Do machines have moral responsibility?
A number of scientists have been in a philosophical mood lately, and some have decided to fix their
attention on the ancient problem of free will: Do we really have deep freedom to determine our choices and actions, or are we automata (machines) whose thoughts and actions are fully determined by physical laws? Recent scientific discoveries show new details of what kinds of automata we might be. These discoveries are not exactly shocking, since scientists and philosophers have already spent centuries working out what it means to be both a person and an automaton. But the “new” determinists, which include popular authors Sam Harris and Jerry Coyne, argue for major changes in our social and moral understanding based on the alleged logical implications of determinism.
In this post, I summarize some of their arguments along with major problems I see in them. In short, my view is that we cannot dispose of guilt without also disposing of innocence. While I agree with the conclusion that we should seek more empathic approaches to retributive punishment, we cannot entirely dispose of retributive ideas. And whatever we conclude about morality, justice and punishment, it should probably not be deduced from metaphysics.
As a gesture of intellectual modesty, I’ll note that I’m not a professional philosopher; I took a number of university courses on philosophy, including several that covered ethics, meta-ethics, free will, mind and language. I’m still very interested in these subjects, and here are some of my personal thoughts.
Since this is a long post, I’m providing a table of contents:
- Determinism, Punishment and Moral Responsibility
- Moral Frameworks
- Unpleasant Implications
- Case examples
- A case for Harsher Punishments?
- Metaphysics of Morals
- References
- Notes
In a nutshell, the new determinists argue that retributive punishments are unjustifiable, since criminals do not really have free will to determine their actions. Instead, punishments should be based solely on the need for social protection or deterrence of future offenses. In building their case against retribution, they reject the concept that anything can be deserved — criminals don’t deserve their punishments, successful investors don’t deserve their profits, loving parents don’t deserve gratitude.
What I see as a major problem in the hard determinists’ argument is that it implies innocent people don’t deserve to go unpunished, victims don’t deserve to be compensated for their suffering, and so on. You can’t dispose of guilt without also disposing of innocence. Both are retributive concepts that express what we do or do not deserve based on an alleged state of moral responsibility. I believe these are counter intuitive and undesirable conclusions. There are also many situations in which the consequences of determinism seem to be undecidable.
Several of the new determinists are scientists who dismiss or downplay the philosophical discourse that is already in place on the subject. In answer to the 2014 Edge question, “What scientific idea is ready for retirement,” scientist Bruce Hood proposed we should drop the concept of “the free-willing self”:
[The self] is neither scientific nor is this the first time that the concept has been dismissed for lacking empirical support. The self did not have to be discovered as it is the default assumption that most of us experience, so it was not really revealed by methods of scientific enquiry…. It is an illusion because it feels so real, but that experience is not what it seems. The same is true for free will. Although we can experience the mental anguish of making a decision, our free will cannot be some kind of King Solomon in our mind weighing up the pros and cons as this would present the problem of logical infinite regress (who is inside their head and so on?). The choices and decisions we make are based on situations that impose on us. We do not have the free will to choose the experiences that have shaped our decisions.
Hood is trying to make a scientific statement — the “the self” is a problematic or inappropriate concept for theories that predict human behavior — but he stumbles into the ancient free-will conundrum which crosses into the philosophical domain of direct conscious experience. The relevant questions at this level are not simply those of predictive or descriptive science. They are questions of decision: how should I live my life, and how should people be treated?
The real issue isn’t determinism itself. What the new determinists are really talking about is the nature of justice and moral responsibility: Is the concept of moral responsibility compatible with a mechanistic universe? There are two camps: “compatibilists” generally accept determinism, but claim that without much impact on morality and justice. “Incompatibilists” claim that determinism is irreconcilable with certain moral intuitions (especially retributive punishment). The professional discourse on this subject is very well introduced by the Stanford Encyclopedia of Philosophy, with excellent articles on both compatibilism and incompatibilist theories, as well as a nice overview of incompatibilist arguments. There is a long-standing discourse here, which some new determinists dismiss as disingenuous; Coyne, for example, has compared compatibilism to theology and creationism, and says this:
When I saw [an article by Dan Dennett on free will], I realized that what many compatibilists feel is this: science has nothing to say about free will. I think this is because their argument is basically semantic, involving various definitions of “free will”; and sometimes, like Dennett in this article, they don’t even bother to define it. I don’t think they realize that their denigration of scientific studies of free will comes from their feeling that the issue is one that can be resolved only through philosophy. And so they are committed to criticizing every scientific study that undermines traditional notions of free will. Why bother? As I’ll show below, this is one of many ways that compatibilism resembles Sophisticated Theology™: both areas denigrate science as being incapable of resolving the Big Question.
Arguments like this are misdirected. The real issue isn’t whether we are ultimately mechanistic beings who operate according to physical laws. The real issue is moral responsibility. Professional philosophers like Dennett are highly sensitive to the implications the debate has for moral and political theory. The compatibilists’ position is that moral responsibility should not be reductive to these kinds of metaphysical puzzles or semantic games (and to a certain extent the whole topic is a semantic game). To me, the incompatibilist position is akin to a claim that Anselm’s Ontological Argument for God should have some relevance to how I manage my finances; the level of abstraction is unnecessary and unhelpful. The onlological argument also seems deeply flawed and unpersuasive, although it’s challenging to articulate precisely where and why it fails, since it exploits some very abstract semantics.
Given the central importance of morality and justice in the determinists’ arguments, it seems strange that they typically avoid articulating complete theories of morality and justice. Instead their arguments focus on pinpoint issues in the morality of punishment. But we can’t chart out the full implications of their claims without considering a complete moral picture. In this post, I’ll consider three thumbnail sketches of moral theory (by no means an exhaustive list):
- Consequentialism — Moral theories based on outcomes. They include utilitarian ethics. These theories may place varying weight on intended vs actual consequences, and may evaluate preferred outcomes in different ways. As explained by Mr. Spock, “The needs of the many outweigh the needs of the few or one.”
- Respect for Persons — Theories based on the inviolable rights of individuals. Actions must be restrained by moral limits, regardless of consequences. As a representative for this category I will appeal to the means-test, “all persons should be treated as ends-in-themselves and never as a means to some other end.” This theory is probably the most common answer to Mr. Spock, and is often invoked as a defense of minority or individual interests.
- Social Contract — Theories based on entitlements and punishments, incentives and penalties. They vary widely in their criteria for justifying or rejecting particular social rules, power relationships, etc.
The background context of moral theory has a major contribution to how we approach the problem of free will. If we adopt a strict consequentialist theory, for example, then there is already no concept of “blame” or past-tense moral responsibility, hence there is no point in contemplating determinism. If we adopt a theory based on respect for persons, then the means test excludes punishment for the purpose of deterrence, since it uses a person as an instrument (as a means) for social control. Retributive thinking gives the possibility for a narrow exception to the means test: a person can be used as an instrument for deterrence if they deserve to be punished.
If we adopt a social contract view of moral responsibility, then a person “deserves” something precisely because it is established in the contract. Retributive attitudes are often expressed using the language of debt, as in “paying your debt to society.” The contract model is inherently retributive: if you choose to violate a contract, then you incur a penalty. In many cases we feel it is unfair to incur penalties if we could not avoid the violation. If someone steals my identity and obtains a large loan, I should not be liable for that contract. If a bank employee intercepts my mortgage payments, then it would be unfair to foreclose on my home — I don’t deserve to be evicted, or I deserve compensation for the eviction. If the determinists are right, then the outcome should only be determined by social benefits, and the calculus of social utility is not guaranteed to fall in my favor.
The American justice system relies heavily on contract theories and retributive thinking. While retribution is distinct from vengeance, it is still true that retributive punishment can be completely arbitrary and vindictive. Compared to light sanctions, severe punishments may add little marginal value in terms of deterrence, protection or rehabilitation. So I think the incompatibilists have valid points with regard to the logic of punishment. But this point doesn’t have to be made through metaphysical contortions. There is a well established discourse (see here and here) on the ethics of retributive punishment that does not require the metaphysics of free will, and which seems virtually untouched by the incompatibilists’ writing on the subject.
When interpreted as moral philosophy, the incompatibilist arguments sound like an argument by contradiction against the respect-for-persons theory, since this theory is closely tied to the concept of desert. Consequentialism seems to be the presumed moral framework in Sam Harris’s pop-philosophy treatise Free Will. Consequentialism comes with a host of its own problems. To name just a few, there are the problems of correctly forecasting consequences, of discriminating desirable from undesirable consequences, of choosing the preferred level of consequences (short term or distant future?), of imposing punishments based on intended vs actual consequences, and of assigning social roles for those who will assess consequences and dictate social preferences. These problems seem to lie at the heart of a recent exchange between Sam Harris and Noam Chomsky. In part of this exchange, the two argued the morality of particular military action taken by US forces in Yemen. Harris argued that the US administration was justified based on a theory of intended consequences:
Take the bombing of the Al-Shifa pharmaceuticals plant: according to Chomsky, the atrocity of September 11 pales in comparison with that perpetrated by the Clinton administration in August 1998. But let us now ask some very basic questions that Chomsky seems to have neglected to ask himself: What did the U.S. government think it was doing when it sent cruise missiles into Sudan? Destroying a chemical weapons site used by Al Qaeda. Did the Clinton administration intend to bring about the deaths of thousands of Sudanese children? No. Was our goal to kill as many Sudanese as we could? No. Were we trying to kill anyone at all? Not unless we thought members of Al Qaeda would be at the Al-Shifa facility in the middle of the night. Asking these questions about Osama bin Laden and the nineteen hijackers puts us in a different moral universe entirely.
Of course one could argue that justification-by-intention promotes negligent ignorance of consequences. Chomksy’s reply could be read as a mixture of the negligence argument combined with the means-test. He cites a passage of his previous writing from Radical Priorities (2003) [emphasis added]:
Most commentary on the Sudan bombing keeps to the question of whether the plant was believed to produce chemical weapons; true or false, that has no bearing on “the magnitude with which the aggression interfered with key values in the society attacked,” such as survival. Others point out that the killings were unintended, as are many of the atrocities we rightly denounce. In this case, we can hardly doubt that the likely human consequences were understood by US planners. The acts can be excused, then, only on the Hegelian assumption that Africans are “mere things,” whose lives have “no value,” an attitude that accords with practice in ways that are not overlooked among the victims, who may draw their own conclusions about the “moral orthodoxy of the West.”
Comsky continued in a later email [emphasis again added]:
So let’s face it directly. Clinton bombed al-Shifa in reaction to the Embassy bombings, having discovered no credible evidence in the brief interim of course, and knowing full well that there would be enormous casualties. Apologists may appeal to undetectable humanitarian intentions, but the fact is that the bombing was taken in exactly the way I described in the earlier publication which dealt the question of intentions in this case, the question that you claimed falsely that I ignored: to repeat, it just didn’t matter if lots of people are killed in a poor African country, just as we don’t care if we kill ants when we walk down the street. On moral grounds, that is arguably even worse than murder, which at least recognizes that the victim is human.
Here Chomsky has made a compelling argument based on respect for persons. Since Harris appears to be a strict consequentialist, the argument seems to have no impact. On Harris’ side is the question as to whether the US administration is morally responsible for the lives lost. On the other side is the straightforward argument that the people being bombed deserve to live, or at least to be accounted as more than mere collateral damage.
If we admit the incompatibilists’ thesis that no one deserves anything, we could embrace their conclusion that punishment should be no more severe than is required to achieve a desired deterrent effect. But by eliminating the concept of just desert, more problems are created than solved. For example, most of us have the intuition that an innocent person doesn’t deserve to be punished. If our punishments are motivated only by their impact on deterrence, then it is potentially acceptable to punish an innocent person. Innocence is a retributive concept, because it recognizes that only the guilty are eligible to be punished. If I say that it’s wrong to punish a person who has committed no offense, then it must conversely be right or at least permissible to punish a person who has committed an offense. The sole distinction is whether the person actually committed some offense — is the person guilty?
This problem is quite well known in the discourse on justice and punishment. The Stanford Encyclopedia of Philosophy contains a lengthy entry on legal punishment which says (among many things) the following (references removed):
The most familiar objections to consequentialist penal theories are objections to purely consequentialist theories which hold that only the consequences are relevant to question of justification. For, critics argue, quite apart from the difficult question of whether punishment is or could be a cost-effective way of securing its intended benefits, consequentialists would have to regard manifestly unjust punishments (the punishment of those known to be innocent, for instance, or excessively harsh punishment of the guilty) to be in principle justified if they would efficiently serve the aim of crime prevention: but such punishments would be wrong, just because they would be unjust.
In fact, innocents are punished frequently in our justice system, most of us are aware of it, and most of us are only passively concerned about the suffering of exonerated prisoners, since we have no direct experience of that suffering, and it happens to a sufficiently small number of persons that we tend to think of them as collateral damage. There are a few instances that catch public attention, but in aggregate there may be negligible social cost to punishing innocent persons, and there may be arguable benefits to tolerating these cases. Consequentialists often respond that the public would never tolerate such a system, but the proof is all around us.
We also typically have the intuition that crimes should be uniformly and equitably enforced. If a crime is rarely enforced, then it seems unjust to “make examples” of a small number of people who may receive heavy penalties while the majority of offenders go free. But if it turns out that sporadic punishment is equally as effective as uniform punishment, then sporadic punishments should be preferred because there is less total suffering (and less total cost for administering justice).
Many of us have the intuition that victims should be compensated for their suffering. If we do away with the concept of just desert, then victims don’t deserve compensation. Hypothetically speaking, if it were discovered that victim compensation interferes with deterrence (e.g. because offenders can more easily rationalize their crimes), then they should definitely not be compensated. This includes exonerated prisoners, since they don’t deserve any special compensation, at least not more than another comparably disadvantaged person. It should be sufficient to deliver them into whatever social programs are available for the general public and let them stand in line with everyone else.
We further have the intuition that punishment should be designed to deter the specific offense in question. It is possible, however, that punishments can be leveraged to deter actions other than the specific offense, or could be used to deter something that is legally permitted but frowned upon by the authorities.
The practice of asset forfeitures provides an example of all these issues simultaneously. In the US, a person’s assets (usually cash, vehicles or a home) can be seized without any formal criminal charge, if law enforcement claims a suspicion that the assets are related to drugs or other organized crime. This is a punishment: it is a burden or penalty intended to deter criminal activity. Victims of forfeiture are often innocent of any crime; in some cases the crime is committed by a family member, in other cases there is no demonstrated crime at all. Forfeitures are applied seemingly at random, with some people losing millions while most are unaffected. They are applied more heavily against certain racial groups and social classes. They can be used to cross-subsidize enforcement activities unrelated to the forfeiture. They are opposed by 70% of the U.S. public, but the practice continues; the social consequences of this policy are evidently determined by some privileged caste of lawmakers and lobbyists whose informed preferences outweigh those of the lay public.
According to my interpretation of the determinists’ position, there is no case to make against asset forfeitures, unless it is determined that they are ineffective in deterring crime. Since people don’t deserve their wealth, they can’t make any moral claim for compensation. The evaluation of consequences should properly be left to experts in law enforcement and government, since the general public is not equipped to weigh in on such technical scientific questions, therefore the poll data is irrelevant. The racial profiling ought to be acceptable if it is found that those populations have a higher rate of participation in organized crime.
It seems to me that these are the conclusions we must reach if we accept determinist consequentialism and reject any notions of individual guilt, innocence or desert.
In this section I offer a few case examples for which I think the incompatibilist stance gives either counter intuitive conclusions or is ambiguous in its conclusions. These examples are based on real events (some are direct reports of real events).
1. RIAA and MPAA demand action to deter illegal media sharing on the internet. Among tens of millions of offenders, only a few legal actions are taken. One is against a woman who did not directly participate in file sharing. Prosecutors argue that she was responsible for her child’s illegal activities. She is fined several million dollars for the offenses and receives a jail sentence. After her case is concluded, the media industries abandon their pursuit of individuals, making her one of a small number of “examples”. She doesn’t deserve this punishment, but it is the right thing to do if it creates a measurable deterrent (let’s suppose it does). Even though many millions of people casually participated in illegal file sharing, it is acceptable to harshly punish one solitary individual for the greater good. There is negligible aggregate social harm when punishing a single person, but potentially measurable benefits. [See note 1].
2. A man is convicted of homosexual acts and given the option to choose chemical castration. He is permanently damaged, physiologically and psychologically. His name is permanently entered into a sex offender registry, and he is limited in where he is permitted to live and work. Some years later, social attitudes change and his orientation becomes both legal and acceptable in his home country. Society has become more just over the years, but this particular individual deserves no special compensation for how he was treated. Going forward, no one else will have to suffer in this way for their sexual orientation, and that should be enough resolution. [See note 2]
3. Two men are returning home from a legal poker tournament carrying their substantial winnings in a suitcase. After crossing a state border, they are stopped for speeding. The officer claims probable cause to search their vehicle, finds the poker winnings, and confiscates it. We are told the money will be used for highly noble purposes. The two men do not deserve their winnings, perhaps especially since the cash was acquired from games of chance. They are just supremely unlucky. [Based on a real case]
4. Perhaps a better forfeiture case: a young man is traveling with a large amount of cash, and is pulled over. He has several strikes against him: a suspended license, a prior DWI conviction, and the officer believes his car smells like narcotics. A police dog also identifies the scent of narcotics. The man claims his money is intended to purchase farm equipment. Since he is unable to prove he has not transported drugs or that the money is not profit from their sale, his money is confiscated and used to fund police investigations. Under the determinists’ arguments, he does not deserve his wealth, regardless of how it was earned. Forfeitures affect a very small number of people, so the associated suffering is minimal. The police operations are vital and improve the safety and well being of a larger number of people, therefore the forfeitures are justified and the young man is not entitled to be compensated in any way. [Based on another real case]
5. At Popehat, Ken White recently described scenarios related to law enforcement, punishment, and compensation. In one of these scenarios, a young man is caught smoking pot and arrested. He is held in handcuffs, locked in a room, and forgotten for five days. The man received $4.1M in compensation (which he did not deserve), and the officers involved received very light sanctions (they do not, after all, deserve to be punished). White seems to be upset that police officers receive unequal consequences for their offenses, writing,
If I seize someone, handcuff them, lock them in a room, and leave them to die, I will suffer severe consequences. I will lose my job, especially if I acted while performing my duties. I will go to jail. I will suffer catastrophic personal financial losses. My name will be broadcast far and wide.
White is evidently upset that these light sanctions will not deter future offenses by state agents, and that the punishments received by state agents are unequal to those received by ordinary citizens if they perpetrated the same actions. A police advocate might argue that we shouldn’t deter state agents from aggressively executing their duties, even when they make mistakes, since this could reduce their efficacy in protecting the general public from offenders. In addition, one could argue that the victim in this case should not be compensated, as there is a very small societal consequence for his suffering. He is an unlucky casualty in the fight for social order. We should try to minimize the chance that this kind of event will recur in the future, but this young man does not deserve any special compensation for his personal suffering. There are lots of suffering people out there, and he can get in line for the same social services available to everyone else.
New determinists like Harris and Coyne argue that if we eliminate the concept of desert, then we should necessarily reduce the severity of punishments. Coyne is a particularly strong advocate against using the death penalty. He has argued that all criminals are brain damaged in some sense, has opposed the death penalty for Dzokhar Tsarnaev, and has written a number of editorials on the topic. The case for lighter punishments is not self evident. It could be argued, for instance, that the cost of incarceration exceeds the benefit of keeping offenders alive. If the same resources were allocated to social programs, then we could likely achieve a much higher benefit in terms of reduced suffering and lives saved. If killing one anti-social murder can free up resources to provide food and medical care to children, potentially saving numerous lives, then why shouldn’t we proceed with the death penalty?
A second argument can be made from the marginal benefits of harsh punishment. Coyne has argued that the death penalty has a small contribution to deterrence of murder, compared to incarceration. But how small does the marginal effect need to be in order to make it justified? If it were found that by a single execution we could deter two murders, would Coyne change his mind? I’m guessing not, because I suspect that his belief is rooted in something more than an estimation of social consequences.
I agree with many of Coyne’s conclusions about the death penalty and harsh punishment. I think he’s right that many (perhaps all) criminals have no ultimate, deep choice in their criminal behavior. Many are affected by their social circumstances, inadequate upbringing or a lack of socially acceptable options, and we should be empathetic toward them. But I believe these things for reasons that are ultimately retributivist. My own position is adequately summarized by these lines from the Stanford Encyclopedia:
A ‘negative’ retributivist insists that we must not punish the innocent, or punish the guilty more than their crimes warrant: this does not imply that we ought to punish the guilty; it implies only that we may punish the guilty, if we have other good (presumably consequentialist) reasons to do so.
There’s plenty of room to discuss whether or how much we punish a person, and for what specific reasons, without having to abandon the concept of moral responsibility.
I’m now going to reverse Coyne’s gambit and propose that determinists are more similar to theologians than compatibilists are. Like many theologians, determinists argue that the logic of moral responsibility is built on a metaphysical foundation. But I would argue morality doesn’t arise from the structure of the universe, it arises from a dialectic process in which we collectively balance our instincts and desires, our intuitions about fairness and justice, our empathy, and our desire for logical consistency. Metaphysical determinism provides a good argument for empathy toward those who are guilty, but it is not enough to invalidate the concepts of guilt and innocence. We should not be too eager to overturn social conventions that are integral to real institutions and relationships.
I personally don’t think it’s possible to construct a complete account of morality without combined consideration of consequences, respect for persons, and social contract intuitions. I don’t think every moral scenario has an obvious, objective answer, or that it will be obvious to deduce which moral theory gives the most right answer in any particular case. Moral reasoning is often frustratingly under decided. The same is true, I think, of the tension between determinism and moral responsibility. A person’s state of blame is a real, legitimate concept, just like a person’s state of mental competency or sobriety or ignorance. It’s hard to pin down exact meanings for these concepts. They induce fuzzy boundaries, but that doesn’t mean they are empty terms.
Philosopher Saul Smilanski has argued for a synthesis of determinist and compatibilist insights. Smilanski believes that these two positions are applicable in different contexts, at different levels of moral judgement. Part of Smilanksi’s motivation is to retain respect for persons in a deterministic world [1]:
Although we recognize the partial truth of hard determinism (and the limitations of compatibilism), we can see that, nevertheless, there is no reason to put the bar of free will and moral responsibility as high as hard determinists do. Even in a determined world, most people most of the time have the ability to live morally responsible lives, compatibilist distinctions matter, and establishing a Community of Responsibility, and more broadly, the Appreciation of Agency are vital for respect for persons and the good life. It is possible, and personally and socially desirable, to continue to live, by and large, with the ideas of free will and moral responsibility. As we saw, except at the (mostly pathological) margins, human life is fundamentally a life of responsibility. We experience ourselves as choosers, we hold ourselves responsible—and we expect others to behave responsibly toward us. When they do not so behave, and lack a plausible excuse, most people reasonably express the relevant emotions, such as resentment and indignation. I suspect that few if any hard determinists can really live according to their beliefs, when they educate their children, or even choose a babysitter for them. Virtue, trust and gratitude are inherently related to the idea of being a responsible human being, who takes responsibility for his or her actions. Either distinctions about control, moral responsibility, desert, blame and praise and so on are still being made but are merely being called something else, or we are dealing with something very different from normal human life, something that no one should seek, let alone relish.
I’ll leave this as my sole academic reference for this post. I’m recently very taken with Smilanski’s work, as it recognizes the apparent undecidability of this topic, where several sides have some valid points, but no one quite seems to have a fully adequate account. The hard metaphysical questions will probably never be resolved, but we can nevertheless recognize progress (moral, social, scientific and philosophical) without resorting to grand foundational theories or reductive arguments.
[1] Smilanski, S., “Free Will and Moral Responsibility: The Trap, the Appreciation of Agency, and the Bubble”, J Ethics, 16:211–239, 2012.
1. This example is based on the case against Jammie Thomas-Rasset. From Wikipedia:
[This] was the first file-sharingcopyright infringementlawsuit in the United States brought by major record labels to be tried before a jury. After declining a settlement offer of $5,000, the defendant, Jammie Thomas-Rasset, was found liable in a 2007 trial for infringing copyright on 24 songs and ordered to pay $222,000 in statutory damages.The defense argued that Thomas-Rasset had no reason to download music, as she was one of the plaintiffs’ best customers, having legally purchased over 200 CDs, including many of the songs at issue, which she only ever ripped into WMA format, not MP3 as found in the shared folder. On the stand, Thomas-Rasset speculated that maybe her kids or then-boyfriend had installed used Kazaa on her computer without her knowledge. Closing arguments focused on the fact that none of the evidence pointed to Thomas-Rasset personally, only to the IP address assigned to her Internet account.
2. This case is based on that of Alan Turing, who tragically committed suicide decades ago and received a posthumous apology (which i suppose was undeserved) in 2013. Some have called for his family to be awarded monetary compensation for Turing’s suffering.
Fair Coin Toss 