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Value Pluralism

2. The Attraction of Pluralism

2.2 Value Conflicts and Rational Regret

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

Michael Stocker (1990) and Bernard Williams (1973 and 1981) and others have argued that it can be rational to regret the outcome of a correct moral choice. That is,  even when the right choice has been made, the rejected option can reasonably be regretted, and so the choice involves a genuine value conflict. This seems strange if the options are being compared in terms of a supervalue. How can we regret having chosen more rather than less of the same thing? Yet the phenomenon seems undeniable, and pluralism can explain it. If there are plural values, then one can rationally regret not having chosen something which though less good, was different.

Value Pluralism

2. The Attraction of Pluralism

2.2 Value Conflicts and Rational Regret

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

It is worth noting that the pluralist argument is not that all cases of value conflict point to pluralism. There may be conflicts because of ignorance, for example, or because of irrationality, and these do not require positing plural values. Stocker argues that there are (at least) two sorts of value conflict that require plural values. The first is conflict that involves choices between doing things at different times. Stocker argues that goods become different values in different temporal situations, and the monist cannot accommodate this thought. The other sort of case (which Williams also points to) is when there is a conflict between things that have different advantages and disadvantages. The better option may be better, but it does not ‘make up for’ the lesser option, because it isn’t the same sort of thing. Thus there is a remainder—a moral value that is lost in the choice, and that it is rational to regret.

Value Pluralism

2. The Attraction of Pluralism

2.2 Value Conflicts and Rational Regret

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

Both Martha Nussbaum (1986) and David Wiggins (1980) have argued for pluralism on the grounds that only pluralism can explain akrasia, or weakness of will. An agent is said to suffer from weakness of will when she knowingly chooses a less good option over a better one. On the face of it, this is a puzzling thing to do—why would someone knowingly do what they know to be worse? A pluralist has a plausible answer—when the choice is between two different sorts of value, the agent is preferring A to B, rather than preferring less of A to more of A. Wiggins explains the akratic choice by suggesting that the agent is ‘charmed’ by some aspect of the choice, and is swayed by that to choose what she knows to be worse overall (Wiggins 1980, p. 257). However, even Michael Stocker, the arch pluralist, does not accept that this argument works. As Stocker points out, Wiggins is using a distinction between a cognitive and an affective element to the choice, and this distinction can explain akrasia on a monist account of value too. Imagine that a monist hedonist agent is faced with a choice between something that will give her more pleasure and something that will give her less pleasure. The cognitive aspect to the choice is clear—the agent knows that one option is more pleasurable than the other, and hence on her theory better. However, to say that the agent believes that more pleasure is better is not to say that she will always be attracted to the option that is most pleasurable. She may, on occasion, be attracted to the option that is more unusual or interesting. Hence she may act akratically because she was charmed by some aspect of the less good choice—and as Stocker says, there is no need to posit plural values to make sense of this—being charmed is not the same as valuing. (Stocker 1990, p.219).

Value Pluralism

2. The Attraction of Pluralism

2.3 Appropriate Responses to Value

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

Another argument for pluralism starts from the observation that there are many and diverse appropriate responses to value. Christine Swanton (2003, ch. 2) and Elizabeth Anderson (1993) both take this line. As Swanton puts it:

Value Pluralism

2. The Attraction of Pluralism

2.3 Appropriate Responses to Value

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

According to value centered monism, the rightness of moral responsiveness is determined entirely by degree or strength of value…I shall argue, on the contrary, that just how things are to be pursued, nurtured, respected, loved, preserved, protected, and so forth may often depend on further general features of those things, and their relations to other things, particularly the moral agent. (Swanton 2003, p. 41).

Value Pluralism

2. The Attraction of Pluralism

2.3 Appropriate Responses to Value

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

The crucial thought is that there are various bases of moral responsiveness, and these bases are irreducibly plural. A monist could argue that there are different appropriate responses to value, but the monist would have to explain why there are different appropriate responses to the same value. Swanton’s point is that the only explanation the monist has is that different degrees of value merit different responses. According to Swanton, this does not capture what is really going on when we appropriately honor or respect a value rather than promoting it. Anderson and Swanton both argue that the complexity of our responses to value can only be explained by a pluralistic theory.

Value Pluralism

2. The Attraction of Pluralism

2.3 Appropriate Responses to Value

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

Elizabeth Anderson argues that it is a mistake to understand moral goods on the maximising model. She uses the example of parental love (Anderson 1997, p. 98). Parents should not see their love for their children as being directed towards an “aggregate child collective”. Such a view would entail that trade offs were possible, that one child could be sacrificed for another. On Anderson’s view we can make rational choices between conflicting values without ranking values: “…choices concerning those goods or their continued existence do not generally require that we rank their values on a common scale and choose the more valuable good; they require that we give each good its due” (Anderson 1997, p. 104).

Value Pluralism

3. Monist Solutions

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

I began the last section by saying that if foundational values are plural, then choices between them will be complex. It is clear that our choices are complex. However, it would be invalid to conclude from that that values are plural—the challenge for monists is to explain how they too can make sense of the complexity of our value choices.

Value Pluralism

3. Monist Solutions

3.1 Different Bearers of Value

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

One way for monists to make sense of complexity in value choice is to point out that there are different bearers of value, and this makes a big difference to the experience of choice. (See Hurka, 1996; Schaber, 1999; Klocksiem 2011). Here is the challenge to monism in Michael Stocker’s words (Stocker, 1990, p. 272): “[if monism is true] there is no ground for rational conflict because the better option lacks nothing that would be made good by the lesser.” In other words, there are no relevant differences between the better and worse options except that the better option is better. Thomas Hurka objects that there can be such differences. For example, in a choice between giving five units of pleasure to A and ten units to B, the best option (more pleasure for B) involves giving no pleasure at all to A. So there is something to rationally regret, namely, that A had no pleasure. The argument can be expanded to deal with all sorts of choice situation: in each situation,  a monist can say something sensible about an unavoidable loss, a loss that really is a loss. If, of two options one will contribute more basic value, the monist must obviously choose that one. But the lesser of the options may contribute value via pleasure, while the superior option contributes value via knowledge, and so there is a loss in choosing the option with the greater value contribution—a loss in pleasure— and it is rational for us to regret this.

Value Pluralism

3. Monist Solutions

3.1 Different Bearers of Value

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

There is one difficulty with this answer. The loss described by Hurka is not a moral loss, and so the regret is not moral regret. In Hurka’s example, the relevant loss is that A does not get any pleasure. The agent doing the choosing may be rational to regret this if she cares about A, or even if she just feels sorry for A, but there has been no moral loss, as ‘pleasure for A’ as opposed to pleasure itself is not a moral value. According to the view under consideration, pleasure itself is what matters morally, and so although A’s pleasure matters qua pleasure, the moral point of view takes B’s pleasure into account in just the same way, and there is nothing to regret, as there is more pleasure than there would otherwise have been. Stocker and Williams would surely insist that the point of their argument was not just that there is a loss, but that there is a moral loss. The monist cannot accommodate that point, as the monist can only consider the quantity of the value, not its distribution, and so we are at an impasse.

Value Pluralism

3. Monist Solutions

3.1 Different Bearers of Value

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

However, the initial question was whether the monist has succeeded in explaining the phenomenon of ‘moral regret’, and perhaps Hurka has done that by positing a conflation of moral and non-moral regret in our experience. From our point of view, there is regret, and the monist can explain why that is without appealing to irrationality. On the other hand the monist cannot appeal to anything other than quantity of value in appraising the morality of the situation. So although Hurka is clearly right in so far as he is saying that a correct moral choice can be regretted for non-moral reasons, he can go no further than that.

Value Pluralism

3. Monist Solutions

3.2 Diminishing Marginal Value

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

Another promising strategy that the monist can use in order to explain the complexity in our value choices is the appeal to ‘diminishing marginal value’. The value that is added to the sum by a source of value will tend to diminish after a certain point—this phenomenon is known as diminishing marginal value (or, sometimes, diminishing marginal utility). Mill’s higher and lower pleasures, which seem to be plural values, might be accommodated by the monist in this way. The monist makes sense of discontinuities in value by insisting on the distinction between sources of value, which are often ambiguously referred to as ‘values’, and the super value. Using a monist utilitarian account of value, we can distinguish between the non-evaluative description of options, the intermediate description, and the evaluative description as follows:

Value Pluralism

3. Monist Solutions

3.2 Diminishing Marginal Value

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

On this account, painting produces beauty, and beauty (which is not a value but the intermediate source of value) produces value. Similarly, reading a book produces knowledge, and gaining knowledge produces value. Now it should be clear how the monist can make sense of phenomena like higher and lower pleasures. The non-evaluative options (e.g. eating donuts) have diminishing marginal non-basic value.

Value Pluralism

3. Monist Solutions

3.2 Diminishing Marginal Value

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

On top of that, the intermediate effect, or non-basic value, (e.g. experiencing pleasure) can have a diminishing contribution to value. Varying diminishing marginal value in these cases is easily explained psychologically. It is just the way we are—we get less and less enjoyment from donuts as we eat more and more (at least in one sitting). However, we may well get the same amount of enjoyment from the tenth Johnny Cash song that we did from the first. In order to deal with the higher and lower pleasures case the monist will have to argue that pleasures themselves can have diminishing marginal utility—the monist can argue that gustatory pleasure gets boring after a while, and hence contributes less and less to the super value—well being, or whatever it is.[9]

Value Pluralism

3. Monist Solutions

3.2 Diminishing Marginal Value

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

This picture brings us back to the distinction between foundational and non-foundational pluralism. Notice that the monist theories being imagined here are foundationally monist, because they claim that there is fundamentally one value, such as pleasure, and they are pluralist at the level of ordinary choice because they claim that there are intermediate values, such as knowledge and beauty, which are valuable because of the amount of pleasure they produce (or realize, or contain—the exact relationship will vary from theory to theory).

Value Pluralism

3. Monist Solutions

3.3 Theoretical Virtues

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

The main advantage of pluralism is that it seems true to our experience of value. We experience values as plural, and pluralism tells is that values are indeed plural. The monist can respond, as we have seen, that there are ways to explain the apparent plurality of values without positing fundamentally plural values. Another, complementary strategy that the monist can pursue is to argue that monism has theoretical virtues that pluralism lacks. In general, it seems that theories should be as simple and coherent as possible, and that other things being equal, we should prefer a more coherent theory to a less coherent one. Thus so long as monism can make sense of enough of our intuitive judgments about the nature of value, then it is to be preferred to pluralism because it does better on the theoretical virtue of coherence.

Value Pluralism

3. Monist Solutions

3.3 Theoretical Virtues

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

Another way to put this point is in terms of explanation. The monist can point out that the pluralist picture lacks explanatory depth. It seems that a list of values needs some further explanation: what makes these things values? (See Bradley, 2009, p.16). The monist picture is superior, because the monist can provide an explanation for the value of the (non-foundational) plurality of values: these things are values because they contribute to well-being, or pleasure, or whatever the foundational monist value is. (See also the discussion of this in the entry on value theory).

Value Pluralism

3. Monist Solutions

3.3 Theoretical Virtues

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

Patricia Marino argues against this strategy (2016). She argues that ‘systematicity’ (the idea that it is better to have fewer principles) is not a good argument in favour of monism. Marino points out that explanation in terms of fewer fundamental principles is not necessarily better explanation. If there are plural values, then the explanation that appeals to plural values is a better one, in the sense that it is the true one: it doesn’t deny the plurality of values. (2016, p.124-125). Even if we could give a monist explanation without having to trade off against our pluralist intuitions, Marino argues, we have no particular reason to think that explanations appealing to fewer principles are superior.

Value Pluralism

3. Monist Solutions

3.4 Preference Satisfaction Views

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

There is a different account of value that we ought to consider here: the view that value consists in preference or desire satisfaction. On this view, knowledge and pleasure and so on are valuable when they are desired, and if they are not desired anymore they are not valuable anymore. There is no need to appeal to complicated accounts of diminishing marginal utility: it is uncontroversial that we sometimes desire something and sometimes don’t. Thus complexities in choices are explained by complexities in our desires, and it is uncontroversial that our desires are complex.

Value Pluralism

3. Monist Solutions

3.4 Preference Satisfaction Views

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

Imagine a one person preference satisfaction account of value that says simply that what is valuable is what P desires. Apparently this view is foundationally monist: there is only one thing that confers value (being desired by P), yet at the non-foundational level there are many values (whatever P desires). Let us say that P desires hot baths, donuts and knowledge. The structure of P’s desires is such that there is a complicated ranking of these things, which will vary from circumstance to circumstance. The ranking is not explained by the value of the objects,rather, her desire explains the ranking and determines the value of the objects. So it might be that P sometimes desires a hot bath and a donut equally, and cannot choose between them; it might be that sometimes she would choose knowledge over a hot bath and a donut, but sometimes she would choose a hot bath over knowledge. On James Griffin’s slightly more complex view, well-being consist in the fulfillment of informed desire, and Griffin points out that his view can explain discontinuities in value without having to appeal to diminishing marginal utility:

Value Pluralism

3. Monist Solutions

3.4 Preference Satisfaction Views

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

there may well turn out to be cases in which, when informed, I want, say, a certain amount of one thing more than any amount of another, and not because the second thing cloys, and so adding to it merely produces diminishing marginal values. I may want it even though the second thing does not, with addition, lose its value; it may be that I think that no increase in that kind of value, even if constant and positive, can overtake a certain amount of this kind of value. (1986, p. 76).

Value Pluralism

3. Monist Solutions

3.4 Preference Satisfaction Views

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

This version of foundational monism/normative pluralism escapes some of the problems that attend the goods approach. First, this view can account for deep complexities in choice. The plural goods that P is choosing between do not seem merely instrumental. Donuts are not good because they contribute to another value, and P does not desire donuts for any reason other than their donuty nature. On this view, if it is hard to choose between donuts and hot baths it is because of the intrinsic nature of the objects. The key here is that value is conferred by desire, not by contribution to another value. Second, this view can accommodate incomparabilities: if P desires a hot bath because of its hot bathy nature, and a donut because of its donuty nature, she may not be able to choose between them.

Value Pluralism

3. Monist Solutions

3.4 Preference Satisfaction Views

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

However, it is not entirely clear that a view like Griffin’s is genuinely monist at the foundational level: the question arises, what is constraining the desires that qualify as value conferring? If the answer is ‘nothing’, then the view seems genuinely monist, but is probably implausible. Unconstrained desire accounts of value seem implausible because our desires can be for all sorts of things—we may desire things that are bad for us, or we may desire things because of some mistake we have made. If the answer is that there is something constraining the desires that count as value conferring, then of course the question is, ‘what?’ Is it the values of the things desired? A desire satisfaction view that restricts the qualifying desires must give an account of what restricts them, and obviously, the account may commit the view to foundational pluralism.

Value Pluralism

3. Monist Solutions

3.4 Preference Satisfaction Views

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

Griffin addresses this question at the very beginning of his book on well being (Griffin, 1986, ch.2).[10] As he puts it,

Value Pluralism

3. Monist Solutions

3.4 Preference Satisfaction Views

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

The danger is that desire accounts get plausible only by, in effect, ceasing to be desire accounts. We had to qualify desire with informed, and that gave prominence to the features or qualities of the objects of desire, and not to the mere existence of desire. (1986, p. 26).

Value Pluralism

3. Monist Solutions

3.4 Preference Satisfaction Views

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

Griffin’s account of the relationship between desire and value is subtle, and (partly because Griffin himself does not distinguish between foundational and normative pluralism) it is difficult to say whether his view is foundationally pluralist or not. Griffin argues that it is a mistake to see desire as a blind motivational force—we desire things that we perceive in a favorable light- we take them to have a desirability feature. When we try to explain what involved in seeing things in a favorable light, we cannot, according to Griffin, separate understanding from desire:

Value Pluralism

3. Monist Solutions

3.4 Preference Satisfaction Views

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

…we cannot, even in the case of a desirability feature such as accomplishment, separate understanding and desire. Once we see something as ‘accomplishment’, as ‘giving weight and substance to our lives’, there is no space left for desire to follow along in a secondary subordinate position. Desire is not blind. Understanding is not bloodless. Neither is the slave of the other. There is no priority. (1986, p. 30)

Value Pluralism

3. Monist Solutions

3.4 Preference Satisfaction Views

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

This suggests that the view is indeed pluralist at the foundation—values are not defined entirely by desire, but partly by other features of the situation, and so at the most fundamental level there is more than one value making feature. Griffin himself says that “the desire account is compatible with a strong form of pluralism about values” (p. 31).

Value Pluralism

3. Monist Solutions

3.4 Preference Satisfaction Views

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

I shall not pursue further the question whether or not Griffin is a foundational pluralist, my aim in this section is to show first, that monist preference satisfaction accounts of value may have more compelling ways of explaining complexities in value comparison than monist goods approaches, but second, to point out that any constrained desire account may well actually be foundationally pluralist. As soon as something is introduced to constrain the desires that qualify as value conferring, it looks as though another value is operating.

Value Pluralism

4. Pluralism and Rational Choice

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

The big question facing pluralism is whether rational choices can be made between irreducibly plural values. Irreducible plurality appears to imply incommensurability—that is to say, that there is no common measure which can be used to compare two different values. (See the entry on incommensurable values.) Value incommensurability seems worrying: if values are incommensurable, then either we are forced into an ad hoc ranking, or we cannot rank the values at all. Neither of these are very appealing options.

Value Pluralism

4. Pluralism and Rational Choice

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

However, pluralists reject this dilemma. Bernard Williams argues that it is a mistake to think that pluralism implies that comparisons are impossible. He says:

Value Pluralism

4. Pluralism and Rational Choice

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

There is one motive for reductivism that does not operate simply on the ethical, or on the non-ethical, but tends to reduce every consideration to one basic kind. This rests on an assumption about rationality, to the effect that two considerations cannot be rationally weighed against each other unless there is a common consideration in terms of which they can be compared. This assumption is at once very powerful and utterly baseless. Quite apart from the ethical, aesthetic considerations can be weighed against economic ones (for instance) without being an application of them, and without their both being an example of a third kind of consideration. (Williams 1985, p. 17)

Value Pluralism

4. Pluralism and Rational Choice

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

Making a similar point, Ruth Chang points out that incommensurability is often conflated with incomparability. She provides clear definitions of each: incommensurability is the lack of a common unit of value by which precise comparisons can be made. Two items are incomparable, if there is no possible relation of comparison, such as ‘better than’, or ‘as good as’ (1997, Introduction). Chang points out that incommensurability is often thought to entail incomparability, but it does not.

Value Pluralism

4. Pluralism and Rational Choice

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

Defenders of pluralism have used various strategies to show that it is possible to make rational choices between plural values.

Value Pluralism

4. Pluralism and Rational Choice

4.1 Practical Wisdom

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

The pluralist’s most common strategy in the face of worries about choices between incommensurable values is to appeal to practical wisdom—the faculty described by Aristotle—a faculty of judgment that the wise and virtuous person has, which enables him to see the right answer. Practical wisdom is not just a question of being able to see and collate the facts, it goes beyond that in some way—the wise person will see things that only a wise person could see. So plural values can be compared in that a wise person will ‘just see’ that one course of action rather than another is to be taken. This strategy is used (explicitly or implicitly) by McDowell (1979), Nagel (1979), Larmore (1987), Skorupski (1996), Anderson (1993 and 1997) Wiggins (1997 and 1998), Chappell (1998), Swanton (2003). Here it is in Nagel’s words:

Value Pluralism

4. Pluralism and Rational Choice

4.1 Practical Wisdom

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

Provided one has taken the process of practical justification as far as it will go in the course of arriving at the conflict, one may be able to proceed without further justification, but without irrationality either. What makes this possible is judgment—essentially the faculty Aristotle described as practical wisdom, which reveals itself over time in individual decisions rather than in the enunciation of general principles. (1979, p. 135)

Value Pluralism

4. Pluralism and Rational Choice

4.1 Practical Wisdom

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

The main issue for this solution to the comparison problem is to come up with an account of what practical wisdom is. It is not easy to understand what sort of thing the faculty of judgment might be, or how it might work. Obviously pluralists who appeal to this strategy do not want to end up saying that the wise judge can see which of the options has more goodness, as that would constitute collapsing back into monism. So the pluralist has to maintain that the wise judge makes a judgment about what the right thing to do is without making any quantitative judgment. The danger is that the faculty seems entirely mysterious: it is a kind of magical vision, unrelated to our natural senses. As a solution to the comparison problem, the appeal to practical wisdom looks rather like way of shifting the problem to another level. Thus the appeal to practical wisdom cannot be left at that. The pluralist owes more explanation of what is involved in practical wisdom. What follows below are various pluralists’ accounts of how choice between plural values is possible, and whether such choice is rational.

Value Pluralism

4. Pluralism and Rational Choice

4.2 Super Scales

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

One direction that pluralists have taken is to argue that although values are plural, there is nonetheless an available scale on which to rank them. This scale is not rationalized by something that the values have in common (that would be monism), but by something over and above the values, which is not itself a super value. Williams sometimes writes as if this is his intention, as do Griffin (1986 and 1997), Stocker (1990), Chang (1997 and 2004), Taylor (1982 and 1997). James Griffin (1986) develops this suggestion in his discussion of plural prudential values. According to Griffin, we do not need to have a super-value to have super-scale. Griffin says:

Value Pluralism

4. Pluralism and Rational Choice

4.2 Super Scales

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

…it does not follow from there being no super-value that there is no super-scale. To think so would be to misunderstand how the notion of ‘quantity’ of well-being enters. It enters through ranking; quantitative differences are defined on qualitative ones. The quantity we are talking about is ‘prudential value’ defined on informed rankings. All that we need for the all-encompassing-scale is the possibility of ranking items on the basis of their nature. And we can, in fact, rank them in that way. We can work out trade-offs between different dimensions of pleasure or happiness. And when we do, we rank in a strong sense: not just choose one rather than the other, but regard it as worth more. That is the ultimate scale here: worth to one’s life. (Griffin 1986, p. 90)

Value Pluralism

4. Pluralism and Rational Choice

4.2 Super Scales

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

This passage is slightly hard to interpret (for more on why see my earlier discussion of Griffin in the section on preference satisfaction accounts). On one interpretation, Griffin is in fact espousing a sophisticated monism. The basic value is ‘worth to one’s life’, and though it is important to talk about non-basic values, such as the different dimensions of pleasure and happiness, they are ultimately judged in terms of their contribution to the worth of lives.

Value Pluralism

4. Pluralism and Rational Choice

4.2 Super Scales

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

The second possible interpretation takes Griffin’s claim that worth to life is not a supervalue seriously. On this interpretation, it is hard to see what worth to life is, if not a supervalue. Perhaps it is only a value that we should resort to when faced with incomparabilities. However, this interpretation invites the criticism that Griffin is introducing a non-moral value, perhaps prudential value, to arbitrate when moral values are incommensurable. In other words, we cannot decide between incommensurable values on moral grounds, so we should decide on prudential grounds. This seems reasonable when applied to incommensurabilities in aesthetic values. One might not be able to say whether Guernica is better than War and Peace, but one might choose to have Guernica displayed on the wall because it will impress one’s friends, or because it is worth more money, or even because one just enjoys it more. In the case of moral choices this is a less convincing strategy: it introduces a level of frivolity into morality that seems out of place.

Value Pluralism

4. Pluralism and Rational Choice

4.2 Super Scales

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

Stocker’s main strategy is to argue that values are plural, and comparisons are made, so it must be possible to make rational comparisons. He suggests that a “higher level synthesizing category” can explain how comparisons are made (1990, p. 172). According to Stocker these comparisons are not quantitative, they are evaluative:

Value Pluralism

4. Pluralism and Rational Choice

4.2 Super Scales

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

Suppose we are trying to choose between lying on a beach and discussing philosophy—or more particularly, between the pleasure of the former and the gain in understanding from the latter. To compare them we may invoke what might be called a higher-level synthesizing category. So, we may ask which will conduce to a more pleasing day, or to a day that is better spent. Once we have fixed upon the higher synthesizing category, we can often easily ask which option is better in regard to that category and judge which to choose on the basis of that. Even if it seems a mystery how we might ‘directly’ compare lying on the beach and discussing philosophy, it is a commonplace that we do compare them, e.g. in regard to their contribution to a pleasing day. (Stocker 1990, p. 72)

Value Pluralism

4. Pluralism and Rational Choice

4.2 Super Scales

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

Stocker claims that goodness is just the highest level synthesizing category, and that lower goods are constitutive means to the good. Ruth Chang’s approach to comparisons of plural values is very similar (Chang 1997 (introduction) and 2004). Chang claims that comparisons can only be made in terms of a covering value—a more comprehensive value that has the plural values as parts.

Value Pluralism

4. Pluralism and Rational Choice

4.2 Super Scales

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

There is a problem in understanding quite what a ‘synthesizing category’ or ‘covering value’ is. How does the covering value determine the relative weightings of the constituent values? One possibility is that it does it by pure stipulation—as a martini just is a certain proportion of gin and vermouth. However, stipulation does not have the right sort of explanatory power. On the other hand, if a view is to remain pluralist, it must avoid conflating the super scale with a super value. Chang argues that her covering values are sufficiently unitary to provide a basis for comparison, and yet preserve the separateness of the other values. Chang’s argument goes as follows: the values at stake in a situation (for example, prudence and morality) cannot on their own determine how heavily they weigh in a particular choice situation—the values weigh differently depending on the circumstances of the choice. However, the values plus the circumstances cannot determine relevant weightings either—because (I am simplifying here) the internal circumstances of the choice will affect the weighting of the values differently depending on the external circumstances. To use Chang’s own example, when the values at stake are prudence and morality (specifically, the duty to help an innocent victim), and the circumstances include the fact that the victim is far away, the effect this circumstance will have on the weighting of the values depends on external circumstances, which fix what matters in the choice. So, as Chang puts it, “‘What matters’ must therefore have content beyond the values and the circumstances of the choice” (2004, p. 134).

Value Pluralism

4. Pluralism and Rational Choice

4.2 Super Scales

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

Stocker is aware of the worry that appeal to something in terms of which comparisons can be made reduces the view to monism: Stocker insists that the synthesizing category (such as a good life) is not a unitary value—it is at most ‘nominal monism’ in my terminology. Stocker argues that it is a philosophical prejudice to think that rational judgment must be quantitative, and so he claims that he does not need to give an account of how we form and use the higher level synthesizing categories.

Value Pluralism

4. Pluralism and Rational Choice

4.3 Basic Preferences

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

Another approach to the comparison problem appeals to basic preferences. Joseph Raz takes the line that we can explain choice between irreducibly plural goods by talking about basic preferences. Raz approaches the issue of incommensurability by talking about the nature of agency and rationality instead of about the nature of value. He distinguishes between two conceptions of human agency: the rationalist conception, and the classical conception. The rationalist conception corresponds to what we have called the stronger use of the term rational. According to the rationalist conception, reasons require action. The classical conception, by contrast, “regards reasons as rendering options eligible” (Raz 1999, p. 47). Raz favors the classical conception, which regards the will as something separate from desire:

Value Pluralism

4. Pluralism and Rational Choice

4.3 Basic Preferences

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

The will is the ability to choose and perform intentional actions. We exercise our will when we endorse the verdict of reason that we must perform an action, and we do so, whether willingly, reluctantly, or regretting the need, etc. According to the classical conception, however, the most typical exercise or manifestation of the will is in choosing among options that reason merely renders eligible. Commonly when we so choose, we do what we want, and we choose what we want, from among the eligible options. Sometimes speaking of wanting one option (or its consequences) in preference to the other eligible ones is out of place. When I choose one tin of soup from a row of identical tins in the shop, it would be wrong and misleading to say that I wanted that tin rather than, or in preference to, the others. Similarly, when faced with unpalatable but unavoidable and incommensurate options (as when financial need forces me to give up one or another of incommensurate goods), it would be incorrect to say that I want to give up the one I choose to give up. I do not want to do so. I have to, and I would equally have regretted the loss of either good. I simply choose to give up one of them. (Raz, 1999, p. 48)

Value Pluralism

4. Pluralism and Rational Choice

4.3 Basic Preferences

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

Raz’s view about the nature of agency is defended in great detail over the course of many  articles, and all of those arguments cannot be examined in detail here. What is crucial in the context of this discussion of pluralism is whether Raz gives us a satisfactory account of the weaker sense of rational. Raz’s solution to the problem of incommensurability hangs on the claim that it can be rational (in the weak sense) to choose A over B  when there are no further reasons favouring A over B. We shall restrict ourselves to mentioning one objection to the view in the context of moral choices between plural goods. Though Raz’s account of choice may seem plausible in cases where we choose between non-moral values, it seems to do violence to the concept of morality. Consider one of Raz’s own examples, the choice between a banana and a pear. It may be that one has to choose between them, and there is no objective reason to choose one or the other. In this case, it seems Raz’s account of choice is plausible. If one feels like eating a banana, then in this case, desire does provide a reason. As Raz puts it, “A want can never tip the balance of reasons in and of itself. Rather, our wants become relevant when reasons have run their course.” In the example where we choose between a banana and a pear, this sounds fine. However, if we apply it to a moral choice it seems a lot less plausible. Raz admits that “If of the options available to agents in typical situations of choice and decision, several are incommensurate, then reason can neither determine nor completely explain their choices or actions” (Raz, 1999, p. 48). Thus many moral choices are not directed by reason but by a basic preference. It is not fair to call it a desire, because on Raz’s account we desire things for reasons—we take the object of our desire to be desirable. On Raz’s picture then, when reasons have run their course, we are choosing without reasons. It doesn’t matter hugely whether we call that ‘rational’ (it is not rational in the strong sense, but it is in the weak sense). What matters is whether this weak sense of rational is sufficient to satisfy our concept of moral choice as being objectively defensible. The problem is that choosing without reasons look rather like plumping. Plumping may be an intelligible form of choice, but it is questionable whether it is a satisfactory account of moral choice.

Value Pluralism

4. Pluralism and Rational Choice

4.4 Accepting Incomparability

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

One philosopher who is happy to accept that there may be situations where we just cannot make reasoned choices between plural values is Isaiah Berlin, who claimed that goods such as liberty and equality conflict at the fundamental level. Berlin is primarily concerned with political pluralism, and with defending political liberalism, but his views about incomparability have been very influential in discussions on moral pluralism. Bernard Williams (1981), Charles Larmore (1987), John Kekes (1993), Michael Stocker (1990 and 1997), David Wiggins (1997) have all argued that there are at least some genuinely irresolvable conflicts between values, and that to expect a rational resolution is a mistake. For Williams this is part of a more general mistake made by contemporary moral philosophers—he thinks that philosophy tries to make ethics too easy, too much like arithmetic. Williams insists throughout his writings that ethics is a much more complex and multi-faceted beast than its treatment at the hands of moral philosophers would suggest, and so it is not surprising to him that there should be situations where values conflict irresolvably. Stocker (1990) discusses the nature of moral conflict at great length, and although he thinks that many apparent conflicts can be dissolved or are not serious, like Williams, he argues that much of contemporary philosophy’s demand for simplicity is mistaken. Stocker argues that ethics need not always be action guiding, that value is much more complex than Kantians and utilitarians would have us think, and that as the world is complicated we will inevitably face conflicts. Several pluralists have argued that accepting the inevitability of value conflicts does not result in a  breakdown of moral argument, but rather the reverse. Kekes (1993), for example, claims that pluralism enables us to see that irresolvable disagreements are not due to wickedness on the part of our interlocutor, but may be due to the plural nature of values.

Value Pluralism

5. Conclusion

value-pluralism

First published Tue Jun 20, 2006; substantive revision Wed Feb 7, 2018

The battle lines in the debate between pluralism and monism are not always clear. In this entry I have outlined some of them, and discussed some of the main arguments. Pluralists need to be clear about whether they are foundational or non-foundational pluralists. Monists must defend their claim that there really is a unitary value. Much of the debate between pluralists and monists has focussed on the issue of whether the complexity of moral choice implies that values really are plural—a pattern emerges in which the monist claims to be able to explain the appearance of plurality away, and the pluralist insists that the appearance reflects a pluralist reality. Finally, pluralists must explain how comparisons between values are made, or defend the consequence that incommensurability is widespread.

Voting Methods

1. The Problem: Who Should be Elected?

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Suppose that there is a group of 21 voters who need to make a decision about which of four candidates should be elected. Let the names of the candidates be \(A\), \(B\), \(C\) and \(D\). Your job, as a social planner, is to determine which of these 4 candidates should win the election given the opinions of all the voters. The first step is to elicit the voters’ opinions about the candidates. Suppose that you ask each voter to rank the 4 candidates from best to worst (not allowing ties). The following table summarizes the voters’ rankings of the candidates in this hypothetical election scenario.

Voting Methods

1. The Problem: Who Should be Elected?

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Read the table as follows: Each row represents a ranking for a group of voters in which candidates to the left are ranked higher. The numbers in the first column indicate the number of voters with that particular ranking. So, for example, the third row in the table indicates that 7 voters have the ranking \(B\s D\s C\s A\) which means that each of the 7 voters rank \(B\) first, \(D\) second, \(C\) third and \(A\) last. Suppose that, as the social planner, you do not have any personal interest in the outcome of this election. Given the voters’ expressed opinions, which candidate should win the election? Since the voters disagree about the ranking of the candidates, there is no obvious candidate that best represents the group’s opinion. If there were only two candidates to choose from, there is a very straightforward answer: The winner should be the candidate or alternative that is supported by more than 50 percent of the voters (cf. the discussion below about May’s Theorem in Section 4.2). However, if there are more than two candidates, as in the above example, the statement “the candidate that is supported by more than 50 percent of the voters” can be interpreted in different ways, leading to different ideas about who should win the election.

Voting Methods

1. The Problem: Who Should be Elected?

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

One candidate who, at first sight, seems to be a good choice to win the election is \(A\). Candidate \(A\) is ranked first by more voters than any other candidate. (\(A\) is ranked first by 8 voters, \(B\) is ranked first by 7; \(C\) is ranked first by 6; and \(D\) is not ranked first by any of the voters.) Of course, 13 people rank \(A\) last. So, while more voters rank \(A\) first than any other candidate, more than half of the voters rank \(A\) last. This suggests that \(A\) should not be elected.

Voting Methods

1. The Problem: Who Should be Elected?

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

None of the voters rank \(D\) first. This fact alone does not rule out \(D\) as a possible winner of the election. However, note that every voter ranks candidate \(B\) above candidate \(D\). While this does not mean that \(B\) should necessarily win the election, it does suggest that \(D\) should not win the election.

Voting Methods

1. The Problem: Who Should be Elected?

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

The choice, then, boils down to \(B\) and \(C\). It turns out that there are good arguments for each of \(B\) and \(C\) to be elected. The debate about which of \(B\) or \(C\) should be elected started in the 18th-century as an argument between the two founding fathers of voting theory, Jean-Charles de Borda (1733–1799) and M.J.A.N. de Caritat, Marquis de Condorcet (1743–1794). For a history of voting theory as an academic discipline, including Condorcet’s and Borda’s writings, see McLean and Urken (1995). I sketch the intuitive arguments for the election of \(B\) and \(C\) below.

Voting Methods

1. The Problem: Who Should be Elected?

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Candidate \(C\) should win. Initially, this might seem like an odd choice since both \(A\) and \(B\) receive more first place votes than \(C\) (only 6 voters rank \(C\) first while 8 voters rank \(A\) first and 7 voters rank \(B\) first). However, note how the population would vote in the various two-way elections comparing \(C\) with each of the other candidates:

Voting Methods

1. The Problem: Who Should be Elected?

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Condorcet’s idea is that \(C\) should be declared the winner since she beats every other candidate in a one-on-one election. A candidate with this property is called a Condorcet winner. We can similarly define a Condorcet loser. In fact, in the above example, candidate \(A\) is the Condorcet loser since she loses to every other candidate in a one-on-one election.

Voting Methods

1. The Problem: Who Should be Elected?

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Candidate \(B\) should win. Consider \(B\)’s performance in the one-on-one elections.

Voting Methods

1. The Problem: Who Should be Elected?

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Candidate \(B\) performs the same as \(C\) in a head-to-head election with \(A\), loses to \(C\) by only one vote and beats \(D\) in a landslide (everyone prefers \(B\) over \(D\)). Borda suggests that we should take into account all of these facts when determining which candidate best represents the overall group opinion. To do this, Borda assigns a score to each candidate that reflects how much support he or she has among the electorate. Then, the candidate with the largest score is declared the winner. One way to calculate the score for each candidate is as follows (I will give an alternative method, which is easier to use, in the next section):

Voting Methods

1. The Problem: Who Should be Elected?

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

The candidate with the highest score (in this case, \(B\)) is the one who should be elected.

Voting Methods

1. The Problem: Who Should be Elected?

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Both Condorcet and Borda suggest comparing candidates in one-on-one elections in order to determine the winner. While Condorcet tallies how many of the head-to-head races each candidate wins, Borda suggests that one should look at the margin of victory or loss. The debate about whether to elect the Condorcet winner or the Borda winner is not settled. Proponents of electing the Condorcet winner include Mathias Risse (2001, 2004, 2005) and Steven Brams (2008); Proponents of electing the Borda winner include Donald Saari (2003, 2006) and Michael Dummett (1984). See Section 3.1.1 for further issues comparing the Condorcet and Borda winners.

Voting Methods

1. The Problem: Who Should be Elected?

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

The take-away message from this discussion is that in many election scenarios with more than two candidates, there may not always be one obvious candidate that best reflects the overall group opinion. The remainder of this entry will discuss different methods, or procedures, that can be used to determine the winner(s) given the a group of voters’ opinions. Each of these methods is intended to be an answer to the following question:

Voting Methods

1. The Problem: Who Should be Elected?

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Given a group of people faced with some decision, how should a central authority combine the individual opinions so as to best reflect the “overall group opinion”?

Voting Methods

1. The Problem: Who Should be Elected?

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

A complete analysis of this question would incorporate a number of different issues ranging from central topics in political philosophy about the nature of democracy and the “will of the people” to the psychology of decision making. In this article, I focus on one aspect of this question: the formal analysis of algorithms that aggregate the opinions of a group of voters (i.e., voting methods). Consult, for example, Riker 1982, Mackie 2003, and Christiano 2008 for a more comprehensive analysis of the above question, incorporating many of the issues raised in this article.

Voting Methods

1. The Problem: Who Should be Elected?

1.1 Notation

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

In this article, I will keep the formal details to a minimum; however, it is useful at this point to settle on some terminology. Let \(V\) and \(X\) be finite sets. The elements of \(V\) are called voters and I will use lowercase letters \(i, j, k, \ldots\) or integers \(1, 2, 3, \ldots\) to denote them. The elements of \(X\) are called candidates, or alternatives, and I will use uppercase letters \(A, B, C, \ldots \) to denote them.

Voting Methods

1. The Problem: Who Should be Elected?

1.1 Notation

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Different voting methods require different types of information from the voters as input. The input requested from the voters are called ballots. One standard example of a ballot is a ranking of the set of candidates. Formally, a ranking of \(X\) is a relation \(P\) on \(X\), where \(Y\mathrel{P} Z\) means that “\(Y\) is ranked above \(Z\),” satisfying three constraints: (1) \(P\) is complete: any two distinct candidates are ranked (for all candidates \(Y\) and \(Z\), if \(Y\ne Z\), then either \(Y\mathrel{P} Z\) or \(Z\mathrel{P} Y\)); (2) \(P\) is transitive: if a candidate \(Y\) is ranked above a candidate \(W\) and \(W\) is ranked above a candidate \(Z\), then \(Y\) is ranked above \(Z\) (for all candidates \(Y, Z\), and \(W\), if \(Y\mathrel{P} W\) and \(W\mathrel{P} Z\), then \(Y\mathrel{P} Z\)); and (3) \(P\) is irreflexive: no candidate is ranked above itself (there is no candidate \(Y\) such that \(Y\mathrel{P} Y\)). For example, suppose that there are three candidates \(X =\{A, B, C\}\). Then, the six possible rankings of \(X\) are listed in the following table:

Voting Methods

1. The Problem: Who Should be Elected?

1.1 Notation

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

I can now be more precise about the definition of a Condorcet winner (loser). Given a ranking from each voter, the majority relation orders the candidates in terms of how they perform in one-on-one elections. More precisely, for candidates \(Y\) and \(Z\), write \(Y \mathrel{>_M} Z\), provided that more voters rank candidate \(Y\) above candidate \(Z\) than the other way around. So, if the distribution of rankings is given in the above table, we have:

Voting Methods

1. The Problem: Who Should be Elected?

1.1 Notation

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

A candidate \(Y\) is called the Condorcet winner in an election scenario if \(Y\) is the maximum of the majority ordering \(>_M\) for that election scenario (that is, \(Y\) is the Condorcet winner if \(Y\mathrel{>_M} Z\) for all other candidates \(Z\)). The Condorcet loser is the candidate that is the minimum of the majority ordering.

Voting Methods

1. The Problem: Who Should be Elected?

1.1 Notation

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Rankings are one type of ballot. In this article, we will see examples of other types of ballots, such as selecting a single candidate, selecting a subset of candidates or assigning grades to candidates. Given a set of ballots \(\mathcal{B}\), a profile for a set of voters specifies the ballot selected by each voter. Formally, a profile for set of voters \(V=\{1,\ldots, n\}\) and a set of ballots \(\mathcal{B}\) is a sequence \(\bb=(b_1,\ldots, b_n)\), where for each voter \(i\), \(b_i\) is the ballot from \(\mathcal{B}\) submitted by voter \(i\).

Voting Methods

1. The Problem: Who Should be Elected?

1.1 Notation

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

A voting method is a function that assigns to each possible profile a group decision. The group decision may be a single candidate (the winning candidate), a set of candidates (when ties are allowed), or an ordering of the candidates (possibly allowing ties). Note that since a profile identifies the voter associated with each ballot, a voting method may take this information into account. This means that voting methods can be designed that select a winner (or winners) based only on the ballots of some subset of voters while ignoring all the other voters’ ballots. An extreme example of this is the so-called Arrovian dictatorship for voter \(d\) that assigns to each profile the candidate ranked first by \(d\). A natural way to rule out these types of voting methods is to require that a voting method is anonymous: the group decision should depend only on the number of voters that chose each ballot. This means that if two profiles are permutations of each other, then a voting method that is anonymous must assign the same group decision to both profiles. When studying voting methods that are anonymous, it is convenient to assume the inputs are anonymized profiles. An anonymous profile for a set of ballots \(\mathcal{B}\) is a function from \(\mathcal{B}\) to the set of integers \(\mathbb{N}\). The election scenario discussed in the previous section is an example of an anonymized profile (assuming that each ranking not displayed in the table is assigned the number 0). In the remainder of this article (unless otherwise specified), I will restrict attention to anonymized profiles.

Voting Methods

1. The Problem: Who Should be Elected?

1.1 Notation

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

I conclude this section with a few comments on the relationship between the ballots in a profile and the voters’ opinions about the candidates. Two issues are important to keep in mind. First, the ballots used by a voting method are intended to reflect some aspect of the voters’ opinions about the candidates. Voters may choose a ballot that best expresses their personal preference about the set of candidates or their judgements about the relative strengths of the candidates. A common assumption in the voting theory literature is that a ranking of the set of candidates expresses a voter’s ordinal preference ordering over the set of candidates (see the entry on preferences, Hansson and Grüne-Yanoff 2009, for an extended discussion of issues surrounding the formal modeling of preferences). Other types of ballots represent information that cannot be inferred directly from a voter’s ordinal preference ordering, for example, by describing the intensity of a preference for a particular candidate (see Section 2.3). Second, it is important to be precise about the type of considerations voters take into account when selecting a ballot. One approach is to assume that voters choose sincerely by selecting the ballot that best reflects their opinion about the the different candidates. A second approach assumes that the voters choose strategically. In this case, a voter selects a ballot that she expects to lead to her most desired outcome given the information she has about how the other members of the group will vote. Strategic voting is an important topic in voting theory and social choice theory (see Taylor 2005 and Section 3.3 of List 2013 for a discussion and pointers to the literature), but in this article, unless otherwise stated, I assume that voters choose sincerely (cf. Section 4.1).

Voting Methods

2. Examples of Voting Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

A quick survey of elections held in different democratic societies throughout the world reveals a wide variety of voting methods. In this section, I discuss some of the key methods that have been analyzed in the voting theory literature. These methods may be of interest because they are widely used (e.g., Plurality Rule or Plurality Rule with Runoff) or because they are of theoretical interest (e.g., Dodgson’s method).

Voting Methods

2. Examples of Voting Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

I start with the most widely used method:

Voting Methods

2. Examples of Voting Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Plurality Rule: Each voter selects one candidate (or none if voters can abstain), and the candidate(s) with the most votes win.

Voting Methods

2. Examples of Voting Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Plurality rule (also called First Past the Post) is a very simple method that is widely used despite its many problems. The most pervasive problem is the fact that plurality rule can elect a Condorcet loser. Borda (1784) observed this phenomenon in the 18th century (see also the example from Section 1).

Voting Methods

2. Examples of Voting Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Candidate \(A\) is the Condorcet loser (both \(B\) and \(C\) beat candidate \(A\), 13 – 8); however, \(A\) is the plurality rule winner (assuming the voters vote for the candidate that they rank first). In fact, the plurality ranking (\(A\) is first with 8 votes, \(B\) is second with 7 votes and \(C\) is third with 6 votes) reverses the majority ordering \(C\mathrel{>_M} B\mathrel{>_M} A\). See Laslier 2012 for further criticisms of Plurality Rule and comparisons with other voting methods discussed in this article. One response to the above phenomenon is to require that candidates pass a certain threshold to be declared the winner.

Voting Methods

2. Examples of Voting Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Quota Rule: Suppose that \(q\), called the quota, is any number between 0 and 1. Each voter selects one candidate (or none if voters can abstain), and the winners are the candidates that receive at least \(q \times \# V\) votes, where \(\# V\) is the number of voters. Majority Rule is a quota rule with \(q=0.5\) (a candidate is the strict or absolute majority winner if that candidate receives strictly more than \(0.5 \times \# V\) votes). Unanimity Rule is a quota rule with \(q=1\).

Voting Methods

2. Examples of Voting Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

An important problem with quota rules is that they do not identify a winner in every election scenario. For instance, in the above election scenario, there are no majority winners since none of the candidates are ranked first by more than 50% of the voters.

Voting Methods

2. Examples of Voting Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

A criticism of both plurality and quota rules is that they severely limit what voters can express about their opinions of the candidates. In the remainder of this section, I discuss voting methods that use ballots that are more expressive than simply selecting a single candidate. Section 2.1 discusses voting methods that require voters to rank the alternatives. Section 2.2 discusses voting methods that require voters to assign grades to the alternatives (from some fixed set of grades). Finally, Section 2.3 discusses two voting methods in which the voters may have different levels of influence on the group decision. In this article, I focus on voting methods that either are familiar or help illustrate important ideas. Consult Brams and Fishburn 2002, Felsenthal 2012, and Nurmi 1987 for discussions of voting methods not covered in this article.

Voting Methods

2. Examples of Voting Methods

2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

The voting methods discussed in this section require the voters to rank the candidates (see section 1.1 for the definition of a ranking). Providing a ranking of the candidates is much more expressive than simply selecting a single candidate. However, ranking all of the candidates can be very demanding, especially when there is a large number of them, since it can be difficult for voters to make distinctions between all the candidates. The most well-known example of a voting method that uses the voters’ rankings is Borda Count:

Voting Methods

2. Examples of Voting Methods

2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Borda Count: Each voter provides a ranking of the candidates. Then, a score (the Borda score) is assigned to each candidate by a voter as follows: If there are \(n\) candidates, give \(n-1\) points to the candidate ranked first, \(n-2\) points to the candidate ranked second,…, 1 point to the candidate ranked second to last and 0 points to candidate ranked last. So, the Borda score of candidate \(A\), denoted \(\BS(A)\), is calculated as follows (where \(\#U\) denotes the number elements in the set \(U)\): \[\begin{align} \BS(A) =\ &(n-1)\times \# \{i\ |\ i \text{ ranks \(A\) first}\}\\ &+ (n-2)\times \# \{i\ |\ i \text{ ranks \(A\) second}\} \\ &+ \cdots \\ &+ 1\times \# \{i\ |\ i \text{ ranks \(A\) second to last}\}\\ &+ 0\times \# \{i\ |\ i \text{ ranks \(A\) last}\} \end{align}\] The candidate with the highest Borda score wins.

Voting Methods

2. Examples of Voting Methods

2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Recall the example discussed in the introduction to Section 1. For each alternative, the Borda scores can be calculated using the above method:

Voting Methods

2. Examples of Voting Methods

2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Borda Count is an example of a scoring rule. A scoring rule is any method that calculates a score based on weights assigned to candidates according to where they fall in the voters’ rankings. That is, a scoring rule for \(n\) candidates is defined as follows: Fix a sequence of numbers \((s_1, s_2, \ldots, s_n)\) where \(s_k\ge s_{k+1}\) for all \(k=1,\ldots, n-1\). For each \(k\),  \(s_k \) is the score assigned to a alternatives ranked in position \(k\). Then, the score for alternative \(A\), denoted \(Score(A)\), is calculated as follows:

Voting Methods

2. Examples of Voting Methods

2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Borda count for \(n\) alternatives uses scores \((n-1, n-2, \ldots, 0)\) (call \(\BS(X)\) the Borda score for candidate \(X\)). Note that Plurality Rule can be viewed as a scoring rule that assigns 1 point to the first ranked candidate and 0 points to the other candidates. So, the plurality score of a candidate \(X\) is the number of voters that rank \(X\) first. Building on this idea, \(k\)-Approval Voting is a scoring method that gives 1 point to each candidate that is ranked in position \(k\) or higher, and 0 points to all other candidates. To illustrate \(k\)-Approval Voting, consider the following election scenario:

Voting Methods

2. Examples of Voting Methods

2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Note that the Condorcet winner is \(A\), so none of the above methods guarantee that the Condorcet winner is elected (whether \(A\) is elected using 1-Approval or 3-Approval depends on the tie-breaking mechanism that is used).

Voting Methods

2. Examples of Voting Methods

2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

A second way to make a voting method sensitive to more than the voters’ top choice is to hold “multi-stage” elections. The idea is to successively remove candidates that perform poorly in the election until there is one candidate that is ranked first by more than 50% of the voters (i.e., there is a strict majority winner). The different stages can be actual “runoff” elections in which voters are asked to evaluate a reduced set of candidates; or they can be built in to the way the winner is calculated by asking voters to submit rankings over the set of all candidates. The first example of a multi-stage method is used to elect the French president.

Voting Methods

2. Examples of Voting Methods

2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Plurality with Runoff: Start with a plurality vote to determine the top two candidates (the candidates ranked first and second according to their plurality scores). If a candidate is ranked first by more than 50% of the voters, then that candidate is declared the winner. If there is no candidate with a strict majority of first place votes, then there is a runoff between the top two candidates (or more if there are ties). The candidate(s) with the most votes in the runoff elections is(are) declared the winner(s).

Voting Methods

2. Examples of Voting Methods

2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Rather than focusing on the top two candidates, one can also iteratively remove the candidate(s) with the fewest first-place votes:

Voting Methods

2. Examples of Voting Methods

2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

The Hare Rule: The ballots are rankings of the candidates. If a candidate is ranked first by more than 50% of the voters, then that candidate is declared the winner. If there is no candidate with a strict majority of first place votes, repeatedly delete the candidate or candidates that receive the fewest first-place votes (i.e., the candidate(s) with the lowest plurality score(s)). The first candidate to be ranked first by strict majority of voters is declared the winner (if there is no such candidate, then the remaining candidate(s) are declared the winners).

Voting Methods

2. Examples of Voting Methods

2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

The Hare Rule is also called Ranked-Choice Voting, Alternative Vote, and Instant Runoff. If there are only three candidates, then the above two voting methods are the same (removing the candidate with the lowest plurality score is the same as keeping the two candidates with highest and second-highest plurality score). The following example shows that they can select different winners when there are more than three candidates:

Voting Methods

2. Examples of Voting Methods

2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Candidate \(A\) is the Plurality with Runoff winner: Candidates \(A\) and \(B\) are the top two candidates, being ranked first by 7 and 5 voters, respectively. In the runoff election (using the rankings from the above table), the groups voting for candidates \(C\) and \(D\) transfer their support to candidates \(B\) and \(A,\) respectively, with \(A\) winning 10 – 9.

Voting Methods

2. Examples of Voting Methods

2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Candidate \(D\) is the Hare Rule winner: In the first round, candidate \(C\) is eliminated since she is only ranked first by 3 voters. This group’s votes are transferred to \(D\), giving him 7 votes. This means that in the second round, candidate \(B\) is ranked first by the fewest voters (5 voters rank \(B\) first in the profile with candidate \(C\) removed), and so is eliminated. After the elimination of candidate \(B\), candidate \(D\) has a strict majority of the first-place votes: 12 voters ranking him first (note that in this round the group in the second column transfers all their votes to \(D\) since \(C\) was eliminated in an earlier round).

Voting Methods

2. Examples of Voting Methods

2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

The core idea of multi-stage methods is to successively remove candidates that perform "poorly" in an election. For the Hare Rule, performing poorly is interpreted as receiving the fewest first place votes. There are other ways to identify "poorly performing" candidates in an election scenario. For instance, the Coombs Rule successively removes candidates that are ranked last by the most voters (see Grofman and Feld 2004 for an overview of Coombs Rule).

Voting Methods

2. Examples of Voting Methods

2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Coombs Rule: The ballots are rankings of the candidates. If a candidate is ranked first by more than 50% of the voters, then that candidate is declared the winner. If there is no candidate with a strict majority of first place votes, repeatedly delete the candidate or candidates that receive the most last-place votes. The first candidate to be ranked first by a strict majority of voters is declared the winner (if there is no such candidate, then the remaining candidate(s) are declared the winners).

Voting Methods

2. Examples of Voting Methods

2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

In the above example, candidate \(B\) wins the election using Coombs Rule. In the first round, \(A\), with 9 last-place votes, is eliminated. Then, candidate \(B\) receives 12 first-place votes, which is a strict majority, and so is declared the winner.

Voting Methods

2. Examples of Voting Methods

2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

There is a technical issue that is important to keep in mind regarding the above definitions of the multi-stage voting methods. When identifying the poorly performing candidates in each round, there may be ties (i.e., there may be more than one candidate with the lowest plurality score or more than one candidate ranked last by the most voters). In the above definitions, I assume that all of the poorly performing candidates will be removed in each round. An alternative approach would use a tie-breaking rule to select one of the poorly performing candidates to be removed at each round.

Voting Methods

2. Examples of Voting Methods

2.2 Voting by Grading

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

The voting methods discussed in this section can be viewed as generalizations of scoring methods, such as Borda Count. In a scoring method, a voter’s ranking is an assignment of grades (e.g., "1st place", "2nd place", "3rd place", ... , "last place") to the candidates. Requiring voters to rank all the candidates means that (1) every candidate is assigned a grade, (2) there are the same number of possible grades as the number of candidates, and (3) different candidates must be assigned different grades. In this section, we drop assumptions (2) and (3), assuming a fixed number of grades for every set of candidates and allowing different candidates to be assigned the same grade.

Voting Methods

2. Examples of Voting Methods

2.2 Voting by Grading

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

The first example gives voters the option to either select a candidate that they want to vote for (as in plurality rule) or to select a candidate that they want to vote against.

Voting Methods

2. Examples of Voting Methods

2.2 Voting by Grading

voting-methods

First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019

Negative Voting: Each voter is allowed to choose one candidate to either vote for (giving the candidate one point) or to vote against (giving the candidate –1 points). The winner(s) is(are) the candidate(s) with the highest total number of points (i.e., the candidate with the greatest score, where the score is the total number of positive votes minus the total number of negative votes).