possibility: the question, ‘What is the evaluative difference between A and B with respect to V’ is not well-defined. This is what I call noncomparability, which holds, for example, between the number four and fried eggs with respect to tastiness; see Chang [Reference Chang and Chang1997] for further discussion).

An evaluative difference can have magnitude or lack it. If it lacks magnitude, even a zero magnitude, then the ranking to which it gives rise is merely ordinal; the idea that the evaluative difference between the items has magnitude does not apply. We can set aside merely ordinal evaluative differences (which is not to say that parity is only a cardinal relation). Our interest is in evaluative differences with magnitude; the ranking arising from such differences is cardinal. ‘Cardinality’’ is typically understood narrowly to refer to rankings of items that can be measured by a scale of units. As we've seen, however, it is implausible to think that there is always a scale of units that measures the value of items. So we should use ‘cardinal’ more broadly to refer to rankings of items in which there is some magnitude of difference between items, but that difference may not be measurable by a scale of units. Our interest is evaluative differences that describe cardinal rankings in this broad sense.

Evaluative differences with magnitude can, in turn, be analyzed along two dimensions: (1) whether they have ‘bias’ or ‘direction’, and (2) whether the magnitude of difference is zero or nonzero. Consider the evaluative difference in tastiness between, say, a bowl of lemon sorbet and a saucer of mud. The evaluative difference in tastiness between them has bias, that is, it favors or ‘points’ in the direction of the lemon sorbet since the lemon sorbet tastes better. Since it has bias, it follows that its magnitude is nonzero; the difference in their tastiness, for example, is greater than the difference in the tastiness between lemon and pineapple sorbet, and it is not zero like the difference in the tastiness between lemon sorbet and itself. When one item is better than another, there is a biased, nonzero difference between them. When the difference between them is unbiased and zero, they are equally good.

Now consider the evaluative difference in tastiness between a bowl of lemon sorbet and a slice of apple pie. There is an evaluative difference in their tastiness; after all, they both taste delicious, one in a tart, refreshing way and the other in a sweet, comforting way. However, the difference in their tastiness doesn't favor one over the other and so has no bias, nor is the magnitude of the difference between them zero—again, the magnitude of the difference in tastiness between the lemon sorbet and apple pie isn't the same as the magnitude of the difference in tastiness between the lemon sorbet and itself. The lemon sorbet and apple pie are on a par with respect to tastiness. Two items are on a par when their evaluative difference is unbiased but has nonzero magnitude.

We can systematize four kinds of evaluative differences with magnitude as follows:

The idea that alternatives can have an evaluative difference that has a nonzero magnitude and yet is not biased toward an alternative can be explained by appealing to the widely accepted fact that many values have qualities. Take pleasure. You get gustatory pleasure from eating the lemon sorbet. You get both a quantity of pleasure—perhaps not measurable by a scale of units—and a quality of pleasure. Both quantity and quality work together to determine the overall gustatory pleasure of having the lemon sorbet, having the apple pie, and the overall difference in pleasure between them. Suppose that the evaluative difference in pleasure between the sorbet and apple pie is a function of both the qualities and the quantities of pleasure each item manifests or bears. If that difference were determined simply by quantity of pleasure, it might be plausible to assume trichotomy—that one dessert must be better, worse, or equal to the other since those relations are isomorphic with ‘more’, ‘less’, and ‘equal’. But given that values also have qualitative dimensions, we should not simply assume that the usual trichotomy holds.

While I have talked of quality and quantity of a value as if they are independent determinants of the evaluative difference in V-ness between two items, things are typically more complicated, with quality and quantity being interdependent, giving rise to organic unities, and so on. In some cases the quantitative and qualitative dimensions of a value borne by two items will interact in such a way as to give rise to an evaluative difference with magnitude but no bias. The quality and quantity of pleasure you get from having lemon sorbet and the quality and quantity of pleasure you get from having apple pie, for example, are such that the difference in pleasure between them has nonzero magnitude, but it is nevertheless unbiased, favoring neither alternative. They are on a par with respect to pleasurableness.

We can unpack the possibility of unbiased, non-zero evaluative differences by first considering the idea of being unbiased and then defending the idea that unbiased differences can be nonzero. Consider a choice between a thimbleful of lemon sorbet and a generous slice of apple pie. Perhaps the quantity and quality of pleasure of the apple pie as it interacts with the quantity and quality of the pleasure of thimbleful of sorbet is such that the evaluative difference favors the apple pie. Having a tiny bit of tart and refreshing pleasure, as manifested by the thimbleful of sorbet, is overall worse in pleasurableness than having a generous amount of sweet, comforting pleasure, as manifested by a big slice of pie. Just as the quantitative and qualitative manifestations of two alternatives can give rise to a biased evaluative difference between them, so too can the quantitative and qualitative manifestations give rise to an unbiased evaluative difference between items. Although a thimbleful of sorbet is worse than a large slice of apple pie, a nice-sized bowl of sorbet and a regular slice of apple pie are ‘in the same neighborhood’ of overall pleasurableness. Two items are in the same neighborhood of V-ness when there is some magnitude of difference between them, but the difference does not favor one over the other. Being ‘in the same neighborhood’ of V marks the idea that the evaluative difference in V-ness is not biased toward one item rather than the other.

Must all unbiased evaluative differences have a zero magnitude? That is, can items that are in the same neighborhood of V-ness not be equally good? It is easiest to see that items with an unbiased evaluative difference can have a nonzero magnitude when the items are qualitatively very different with respect to V. A tart, refreshing pleasure is qualitatively very different from a sweet, comforting one, and so it seems plausible that the evaluative difference in pleasurableness between the two could be nonzero. In general, the more similar two items are with respect to V, the more plausible it is to think that the evaluative difference between them could be zero. This is not to say that items that are evaluatively very different with respect to V can never have a zero magnitude of difference but only that the more evaluatively different they are, the more plausible it is that their evaluative difference can be nonzero.

Putting these points together, we have an intuitive gloss of how parity—unbiased differences with nonzero magnitude—might arise. Sometimes, given their quantitative and qualitative manifestations of V-ness, items are in the same neighborhood of V-ness; roughly, the evaluative difference between them has magnitude but does not favor one item over the other. At the same time, the items are qualitatively very different in V-ness, and so that difference, in conjunction with the quantities of V-ness manifested, makes that evaluative difference in their V-ness nonzero.

In short, two items may be on a par with respect to V if they are qualitatively very different in V-ness but nevertheless in the same neighborhood overall of V-ness. Being qualitatively very different in V and in the same neighborhood of V overall, taken together, are sufficient conditions for parity with respect to V. While these two conditions are by their nature not precise, we have an intuitive grasp of them. We don't understand the value of pleasure, for instance, without also understanding that a soothing pleasure we might get from lounging in the sun is qualitatively very different from a sharp pleasure we might get from winning the lottery. Our understanding of qualitatively very different values is built into our understanding of the values themselves. And the idea of being ‘in the same neighborhood’ of value is also a familiar one. When you grade papers, you are assessing them with respect to their ‘goodness as a paper’. You might give two papers a grade of B; they belong to the same category or neighborhood of ‘goodness as a paper’ in that they are both good but not excellent. Sometimes, with respect to goodness as a paper, one B paper will be better than another. But sometimes two B papers will be on a par.Footnote ⁴

We can now see how hard choices might plausibly be thought to be choices between alternatives that are on a par. In paradigmatic hard choices between careers, places to live, and people to marry, the alternatives are in the same neighborhood of overall V-ness, and yet they are qualitatively very different in V-ness. Suppose you face a hard choice over whether to pursue a career in philosophy. You could be a lawyer instead. The legal and philosophical careers before you are in the same neighborhood of ‘goodness as a career for you’; if they were not, you could rationally conclude that one was better. At the same time, the careers manifest very different qualities of what makes a career good for you; the legal career, for example, might afford you the financial security you crave while the philosophical career gives you a life of intellectual excitement. Although the alternatives are in the same neighborhood with respect to ‘goodness as a career for you’, they are not equally good. If they were, the Small Improvement Argument would fail to hold of them—a small improvement in one career, say a higher salary or corner office, would make it better than the other. But this is not so, and it would be intrinsically irrational to choose between them by flipping a coin. The significant qualitative difference between the alternatives—along with their quantitative manifestations of V—make it implausible to think that they are equally good. A choice can be hard, then, because the alternatives are in the same neighborhood with respect to whatever matters in the choice, but neither is better than the other and nor are they equally good. They are on a par.

Is parity just some souped up version of one of the usual relations? If so, we can retain The Trichotomy Thesis. Indeed, parity is in one way like betterness (and worseness) in that the evaluative difference between items so related has a nonzero magnitude, and it is also in one way like equality in that the evaluative difference has no bias. But parity is not a version of betterness (or worseness) or of equality. We can see this most clearly by noting that each relation has different logical properties (Chang Reference Chang2016c). Unlike ‘better than’, ‘on a par with’ is symmetric: if A is on a par with B, then B is on a par with A, where A and B are distinct. Moreover, parity is nontransitive while betterness is transitive; if apple-pie-with-whipped-cream is on a par with lemon sorbet, which is on a par with apple pie, it does not follow that apple-pie-with-whipped-cream is on a par with apple pie. As we have seen, it is better. Parity, although holding when there is a nonzero difference between items, is not a kind of betterness since it has no bias. Finally, unlike ‘equally good’, ‘on a par’ is not only nontransitive but also irreflexive; everything is equally good as itself and nothing is on a par with itself. And nor does parity satisfy the Principle of the Substitutability of Equality encountered above. Parity, although holding when there is an unbiased difference between items, is not a kind of equality since it has magnitude. In short, parity is irreflexive, symmetric, and nontransitive and thus distinct from both betterness and equality.

A final upshot of parity is worth mentioning here. Granting full comparability, parity entails that the ‘negative’ relations, ‘not worse than’ and ‘not better than’, are nontransitive, while the usual trichotomy entails that they are transitive. As we have already seen, although pie is not worse than lemon sorbet, which is not worse than pie-with-whipped-cream, pie is worse than pie-with-whipped-cream. And, relatedly, if items can be on a par, certain putatively formal rules of ranking, which presume trichotomy, go by the wayside. So, for example, a ‘relaxed’ version of the (strong) Pareto principle does not hold: if A is not worse than B in any respect and better in one, A is better than B overall. Once we allow that items can be on a par, ‘not worse’ is compatible with being on a par. Just because two careers, such as a legal and philosophical one, are on a par in every respect but one—say, the legal career affords a better salary—it does not follow that the legal career is better overall.

In sum, parity is a sui generis fourth basic relation beyond the usual ‘better than’, ‘worse than’, and ‘equally good’. We should be tetrachotomists, rather than trichotomists, about the structure of normativity.

5. Commitment

We said that in hard choices, there is a sense in which our reasons for choice ‘run out’. We now see that the sense in which reasons run out is that that they—or the underlying alternatives—are on a par. If reasons are on a par, does it follow that we are stuck in hard choices?

To answer this question, it will help to distinguish two kinds of normative practical reasons. Usually reasons are individuated by their ‘contents’, that is, by the fact or consideration that is the reason. This way of individuating reasons, however, prejudges the question of whether the source of reasons—of what ‘makes’ something a reason—is unitary or plural. If there is more than one source of reasons, more than one consideration in virtue of which some fact is a reason, then reasons should be individuated by both their ‘content’ and their source. We should at the very least, understand reasons in a way that allows for this possibility. Thus, the same fact, for example, the fact that it would be pleasurable, can be more than one reason for having some lemon sorbet if it is a reason in virtue of two different sources.

I have proposed elsewhere that we should be hybridists about the source of practical normativity, that reasons can have two different sources, one in either normative facts or facts about how doing something will promote or constitute the satisfaction of some nonvolitional state, such as a desire, and the other in us, our very agency, or our rational will (Chang Reference Chang, Sobel and Wall2009a, Reference Chang2013b). Call the former sorts of reasons, reasons whose source is not in us but in facts outside of us, given reasons, and the latter sorts of reasons, reasons that are reasons in virtue of our rational wills, will-based reasons. Hybrid Voluntarism, the view I have been developing about the nature of practical normativity, recognizes that reasons can be either given or will-based. According to that view, when our given reasons are on a par, will-based reasons may step in to determine what we have most all-things-considered reasons to do. I have given arguments for the view elsewhere, but it might be worth mentioning here that the view has a possible neurological basis. As it turns out, our brains do different things when we choose by following external, given reasons and when we choose according to some internal state or activity, such as willing (Nakao et al., Reference Nakao, Osumi, Ohira, Kasuya, Shinoda and Yamada2009, Reference Nakao, Ohira and Northoff2012).

We do not need to go into the details of the Hybrid Voluntarism—for example, when will-based reasons can step in and how they can do so—in order to extract its key point for our purposes. According to the view, when your given reasons are on a par, you have the normative power to create new will-based reasons for one option over another by putting your agency behind some feature of one of the options. By putting your will behind a feature of an option—by standing for it—you can be that in virtue of which something is a will-based reason for choosing that option.

Thus, in hard choices you need not be stuck. You have the normative power to create for yourself a new will-based reason to pursue one option over the other. And you may now have most all-things-considered reasons—that is, taking into account both given and will-based reasons—to choose one option over the other. Distinctive of Hybrid Voluntarism is the claim that agents can make it true that they have most reason to do one thing rather than another directly through an activity of their own wills.

The idea of putting your will behind something, although seemingly elusive, is perfectly familiar. It is what you do when you commit to a loved one, a cause, or a personal project. When you commit to something, you put your very agency—your very self—behind, say, the needs or interests of your children or spouse, nuclear disarmament, or learning to play the piano. You stand for what you have committed to. Your commitment provides the grounds for new will-based reasons to, say, make a life with your beloved. In the same way, you can commit to the intellectual excitement of a philosophy career and thereby give yourself a new-will-based reason—that the philosophy career will afford you intellectual excitement—that you did not have before. You may thereby make it true that you have most all-things-considered reasons to be a philosopher rather than a lawyer.

Commitments in the sense of interest are internal to the agent and should be distinguished from promises. When you promise to do something—such as pick up your friend's dry cleaning—your promise is external; its being a promise depends on uptake by another. Commitments, by contrast, are solo activities of the will that do not require recognition by another. More important, promises don't make facts reasons—they are not the grounds or that in virtue of which something is a reason—but rather conditions under which some fact, such as that the promisee has a reasonable expectation that you will do what you promised to do, is a reason (see, e.g., Scanlon Reference Scanlon1998 and Enoch Reference Enoch2011). When you commit to something in a way that grounds will-based reasons, by contrast, it is your agency, the very activity of committing, that is the source of the reasons you create. Commitments, unlike promises, can be sources of reasons.

The argument for this view has been explored elsewhere (Chang Reference Chang2013a, cf. Korsgaard Reference Korsgaard1996, Reference Korsgaard2009), but we can summarize it roughly as follows. First, internal commitments of the kind of interest cannot be understood in terms of the usual tools of normative explanation, such as belief, desire, emotion, valuing, intention, plans, policies, and the like, but essentially involve the sui generis idea of willing something to be a reason. Second, it is in the nature of willing something to be a reason that the activity presupposes the possibility of success in much the way that it is in the nature of stipulating the meaning of word that that activity presupposes the possibility of success in conferring meaning on the word. And, third, it is highly implausible to think that there could be a principle, not grounded in the will, according to which a condition for you to have a given reason is for you to engage in an activity that presupposes that you can create reasons. In short, then, if the internal commitments of interest change the reasons we have, they do so as grounds of reasons and not as conditions of given reasons we already have waiting, as it were, to be triggered by an act of our will. Promises change our reasons not by being grounds of reasons but by triggering reasons we have according to the given principle, ‘If you promise to X, ceteris paribus you have a reason to X’.

Commitments also differ from what decision theorists call ‘resolute choice’. A resolute choice is a decision to follow a plan of action that takes into account what you have done in the past and normatively binds you in the future (McClennen Reference McClennen1990; Rabinowicz Reference Rabinowicz1995; see also Gauthier Reference Gauthier1997). Such choices allow rational agents to avoid money pumps and to solve collective action problems such as the prisoners’ dilemma. But commitments are not resolute choices; they need not depend on what you have done in the past nor do they bind you in the future. You can commit to building a life with George, for example, even though in the past he has been nothing more to you than a casual fling. And your commitment to him now can be undone later, even in the next moment, if you find that you can no longer put yourself behind his needs and interests. (Sometimes this is known as ‘getting cold feet’). This is not to say that commitments lack exit costs; as a consequence of a commitment, you might perform actions, such as promise to marry him, that trigger given reasons, such as to pay him alimony after the divorce. What is special about commitments is that their normative upshots depend entirely on the engagement of your will.

The idea that we can create reasons by committing to something may seem strange. But reflection on freedom and rational agency helps us see how commitments might naturally play this role. Suppose that a commitment (or some related activity of the will) could not ground practical reasons and that reasons were instead grounded in divine commands, informed desires, or a normative reality. Our reasons, then, would be given to us by sources essentially divorced from our own agency, and being rational would simply be a matter of discovering given reasons and conforming ourselves to their dictates. As Kant pointed out, this would make us slaves to our reasons.

We seem, however, to be free—not necessarily in the sense of being first causes—but in the sense of being able to determine that we have most reason to choose one thing over another within the constraints given to us by normative facts. Kantians, in their zeal to win us this rational freedom, have insisted that our wills are the only ground of practical reasons (Korsgaard Reference Korsgaard1996, Reference Korsgaard2009, but cf. Anderson Reference Anderson1993; Herman Reference Herman1996; Hill Reference Hill2002). This leads, notoriously, to the problem of constraining the will in ways that allow us to have the reasons we in fact have. The Kantian view of the will arguably gives us too much freedom; in the absence of adequate constraints on the will, we have the freedom will ourselves reasons to maim, murder, and engage in mayhem as it suits us. Hybrid Voluntarism, by contrast, because it recognizes both given and will-based practical reasons, avoids this problem. By constraining our normative power to create reasons for ourselves by given reasons, we achieve a freedom worth having.

Of course, just because you are free to commit to a feature of an alternative and thereby create a new will-based reason for yourself to choose it does not mean that you are rationally required to do so. You might not exercise your normative power as a rational agent. You might instead drift into one alternative as opposed to another. Since the given reasons are on a par, you do not act against your given reasons whichever option you choose, so drifting is a rational response just as committing is. When we drift into an alternative, we intentionally choose it, but in a way that is noncommittal, that does not involve our putting ourselves behind some feature of an alternative. So, for example, you might drift into the legal career because it is the path of least resistance or the safest or the one that will please your parents most, where none of these explanations of why you choose to be a lawyer involve features you put your agency behind. Law schools are populated with drifters.

What you do in the face of a hard choice helps to constitute your identity as a rational agent. If you commit to the intellectual excitement afforded by a philosophy career, for instance, you make yourself into a rational agent who has a will-based reason to pursue intellectual excitement, and perhaps thereby, someone who has most all-things-considered reasons to become a philosopher instead of a lawyer. Another rational agent in a similar situation might commit instead to the financial security of being a lawyer and thereby have most reason to become a lawyer. Still another agent might drift into one or other career. What we do in hard choices makes us rationally different from one another; it is what gives each of us his or her distinctive rational identity. Moreover, since what makes a choice hard is structural, hard choices in principle include choices about how to wear your hair, what to have for dessert, and which toaster oven to buy. You can make your rational identity by committing to the ease of wearing your hair short or to the aesthetic flexibility of wearing your hair long or to the social meaning associated with sporting a Mohawk. But you might instead drift into adopting a hairstyle—whatever Supercuts was offering that day. That your hairdo is or is not something you commit to says something about who you are.

We now have an answer to the question, ‘What should you do in a hard choice?’ You should commit or drift. What you do will be an act of self-constitution, making you into the distinctive agent that you are. Parity is special because it is the relation that allows us to make it true, through an exercise of our normative powers, that we have most all-things-considered reasons to do one thing rather than another. It is the point at which we come into our own as self-governing agents.

6. Rational Agency

I want to end by returning to the deeper question implicated in our discussion of how to understand hard choices: what it is to be a rational agent?

The standard conception of rational agency recognizes only given reasons. Our job as rational agents, recall, is to recognize reasons given to us, not created by us, and then to respond to them appropriately. In hard choices, however, our given reasons run out—they are on a par. On the standard conception, then, we are stuck in hard choices. Since given reasons are the only reasons there are, when those reasons run out, we are left without normative resources for responding to hard choices.

More important, the standard conception leaves no room for agency in rational agency; agency has no direct role in determining what we have most reason to do. Return to your imagined choice between a life in philosophy and one in law. According to the standard conception, what you should do is always dictated by your given reasons. If you have most given reason to be a lawyer, you should be a lawyer. If you have most given reason to be a philosopher, you should be philosopher. If your given reasons are equally strong, then you should just pick—flip a coin—between the two careers. And if your given reasons are incomparable, then you are out of luck; the choice lies beyond the scope of your rational agency, and all you can do is plump for one or the other alternative. This way of thinking about rational agency leaves no room for us—for our very selves—to determine what we have most reason to do. It makes us into passive discoverers of reasons rather than active creators of them.

But there is an attractive and, I think, plausible, alternative view of rational agency that both gives us the resources to deal with hard choices and frees us from the dictatorship of given reasons. When our given reasons are on a par, as they are in hard choices, we have the normative power to create will-based reasons for ourselves to choose one alternative over the other. It is not facts beyond our agency that determine whether we should lead this kind of life rather than that, but us. In this way, we make ourselves who we are through the exercise of our normative powers in hard choices.