Philpropsophy – Philosophy Articles and Article Summaries

It is not uncommon to hear in a discussion the accusation “you’re contradicting yourself.” But what is the role of contradictions in human thought? It is certainly a meaningful statement as evidenced by its use, but what does that actually mean? Using a particular set of grammatical rules and language guidelines (i.e. strict word definitions), it is certainly possible to write down two contradictory things. One popular, almost hack-neyed example often used in philosophy is the classic “round square.” We can certainly write it, though it is a contradiction “on paper.” In other words, with the definitions of “round” and “square” as we know them, no such thing exists or could ever exist. One valid test is whether you can think of – or more precisely, conceive of – the purported object. Can you think of a “round square”? Some people might think they have come up with a solution, but I can assure you that it’s impossible, though my assurances aren’t worth jack (which is why I will discuss it in better detail later on). More generally, the question to ask is, “can someone ever think a contradiction?”

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In summation, consider the following hypothetical imperatives: if you are looking for an unambiguous explanation of why the concept of intrinsic value is metaphysically and epistemologically bizarre, read Mackie’s “The Subjectivity of Values”; if you are looking for a normative validation of a moral free-for-all, read Gilbert Harman’s “Moral Relativism Defended” instead; if you are looking for proof that objective values do not exist, you must extend your search a bit farther than Mackie’s limited, albeit excellent, article.

Source:

Mackie, J. L. “The Subjectivity of Values” In Ethical Theory: Classical and Contemporary Readings, edited by Louis Pojman, 446-456. Belmont: Wadsworth, 2002.

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[1] In this essay I am speaking about a very specific counter-example to Mackie’s claims; it is conceivable that someone could argue for other kinds of objective values that are not intrinsic (such as a collective “that is good which contributes to human prosperity”)

[2] “What if I don’t want to live? ” is a question that merits some serious discussion beyond the scope of this paper. My summarized response is that life is a necessary precondition for all possible values that follow. One who does not want to live constitutes one who has chosen to reject interaction with reality, which cannot be replaced by something else.

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First, we must ponder the exact notion of value. With no need to assert psychological egoism, we can say that all human action is disposed toward the pursuit of value (subjective or objective), whether it is in seeking worldly pleasures, peace of mind, good conscience, or a healthy soul, and whether these actions are self- or other-oriented. Consider value as a means by which things can be preferred over others; in essence, how an agent values something will affect how he acts in order to attain or keep it. The objectivity of such values arises from the fact that agents, specifically humans, possess a physical nature that generates the material basis for a standard of evaluation, from which “the good” is generated. The presence of the fundamental alternatives of existence or nonexistence (“to be or not to be”) is a necessary precursor of value for humans. [1] Without some fundamental alternative, an agent’s course of action would have no purpose and thus no value, if he would even act at all.

Value, then, is derived from a system of conditional imperatives that reduce to the fundamental alternatives and the respective facts pertaining to them. If one wants to live, he ought to eat; if one wants to eat, he ought to produce food; if one wants to produce food, he ought to learn about agriculture, gathering, or hunting, etc. Because the achievement of prolonged existence or one of its corollaries is the achievement of a material state, there is a consistent and empirically-derived basis for resolving the content of the latter portion of conditional imperatives. In this sense, values are objective; they can not be achieved consistently by arbitrary whim.

Without any further elaboration, Mackie’s argument from relativity will pose a problem for the objectivity of value. One could simply argue that there was never a contention in the first place that the optimal fulfillment of hypothetical imperatives was not a matter of objective fact- that it is only the content of the “if” portions of the imperatives that lend themselves to subjectivity, and this is our concern. The problem with this assertion is that it ignores the essential commonality among human beings. In one way, relativity has merit: if you want to grow food in Italy, grow wheat; if you want to grow food in Ireland, grow potatoes. These are two different “ways” of life, both of which can be correct. However, those statements are merely higher-order expressions of the basic imperative, “if you want to live, eat,” which is one of the many imperatives relating to the agent’s relationship to the fundamental outcomes of existence versus non-existence. In other words, by their being what they are, humans are committed to the conditional imperative “if you are human, and if you want to live, satisfy your physical needs. ”[2] The chief difference between a condition such as “if you desire a grade of ‘A’” and “if you are human” is that the products of the latter have claim to objectivity, because the agent does not choose it, whether as an end or a means to an end; it is only a fact given by nature. The result is the existence of an objective value which is not intrinsic, but is logically dependent on the presence of humankind.

In the end, Mackie’s argument for the subjectivity of values makes a strong case against the existence of intrinsic values. He draws attention to several important inconsistencies and difficulties encountered by the philosophical daydreams of Platonic ideals, intrinsic values, and others of their conceptual family. Nevertheless, his argument is insufficient as proof for the subjectivity of values across different agents of the same kind (humans, as the only relevant case).

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The definition at hand here, of course, is that of “objective value. ” If Mackie presupposes that it comes with a Platonic conception attached (the two implicit assumptions listed above), then his argument is unproblematic, but it fails to account for all “objective” moral theories. For the remainder of the discussion, we can understand “objective moral theories” to mean sets of propositions about morality that are true through time, regardless of whether agents believe that they are true, false, or meaningless. What Mackie has successfully refuted is only a subset of the above, that is, he has only challenged those theories which hold values as features of the inanimate universe.

Though ultimately inadequate, Mackie’s argument from queerness offers some valid insight. It is true that there is no logical necessity linking actions with values of the fantastical kind to which Mackie is actually referring. To better illustrate, take the case of any hypothetical imperative: it begins with a conditional “if,” and then a prescribed course of action to best fulfill that condition. The first part sets the desired factual state of affairs, and the second part describes the physical action required to best achieve it. Thus, when an action takes place, a direct connection can be drawn to the corresponding hypothetical value, which is brought about by the achievement of a standard. Suppose the imperative, “if one wants to get an ‘A’ in ethics, he ought to do his final paper. ” Then, when Chris does his paper, his action can be linked to the fulfillment of the goal of Chris having an ‘A’ appear on his transcript. Both parts of the statement pertain to material cause and effect, which can be observed and predicted scientifically (i. e. rationally). Suppose, on the other hand, the imperative, “Chris ought to do his final paper (because it is good/his duty/etc. )” If it is true, when Chris does his paper, his action achieves a good- not a good to him, or for him, but a good in itself. How does he know which actions best bring about that good in the first place, if this good simply occurs with no tangible effect upon him? This, in light of Mackie’s argument, is a very difficult question to answer. In contrast, so long as an imperative is conditional, the link between an action and a respective value is quite clear.

The next question leads ultimately to the defectiveness of moral scepticism: must a value be unconditional or categorical in order to be objective? The argument from queerness incorporates the assumption about the impossible kind of “entity or object or relation” that an objective value must be. Mackie’s faulty epistemology may be part of the problem. In particular, objectivity does not necessarily imply intrinsicality. A concept, for example, does not represent some intrinsic feature of the universe, but only comes about as the product of a particular process of integration of sensory information. Likewise, values are not an intrinsic part of reality. For value to exist at all there must be a valuator- an agent- to impose a standard on what is otherwise an indifferent universe. Things are good to agents, for the sake of attaining some goal; they are not simply good in themselves. Put differently, reality comes before morality. Prior to all good and evil, there must be a world of things that can become good, evil, or neither. In that regard, value is conditional: it predicates on the existence of agents who have some standard for the material state of affairs.

Our next concern is what makes these conditional values objective.

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However, scientific disagreement relies on differences in speculative inferences and explanatory hypotheses based on gathered evidence, to which moral disagreement does not have any claim. On the contrary, moral dissimilarity is more indicative of adherence to different ways of living. The causal connection is reversed: people approve of monogamy because they live monogamously, not the other way around. “Universalizable” or other general, basic principles not only come about because of widespread implicit acceptance, but individually because of the strength of one’s response to it, despite the fact that others may respond quite differently.

The argument from queerness itself has two parts, one metaphysical, and one epistemological. Its metaphysical claim, in summary, is that objective values would be radically different from anything in our experience; “if there were objective values, then they would be entities or qualities or relations of a very strange sort, utterly different from anything else in the universe. ” In turn, the crux of its epistemological claim is that there would be no way to know these queer things without a special, non-empirical means of knowing them (intuition). The central idea of intuitionism, which is that there is some specific and unique interface with which humans come to realize objective moral values, is thus the logical reduction of all theories of objective values. At some point in these theories, some essential concept or inference will only be known via intuition, thus committing any consistent objectivist theory to a “lame answer” to this problem.

Mackie cites Plato’s Theory of Forms as an extreme example of what an objective moral theory entails. Either objective goods have “to-be-pursuedness” built into them, or situations must somehow have a demand for a specific kind of action. Because of this queerness, Mackie questions the connection between an action and a value, and how, if it were to exist, humans could know it. The wrongness of an action must somehow be “consequential” or “supervenient” upon the action; thus, if the natural class of an action is deliberate cruelty, it must be wrong because it is a piece of deliberate cruelty, to which Mackie inquires, “but just what in the world is signified by this ‘because’? ” Whatever it is must be beyond the realm of empirical observation, to which the only intrinsicist response is to find “companions in guilt”: identity, number, the infinite extension of time and space, among other things for which empiricism allegedly can not account. Mackie properly acknowledges that the only valid approach to this objection is by providing empirical accounts of such things, and applying the argument from queerness to those “supposed metaphysical necessities” which cannot be explained.

Critique

It is evident that Mackie’s argument is guilty of a straw-man fallacy, or, at least, of incompleteness. At first glance, it may appear that Plato’s Theory of Forms is used as a straw-depiction of utilitarianism, Kantianism, and other objective moral systems. Indeed, he acknowledges that few philosophers actually believe in the Forms. Nonetheless, as Mackie cites it, Plato’s theory is actually appropriately representative of those systems. He makes two implicit assumptions about objective moral theories: first, that if they are to have objective values, that these values must have an existence in reality as objects or relations have existence; second, that knowledge of such objective values compels the agent to comply. Seeing that, the actual shortcoming of Mackie’s argument is much more subtle: he is essentially claiming that all objective moral theories must possess these properties.

As will be seen, that is clearly not the case. While the following discussion can be construed as a debate resolved by clarifying definitions, the misinterpretation of definitions which Mackie does not clarify may lead to misinterpretations of the implications of his argument.

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The following is a summary and critique of J. L. Mackie’s “The Subjectivity of Values,” an absolute MUST-READ for anyone interested in ethics. As the professor who graded the original version of this adequately pointed out, I addressed the Mackie’s relativity argument but not so much the queerness argument.

In “The Subjectivity of Values,” a chapter in Ethics: Inventing Right and Wrong, J. L. Mackie develops his theory of “moral scepticism. ” In the first sentence, he states his thesis plainly: “there are no objective values. ” He goes on to fully define his position, by clarifying the sense in which he means it: that there do not exist in the world any such values. Though Mackie’s moral scepticism is a strong explanation for the failure of theories which posit values that are intrinsic features of the universe, such theories do not account for all theories which hold objective values; in short, not all objective theories are of the kind that Mackie describes and critiques. –more–>Initial Discussion

Mackie spends the first portion of the chapter emphasizing a critical set of distinctions to understand his argument: namely, that his theory is not a first-order (normative) form of subjectivism or scepticism, but a second-order (metaethically descriptive) one. For example, his position is not one of a moral skeptic who would argue that we ought to reject all conventional moral judgments (and thus make a positive, first-order statement about morality). Likewise, he is sure to distinguish between other second-order theses and his own. Subjectivist theories such as emotivism attempt to provide an explanation for what constitutes moral speech. An emotivist would argue that all moral speech is merely an instance of the speaker expressing his own attitude toward the subject (“stealing is wrong” means “boo for stealing! ”) In contrast, Mackie is simply describing the nature of normative statements and their respective ontological projections (or lack thereof). “Moral scepticism” is concerned with saying what does not exist, as opposed to what does; it is a negative, as opposed to a positive, doctrine.

Mackie does hold that there are clear factual descriptions of acts which we commonly ascribe to moral actions: “the present issue is with regard to the objectivity specifically of value, not with regard to the objectivity of those natural, factual differences on the basis of which differing values are assigned. ” In other words, kindness and cruelty can be described in totally non-normative terms; they simply are different classes of behavior to which moral values are commonly attached. However, value statements like “killing is wrong” are not propositional (true or false) like “three plus seven is ten” or “the earth is flat. ” The only exception is when there is an agreed upon standard of value (in a sense, an implicit transformation of a hypothetical imperative) for the subject of such a statement. For example, if it were agreed that a good ethics class is one which has a lecture on subjectivism and Hauptli’s ethics class did not have one, then the statement “Hauptli’s ethics class is good” has a truth-value (false). Morality can thus be derived from standards of evaluation, but Mackie argues that appealing to a standard of evaluation simply shifts the question posed by his scepticism to the standard.

The Arguments from Relativity and Queerness

After his introductory discussion, Mackie’s theory branches into two primary sections: the argument from relativity, and the argument from queerness. The argument from relativity begins from a point about the obvious historical variations in the content of moral beliefs across groups, classes, and societies. Of course, the presence of disagreement does not disprove the existence of objective value, just as disagreement does not disprove objective scientific facts.

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Even argued strictly in terms of Rawls’ theory, these observations about redistributive establishments demonstrate that the “pie” is heavily damaged by the presence of such institutions.

Some would argue that wealth redistribution and other forms of economic interventionism are institutions we need or ought to have, and that they can work if they are designed correctly or if the right people staff them. To some degree, that is true, but only in as much as it is true of all institutions and forms of government. If people of the appropriate mindset who possess the appropriate values are readily available, then almost any system of any values will not produce unbearable results. Small, Republican city-states of the kind that Rousseau so often praised are examples of such agreement between people and state. Nonetheless, this is an ambitious and unrealistic necessary precondition for any system, which is more than often faced with the reality of many people with many competing interests. The fact that so many brilliant minds are and have been ideologically committed to the construction of wealth-redistributive institutions, yet at the same time have not succeeded in designing comprehensive ones that have proven to be effective, sustainable, and cost-efficient, is testament to the fact that the inherent nature of such institutions conflicts with the inherent nature of humans and reality. Of course, by no means does this paper claim to be the last word: to do justice to Rawls’ Theory of Justice (no pun intended), a fuller exposition of Rawls’ potential counter-objections as well as greater clarification of the assumptions at play are required. Nevertheless, the essence of the argument stands that Rawls, as one of the most prominent supporters of the liberal welfare state, must address several problems- both theoretical and empirical- with his conception of justice.

Sources:

Rawls, John. 1971. A Theory of Justice. Harvard University Press (1999).

Nozick, Robert. 1974. Anarchy, State, and Utopia. Basic Books, Inc.

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[1] Some have argued with much vigor that government should do none of that (i. e. disappear altogether). Those arguments are beyond the scope of this paper.

[2] Nozick’s position in totality is much less linear, and much more difficult to summarize, than Rawls’. That is not to say that Rawls’ position is simpler or dumber, but just that his account is easier to capture briefly. My exposition of Nozick will thus be limited to his position vis-à-vis Rawls’ view on distributive justice.

[3] Evidence generally supporting my argument are nations with major government intervention and spending that have descended into massive debt. The United States is one such example. Also, most of the nations of Europe (notably France and Germany) are suffering from large debts and unfunded welfare liabilities which account for as much as 250% of GDP. Enumerating many specific institutional cases would be an interesting basis for further study of my assertions.

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” The difference between the two is clear: the former merely reflects the value-neutrality of natural outcomes, allowing one the right to individually benefit from them; the latter clearly describes a situation which normatively requires redress. It appears that Rawls- if he chooses to reject a person’s entitlement to the benefits of his own natural states- will be caught in between contradictorily ignoring individual merit and holding a view of humans as deterministic zombies.

Empirical issues?

Another major area of contention against the general idea of government-enforced “distributive justice” lies in the historical and expected performance of institutions manifesting those principles. [3] There is little doubt that humans are, at least generally, self-interested. Their admission into a government post does little to alter that fact: agents will always seek to maximize their own utility, which is for the most part only checked by externally-imposed penalties. As a point of clarification, self-interested activity need not be self-oriented; the defining feature of self-interest is the pursuit of one’s conception of the good, no matter what it is. Other-oriented behavior is still detrimental to the efficiency of operating a government post, so long as the objectives of an action are not functionally isomorphic with having an interest in the efficiency or proper operation of government (e. g. one gives preference to one’s family, or ethnic group, etc. Institutional design should ideally be aimed to create this isomorphism of personal to public interest, in the theoretical tradition of Madison, established in Federalist No. 51; though this may be the best solution, this does not mean that it is totally successful in absolute terms.

The operation of institutions to enforce justice in general is faced by many challenges. Simply dealing with the basics military, police, and courts is already a daunting task to do correctly. Even on the comparatively simple starting point of individual rights to life, liberty, and property, cases of conflicting obligation arise on a frequent basis, particularly in establishing “reasonable expectations” in cases where a contract was not explicitly written and signed. The incorporation of distributive justice into the system of obligations complicates it immensely. Now, those tasked with adjudicating disputes must appeal to a broader host of laws and guarantees, while adapting to the constraints of equality, scarce resources, and respecting Rawls’ first principle of justice.

The cost of oversight is borne by more institutional expenditure (bureaucracy to watch bureaucracy, which may require some oversight of its own) which ultimately is borne by the constituent public. Besides taxes, the individuals must be attentive to their tax dollars at work. End-state distributive justice, as in the case of adjudication, not only necessitates the creation of more laws and more bureaucracies to execute those laws, but requires more lawyers, advocates, lobbyists, action groups, and others of their kind. Essentially, an entire sector of labor and knowledge must be dedicated to navigating complex institutions instead of those resources being applied to more productive endeavors. Furthermore, for the average citizen, a greater level of education and attentiveness to current affairs is required to ensure that he is not being swindled by special interest groups via these institutions. The bottom line is that he must trade off work hours or leisure in order to protect his “investment” in the government. His alternative is that his tax dollars go to waste-a problem plaguing governments worldwide today.

On the flip side of the problem of Rawls ignoring individual merit is the issue of diminished incentives to produce. In a market setting, wealth redistribution can be construed as a subsidy (or a kind of de facto tax) on a particular kind of behavior, namely labor. Rawls cannot simply assume that individuals will work and produce as they would have before; with an expectation of a certain level of well-being, many recipients of welfare benefits will be far less likely to produce the value of the goods and services they are guaranteed. From their perspective, they possess an exogenous level of utility irrespective of their action (sans filing the correct forms). Not all of them will be dependent on government services for factors supposedly beyond their control. The presence of those institutions will have a distortionary effect on how wealth is generated in the economy.

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This coin is known as the maximin option, the uncertain game with the best worst outcome. In distributive justice, the maximin option would be the one in which the least advantaged, whoever it may be, will be guaranteed a certain payoff by society, whether it is in food, shelter, employment, healthcare, or education, at the expense of a higher payoff for others.

Rawls’ position is thus unique, in that he constructs it from no particular conception of the good except that of respecting individual autonomy at the inception of political principles. Unlike most advocates of distributive justice, he does not conclude his principles from some objective conception of the good, but only from a rational contractarian decision by agents to properly define the rules of social cooperation.

Objections a la Nozick and me

In opposition to Rawls, Nozick questions the validity of defining justice as some pattern of holdings- a material end-state. He holds that any theory of justice must either be end-result or historical, and either patterned or unpatterned. Nozick’s “entitlement” theory is historical and unpatterned; in short, a just distribution of wealth does not require any correspondence to some pattern (moral merit, need, etc. but merely the appropriate history of how it was acquired. Nozick thus emphasizes the importance of “justice in acquisition” and “justice in transfer,” as opposed to “justice in holdings,” an important concept in the thought of the economic left.

Central to Nozick’s objections to Rawls is his assertion that liberty inevitably disrupts patterned holdings. An important part of ownership is the freedom to transfer things to others. This means that any given distribution, after it is allocated, will be immediately changed so long as individuals choose to freely exchange their possessions. In order for a principle of patterned distributive justice to be consistent, it must always be applied; thus, the only means of guaranteeing any specific distribution is by constant interference in the economy or the abolition of free individual exchange. In light of that, Nozick observes the alienation from the source of wealth caused by patterned distribution principles. Wealth is implicitly taken as a given thing to be divided, when, in fact, how it is divided affects how much wealth there will be over time.

Rawls’ general process of justification for welfare merits interpretation and criticism. The original position (OP) is flawed as an accurate representation of the frame in which valid principles of government, if there are any which do exist, should be determined. Assuming a group has no choice but to endure conditions in the OP as set forth by Rawls, their strategy makes sense. Discussing the OP from a different angle yields additional insight into its nature. With a specific focus on those issues of justice relating to property, we can reformulate the OP as a new thought experiment, in this manner: our world as we know it- with the rich and poor, the talented and untalented, etc. must have a “Rawlsian original position” convention in order to determine the proper principles of justice. In order to do so, everyone must leave his actual person and move behind the veil of ignorance. Thus, an agent whose actual person is rich by talent and hard work will be unaware of his actual status, and, in accordance with his rational interest in the original position, will have no choice but to accept the maximin set of rules and unwittingly sacrifice his wealth.

To implicitly reiterate this formulation, Nozick cites an example of students taking an examination who decide to go to the original position to determine what the criteria for grading the test should be. Each party in this contract will seek to secure the best arrangement for himself. The maximin option will likely entail that what will not be chosen is a policy based on what students earn through their performances.

This exposes a pair of critical observations about Rawls’ argument: first, that it depends on the notion that gains from differences in nature are “unfair,” “undeserved,” or “morally arbitrary”; second, that individual merit (such as choosing to work hard to develop one’s talents instead of lazily watching television) is not relevant. His argument shifts from one position which (reasonably) says that “deserved” is not a valid descriptor of natural endowments, to another that holds that those endowments are explicitly “undeserved.

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” One essential implication in this statement is that institutionally, the course of action we should take (as constrained by the equality principle) is an empirical question. If general property rights, freedom of association, and other facets of laissez-faire capitalism most frequently lead to material inequality compared to centrally planned production, yet produce a level of output that makes everyone better off, then they ought to be instituted.

The Original Position

He arrives at his principles of justice by creating a thought experiment, the “original position,” from which he derives his notion of “justice as fairness. ” Before doing so, he establishes two primary premises. The first is a constraint of social unity; the freedom and equality of citizens must be respected. The second pertains to the fact that there always exists a plurality of conceptions of the good; these include one’s fundamental beliefs, values, projects, personal loyalties, and so forth. Because of these underlying necessities, Rawls holds a contractualist position in order to create a theory of justice which does not depend on any of those conceptions, but one with which free and equal citizens could be expected to reasonably agree. The establishment of a contract (a consensual agreement) would be the only way of respecting the autonomy of individuals totally, while at the same time providing a framework for universal governance. For a simple example, a comprehensive moral doctrine such as utilitarianism (“always act in such a way that leads to the greatest happiness”) would not, in Rawls’ view, be used as a starting point from which societal institutions would be designed, because one can always reasonably disagree with such a doctrine. Instead, the principles of justice would be determined by the hypothetical rational agreement in what Rawls argues to be the fair conditions of the original position (hence “justice as fairness”).

The original position has several necessary characteristics to achieve Rawls’ conclusions about justice. Firstly, he defines the participants, positing rational agents, who, in the negotiation, seek the guarantee of rights and resources to pursue their individual conceptions of the good, reflect on them and change them, and apply them. These assumptions are responsible for traditional liberal institutions (rights) of “freedom of conscience”: freedom of speech, press, religion, etc. Likewise, they are partially explanatory of common, universally accessible public resources: free primary schooling, public libraries, universities, etc. Secondly, he delineates the critical constraints: the finality of the contract, and most importantly, the “veil of ignorance. ” Those participating in the original position have no knowledge of what their natural endowment, their place in society, or their conception of the good will be, but they will have general knowledge of how the world works and expect moderate scarcity of resources. The purpose of the veil of ignorance is to prevent these self-interested agents from supporting principles of justice that are biased in favor of their characteristics, instead forcing them to adopt universalizable principles. They will not know who they will be when they enter society (rich or poor, utilitarian or Kantian, etc. and thus any preferential policy which they advocate in the original position is equally likely (from their perspective) to be to their benefit as their detriment.

Rawls on Wealth Distribution

This leads to Rawls’ position on wealth redistribution. Its primary cause extends from the condition of utility maximization in the context of a lack of information about the distribution of outcomes. In effect, Rawls is appealing to the choices rational economic actors ought to make in the face of uncertainty. Imagine the following example of choice relating to uncertain outcomes. Someone must choose between two different coin-flip games: in one, the heads payoff is $5000, and the tails payoff is $0; in the other, the heads payoff is $2000, and the tails payoff is $1000. The coin is being flipped by a well-known trickster, who is reputable for his pleasure in biasing coins to any possible distribution. The player is aware of this, and thus does not know the probability that either heads or tails will occur on the coin, entailing a situation of total uncertainty. By Rawls’ (and standard game theoretic) reasoning, the player’s rational choice would be to choose the $2000-or-$1000 coin, in effect maximizing the outcome of the worst-case scenario.

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