Proposed Failures of Utility Theory

There have been many claims made throughout history that utility and expected utility theory do not accurately formalize human decision making, partially due to the beliefs that utility theory assumes rationality and that humans are not always rational.

To begin examining these claims, we must first establish a set definition of rationality. According to Wikipedia,  a rational decision is not just one that is reasoned, but one that is optimal for solving a problem, or achieving a goal. Thus, whether a decision is rational or not ultimately depends on the nature of the situation.  A rational decision in one case may be an irrational one in another case. Also, not only does the definition of a rational decision change with the problem being solved, but also with the individual. Since a rational decision is one that maximizes utility, and since everyone's utility function is assumed to be largely unique, a supposedly rational decision for one person to make in a specific situation may be irrational for another person in that same situation.

But something interesting arises from this conception. If the rationality of a decision depends on the individual's utility function, and everyone's utility function is unique, does this not imply that we, as outside observers, can never pass judgment of rationality or irrationality on another individual's decisions?

By this very definition of rationality, I contest that it is impossible for any failures of utility theory ever to occur. A failure of utility theory would imply that an individual was unable to maximize his expected utility through reasoned decision making, but, by definition, the only person who can really know if he has maximized his utility is the individual, since his utility function is specific to him.

But then, how do we explain individuals regretting their decisions, or being otherwise unhappy with the choices that they have made? The answer has to do with foresight and incomplete information. I contest that each individual makes the best decisions for himself 100% of the time, given the data and forward looking ability that he has available to him at that current moment. The maximization of a shorter term utility function can lead to very different actions than the maximization of a longer term utility function, and likewise for varying sets of information.

One common scenario often depicted involves expected value experiments, in which, for example, a person could either take $50 outright, or play a 50-50 chance game where he could possibly win, say $120, or walk away with nothing. The conclusion often found is that most people will choose to take the $50 straight up instead of playing the game. This is worth a thought, since the expected value of the wager is $60, and it is thus superior to the first choice in terms of pure monetary value. However, interpreting the results in this way places a very narrow conception on the idea of utility. Utility doesn't just base itself on the total amount of profit received. It also has to do with the stress levels associated with possibly losing a wager, with the lingering doubt that the wager is even fair, etc. All these factors have different weights on them depending on the individual, so all that the experiment ultimately shows is that more people have utility functions of a form that places higher weight on the dis-utility of experiencing the stress and uncertainty inherent in a wager.

Another fault that people often find with utility theory is that it cannot account for human unselfishness. These arguments are equally unfounded, and for mainly the same reason. I believe this is again not so much a failure of the utility model, as it is a failure of extending the concept of utility far enough into the future. 

For instance, the example of parents taking care of children is often cited an infallible demonstration of good will. It can be argued that the reason parents care for their children is because children could potentially provide them with certain benefits in the future, such as money if they're successful, or simply by taking care of them when they're older. Another way to think about it is that not taking care of one's children results in serious negative consequences, consequences that far outweigh the hardships of raising them. In this sense, I believe every altruistic action that humans are capable of can be argued to ultimately be for utility maximization purposes. It's only a matter of how far into the future that we would like to consider. Another often cited example is donating to charity. Is this not completely altruistic? Not quite. Upon closer consideration, we can see that there is something in an individual's utility function that causes him to want to donate. He may derive some form of happiness from giving to others, or fulfill some moral obligation that would otherwise nag at him incessantly.

Thus, this individual doesn't donate to charity for the sake of doing something selfless, but because it either makes him feel better, gives him peace of mind, etc. Consequently, I believe any action can be boiled down to these "selfish" incentives, and I do not think there is anything morally wrong with that. We are simply wired to make decisions based on introspection and self-involvement. It is what has worked best for our species for many generations and is clearly the method of survival heretofore chosen by evolution.

The Political Economy of War

Before beginning an examination of the political economy of war, it is important to understand that combat decisions are made not by entire nations, but only by a handful of key influential agents within those nations. In constructing an incentive model for these agents, it is helpful to think about it in terms of the maximization of not only a personal utility function, but also a national utility function, which is composed of the aggregate personal utilities of all that nation’s constituents and which affects and is affected by that agent’s personal utility function.
 
The stages of a war can roughly be broken down into an opening, a middle play, and the endgame. The opening is characterized, at least in the United States, by multiple cases that could occur between Congress and the president, cases that are naturally constrained by the design of the United States governmental system and Constitution. A model can be constructed to provide a common framework for thinking about all these cases, a model that utilizes the concept of how pro-war or anti-war the preferences of the president and median Congress member are.
 
The middle play centers on the fact that nations will continue to do battle against one another until they can be no better off. This can be modeled with a simple expected costs and benefits model that a nation attempts to equate with 0. An equilibrium is eventually established when all nations equate this model with 0 and the war ends.
 
The endgame revolves around peace treaties, and a simple model of expected costs and benefits can be modeled to establish this game as well. Depending on the outcome of a war, the United States may experience substantial changes to its leadership and way of life due to the backlash of a dissatisfied electorate, or the spoils of war that have been acquired.
 
Multiple works have been written that examine many of the same concepts presented in this paper. We relate to some of them within the main text.
 
Political Economy of War

The political economy of warfare is a rich topic of study for many reasons. First, it helps one to get to the very heart of why it is that nations choose to engage in an activity that would at first glance seem so destructive for all parties involved (and even some that are not involved). It also helps us to understand what the political and economic consequences are, both inter and intra-nationally, of conducting war. The popular expression goes: “Why can’t we all just get along?” Hopefully the methodologies of political economy will be able to shed some light on this age old question, and possibly also illuminate ways in which warfare can practically be avoided in the future.

In discussing these issues, we will choose to focus almost exclusively on the political structure of the United States in order to more effectively get to the meat of the matter, rather than risk getting bogged down in the details of other political structures. It can be found by the reader, however, that the concepts presented here should be robust to creative extension to other systems of governance.

It would probably be most logical to begin the discussion by examining what causes nations to begin engaging in war. To facilitate this examination, we should probably refresh ourselves on how the United States in particular politically authorizes wars within its system. According to the U.S. Constitution, the power to deploy the army to engage in warfare is split between the executive and the legislative branches. Congress has the power to declare war and raise/support the military. The president, however, as commander-in-chief, has the power to repel attacks against the United States, or otherwise act in situations where quick decisions are essential for homeland security. He also has the power to sign or veto Congress’ declarations of war. This veto can then be overridden by a 2/3 vote in both the House of Representatives and the Senate.

In addition, in 1973, Congress passed the War Powers Resolution, which stipulated that the president must notify Congress of his intentions within 48 hours of committing troops to war, as well as obtain a formal declaration of war for the deployment (or withdraw troops) within 60 days. In general, as mentioned before, the president may only commit troops abroad during a national emergency involving an attack on American soil, or with an authorization/formal declaration (an authorization is essentially an informal declaration not explicitly defined by the Constitution) from Congress. There are other corner cases too, as we will examine later on.

While all this may seem relatively well-organized, the fact is that the War Powers Resolution was outright ignored on two separate occasions by two different presidents (Clinton with Kosovo and Obama with Libya), and the point at which the president has reasonable clearance to send troops to war without consulting Congress is shrouded in shades of grey. Additionally, Congress has many times in the past utilized the informal "authorization to use military force" clause mentioned before to substitute for a formal declaration (as in the case of the 2003 Iraq War). These facts together both complicate the interaction between Congress and the president, as well as make the game-theoretic analysis much richer and more interesting to conduct. It should be noted that in producing the theories in this first part of this paper, we will be observing “the new separation-of-powers approach to American politics”, as it is defined by Figueiredo, Jacobi, and Weingast (2006).

So let’s get back to the main question: What causes nations to begin to go to war? To start answering this question, we first need to create the understanding that it is not, ultimately, a nation that goes to war, but the individuals who hold the power to declare war in each nation that go to war. Treating nations as homogeneous actors in the war-time setting will oversimplify the problem to the point of triviality, especially in the case of the United States (as opposed to parliamentary systems, where homogeneity and uniformity both within and between the legislative and executive branches are much more defined, as examined by Laver 2006). We must delve somewhat deeper than this, and realize that it is a specific (relatively very small) group of people in our government who make the ultimate choices regarding whether to invade or defend a nation.

However, it is also worth noting that, because we are choosing to discuss specifically the United States, and the United States is a democracy, the electorate is not completely absolved of all responsibility regarding war-time decisions, as it is to some degree to blame (or to praise) for the individuals in charge. This is not a trivial hair-splitter, but a rather important step in understanding the strategy and incentives involved in the waging of war. We will later on in the paper delve deeper into how the occasionally disparate natures of the public and its representatives commingle to have an effect on the warring process, with the crux of the game theory centering on the slightly ironic fact that politicians are under no obligation to stick to the platforms they advocated during election (save the obligation arising from the fear of not being re-elected, but a president in his last term or a retiring politician need not worry about that).

We will begin, for the time being, with the feasible simplification that the decision to engage in war rests solely with the members of Congress and the president. To proceed from here, it would be best to first examine the multiple cases that could arise in the war game between the president and Congress, and what the actions/motivations of each agent might be within the context of these games. After examining several of these cases, we may begin to think about constructing a model that more succinctly summarizes the various scenarios that could occur.

However, before we jump into these cases, we should first examine the incentive model that we will be using throughout the rest of the paper. For our purposes, we will generally assume that there are two different types of functions that will affect the decisions of a pivotal war-time agent. The first of these is the classical agent utility function. The second of these is the national utility function, which consists of an aggregate sum of the utilities of all the nation's constituents (this includes the agent himself and assumes that each constituent is forward-looking, and thus realizes that the demise of his nation will impact his utility very negatively). Each of these two functions consists of a large variety of terms, and some of these terms are obviously common between the two functions (since greater national utility will often lead to greater personal utility, and since the national utility function directly includes the agent's personal utility function).

So it is very possible that, by coincidence or on purpose, a key war-time decision making agent can either increase or decrease national utility in the process of maximizing his own personal utility. The degree to which this will happen depends on the circumstances and the individual characteristics of the agent. For example, as evidenced by politicians such as Curley, Young, and Mugabe (Glaeser, Shleifer 1995), some politicians are quite comfortable sacrificing the well-being of their total constituency for the increased chance of re-election, while others may behave much more altruistically.

In each of the following cases, we will first assume the United States is conducting an offensive war, which we define as a war clearly not instigated by an initial attack on U.S. soil (such as the Mexican-American war). We will discuss the additional assumptions and complications that arise from a defensive war later on in the paper.

● Case 1: The president suggests a war to Congress, which passes a formal declaration that is then signed into action by the president.

● United States on the offensive

Why would a president suggest an offensive war? Let's look first at the personal utility maximizing incentives that could cause this action. Historically speaking, a president is more likely to be re-elected if he has initiated a war and that war continues to be waged during the time of the next presidential election. The reasons for this are fairly obvious. The public is hesitant to bring somebody new to a situation that requires such large amounts of leadership, so it is generally presumed to be wisest to stick with someone who knows the war the best (presumably the same person who started it).

Thus, technically, if a president really wanted to improve his chances of re-election next term, he could time the initiation of a war to coincide with the start of elections. This would be particularly effective if the president is also aware that a large percentage of the electorate, Congress members, and/or the lobbyist groups is pro-war. These agents could be counted on to support him in the case that he chooses this action. Similarly, a president might be cognizant of the fact that there are a lot of pro-war individuals in the Electoral College, so that, in time to come, appeasing them may prove to be advantageous as well.

Another major incentive to war for the commander-in-chief is to prevent a lame-duck presidency. A president in his last year may be concerned that he was unable to get anything major accomplished or changed during his term. This would provide some incentive to start a war in order to be remembered for something (be that potentially a disaster).

Some more obvious personal utility maximizing reasons are that the president has some form of very strong personal animosity towards the opposing nation(s), or if he seeks to somehow gain financially from the attack.

Let’s now look at some of the national utility maximizing incentives that would cause a president to suggest a war to Congress. Perhaps the president is aware of something that Congress is not (this is feasible due to separation of powers), and chooses to act preemptively on that information (for example, if an enemy country moves missiles to within striking distance of the United States). Perhaps the president fears that Congress will take too long to take belligerent actions itself, so precipitates the process because he believes time is of the essence. This can happen if there is a Congress that is particularly afraid of alienating the president by making the first move (assuming the president is actually against the war), or that is particularly deadlocked.

Basically any decision that must be taken quickly would incentivize the president to make the suggestion himself. However, the heart of the issue when it comes to national utility maximizing reasons for suggesting war is that the action must, in some way, have the potential to improve the country. As a rational agent, the president (at least subconsciously) weighs the costs and benefits of initiating a war. Whether it’s done to acquire new resources or territory, the expected value of the benefits reaped must exceed the expected value of the costs of the war to United States citizens. We will formalize this interpretation a bit more later on.

● Case 2: Congress formally declares a war, which the president then signs into action.

● United States on the offensive.

Although this scenario is very similar to case 1, it is nevertheless distinct. In this case, Congress is the first to break the war ice, so to speak, declaring the war without receiving a suggestion from the president beforehand. This has never occurred in United States history, but it is nevertheless a plausible case. It could potentially occur if, for example, the president fears alienating certain anti-war Congressmen by making the first move towards armed conflict, or if the president is on the fence about initiating a war and needs a powerful push in a certain direction. Similar to the first case, Congress may also be privy to some information that the president is not (an unlikely, but still plausible scenario) and chooses to act on that information.

But why would the members of Congress want to commence a war to begin with? The personal utility maximizing reasons include the obvious: wanting to pander to certain pro-war co-members of Congress (or a pro-war president), to simply make known their positions within the legislature and increase popularity/status, or to pander to a pro-war public/lobby group that will help re-elect them come the right time. National utility maximizing concerns include basically the same ones that would have preoccupied the president.

● Case 3: Congress formally declares a war, which the president vetoes.

● United States on the offensive.

This case has also never occurred previously. The reasons for its rarity are simple enough to postulate about. Since Congress is fully aware that the president has the power to veto a war declaration, it will avoid presenting one unless the expected value of it being signed is greater than the expected cost of it being vetoed. This is a real concern because incurring a veto is expensive for Congress, and makes it look impotent (Figueiredo, Jacobi, and Weingast 2006).

But suppose that Congress misreads the intentions of the president and passes a war declaration anyway. Why would the president choose to veto a war declaration bill? Personal utility reasons include the desire to pander to anti-war Congressmen and voters/lobbyists (or other nations, perhaps those allied with the target country), or perhaps not feeling up to the challenge of handling a war, or maybe even just feeling uncomfortable with the idea of initiating an aggressive offensive action against another nation during his term (these last two could be considered national utility maximizing as well, since the president may be correct that he is incapable of leading the country effectively during a war, and thus not engaging would be ultimately better for the nation).

Other such reasons are that maybe the president wants to send a strong message to a defiant Congress, or perhaps that he just holds very strong anti-war sentiment (a sentiment that may not necessarily be motivated by what’s best for the country). The national utility maximizing reasons for vetoing, on the other hand, would almost certainly include the president believing that the cost of the offensive war will exceed the expected value of a victory.

It is also worth mentioning that in the case that pro-war sentiment is particularly high within Congress, as in the case of a defensive war (which we shall discuss in detail later), it is quite possible that Congress would be able to override the president's veto with a 2/3’s majority. However, this sub-case, as well as all of case 3, is unprecedented in practice and highly unlikely hypothetically, partly due to the fact that the president will avoid vetoing a war bill when he knows Congress has a fair chance of overturning it.

● Case 4: The president commits troops to war without an authorization or formal declaration of war from Congress.

● United States on the offensive.

Technically speaking, the two stipulations we have stated above are an illegal combination according to the War Powers Resolution, as the president may only directly launch a campaign against a foreign nation in the case of a defensive war, or with the authorization of Congress. Nevertheless, both former President Bill Clinton and President Barack Obama have previously disregarded the resolution to wage offensive strikes (bombing campaigns) against foreign forces.

Why would a president risk potential alienation from Congress and the public, as well as impeachment, to wage an unauthorized offensive strike? Moreover, with something as logistically complex as warfare, there must be a very long string of people who are involved in order to properly mobilize and deploy troops. All these people are also risking their careers and well-being by breaking the War Powers Resolution, thus making the question as to why this occurs even more pressing.

After some examination, it becomes painfully obvious that although the War Powers Resolution Act was successfully passed (upon congressional override of a veto by Nixon), it suffers from a severely small amount of authority within the United States. In fact, every president since 1973 has claimed that the War Powers Resolution Act is unconstitutional. This lack of authority probably has much to do with the fact that former President Clinton never faced impeachment charges based on his disregard of the act, seriously hampering any respect that the resolution had commanded up to that point. Thus, the perceived risk of serious repercussions for both the president and his “partners in crime” is quite low.

It is also possible that, to some degree, there is a mob mentality effect that occurs. The fact that so many people are involved, including the army itself, gives everyone involved much more confidence regarding the validity of their actions. Furthermore, it is unclear how credible a potential punishment for all those involved could possibly be given the sheer magnitude of the operation, and the fact that those who are administering the punishment are part of the same group as those who will be receiving that punishment.

But all this doesn’t really answer the question of why the president does not just seek approval from Congress first. Most likely, the sensitivity of certain time constraints makes up at least part of the answer. Looking back at history, both the Clinton and Obama invasions of Kosovo and Libya were waged not to trigger war, but to supplement specific combatants of a war that was already happening. It is likely that a president, faced with the pressing situation of an already ongoing conflict between some foreign groups, would believe that it may take far too long to get either an authorization or a formal declaration from Congress, particularly if his sentiment is that Congress is mainly anti-war at that current period in time (in which case he may have simply believed that he wouldn’t even be able to get an authorization or a formal declaration).

This points us to one of the possible national utility maximizing incentives for the president in this case: there is a time limit on the utility boosts that the country can reap from engaging in a war. Another such incentive may be that the president believes a potential congressional authorization or formal declaration of war would send too belligerent a message to the opposing sides or allies, resulting in negative repercussions from both friends and opponents that could otherwise have been avoided with the use of undeclared strikes.

Some possible personal utility maximizing incentives include, as before, to send a message to Congress (albeit, a very strong one), and to lobby pro-war support from the electorate, Congress, or even other nations. Most of the personal utility incentives from case 1 can be applied to this case as well.

● Case 5: The president commits troops to war with the authorization of Congress.

● United States on the offensive.

This is actually the most common scenario surrounding U.S. military engagements. When would this scenario occur? The answer to that question depends on when the authorization of Congress came about relative to the invasion. If the authorization came about before the beginning of hostilities, perhaps Congress is trying to preemptively save face because it is aware of the fact that the president will soon launch a war without their consent. Perhaps the majority of the Congressmen are simply trying to pander their pro-war support to the president or the electorate/lobbyists. But the question remains as to why Congress would choose an authorization rather than a formal declaration. Congress may also feel that the formal declaration would be too strong a statement for the circumstances, be that from fear of alienating the public/lobbyists, the president, and/or the allies, or from fear of inciting negative repercussions from hostile parties.

Why would the president want an authorization? Perhaps he does not feel comfortable entirely sidestepping Congress before going to war for fear of losing their support or the support of the public/lobbyists. Perhaps he fears breaking the War Powers Resolution or the possible enemy maneuvers inspired by a formal declaration. It’s also possible that both Congress and the president are in agreement that a formal declaration would take too much time or be too drastic, so they synchronize their efforts to produce the authorization.

In the case that the president went to war before the authorization was passed, it is likely that the scenario also involves Congress trying to save face, or perhaps tempering the backlash from the media/public that inevitably follows the unauthorized invasion of a foreign nation. Why an authorization instead of a formal declaration in this instance? Time being short can no longer be a valid excuse, as the hostilities have already begun, so the answer probably goes back to the other reasons we discussed, including the fear of losing ardent anti-war support and inciting fiercer resistance from enemies (this last point can be potentially argued to actually be time sensitive).

● Case 6: The president engages in military engagements authorized by United Nations Security Council Resolutions and funded by Congress.

● United States on the offensive.

This is a scenario we have heretofore left unexamined. The United Nations enters the play as yet another actor that influences the war-time decisions of the United States. When would this scenario occur? Examining it first from the president’s perspective, perhaps he does not feel he will be successful in getting an authorization or a formal declaration from Congress, and decides to save both face and time by appealing to the United Nations instead. Congress, on the other hand, decides to save face later on (or perhaps simply realizes that the war will bring the country benefit after all) by funding the war.

This is all, however, assuming that the president and Congress are not working together. As we previously examined, it’s possible that there was an agreement made between the executive and the legislative branch in which the president would specifically obtain permission from the United Nations while still receiving funding from Congress. This would be done for reasons that fit the general themes we have already seen: authorization from the United Nations gives off an entirely different impression than authorization or formal declaration from Congress. Since the United Nations is an organization meant to sustain global peace, permission from it carries undertones of a much less belligerent nature than those from any action endorsed by Congress.

Defensive War:

It would be needlessly tedious to re-examine each case for the situation of a defensive instead of an offensive war. Nevertheless, it is necessary to make some points that differentiate the defensive scenario. In the case that the United States is attacked (as in the case of World War II), pro-war sentiment from the public, Congress, and the president is likely to be much stronger. This is likely to make the process of pushing out either an authorization or a formal declaration much easier and/or faster. The presidential veto is very unlikely to be used, even if the president truly believes that a retaliation would not be in the best interest of the United States, as such a move would be political suicide.

But why is failing to respond to an attack on U.S. soil political suicide? Much of the answer lies in the fact that the United States is, militarily speaking, the most powerful nation on Earth. Why should the giant lie still while the mosquitos bite at it? America’s public and politicians understand their standing in the world, and thus are much more prone to retaliation than the constituents of a country with a much weaker military would be. As such, it is very unlikely that either Congress or the president would be able to get away with not, at the least, funding a retaliatory action.

For example, although the Iraq War was never formally declared, it was still authorized by Congress before military actions ever began. Much of this had to do with the obvious: The September 11th incidents were an attack on U.S. soil. Additionally, the United Nations is much more likely to support a war where America was initially attacked. Why? It is no secret that America is often looked upon (justifiably or unjustifiably) as the harbinger of freedom and democracy around the world. An attack on the United States is likely to be perceived as an attack on liberty and the Western way of life.

It is worth repeating at this point that such a reaction is unique to countries of the same strength and influence class as the United States, and thus is not a theory that can hold water when expanded to the retaliatory policies of weaker nations.

Now that we have had a relatively thorough examination of the various war-game cases that could arise, let us attempt to model the expected behavior with a model: Consider a point in a multidimensional space labeled P. This point signifies the character of the president's preferences. The location of this point in the space is determined by the personal utility of the president (to reiterate, the personal utility function will most likely contain terms from national utility as well) after maximization. Consider another point in the same space labeled C. As expected, this point represents the equivalent of P, but this time in terms of Congress, or, more specifically, the median Congress member.

The number of dimensions in this multidimensional space is equal to the number of common terms between the personal utility of the president and the personal utility of the median Congress member. What would these common terms consist of? All of the possible incentives that were mentioned in the case studies as belonging with both president and Congress (asymmetric information, pandering, etc) make up these common terms. Obviously there are also many war decision influencing terms belonging with both president and Congress that are not common. These are absorbed by an extra dimension included in this space.

Now picture a straight line segment passing through this multidimensional space. This segment serves the purpose of indicating how pro-war or anti-war any point in the space is, with either end being the most extreme cases of each viewpoint. The halfway mark of the line segment is representative of an agent who is indifferent between going to war and not going to war. If we draw a perpendicular line from each point to this war axis, we will be able to assign a "war intercept" to that point, indicative of how war-like that agent is. We can then logically infer that if two agents (Congress and the president in this case) are both either on the pro-war half or the anti-war half of the line, then the corresponding outcome (war or no war) is ultimately inevitable. The relative speed with which that action will proceed is going to depend on both the distance between the agents and the average extremity of the two agents. We can thus formalize that relative speed as such:

((P+C)/2)/|P-C| (1)

The analysis becomes more interesting if Congress and the president are located on opposite halves of the war line. If we model values on the anti-war half as positive and those on the pro-war half as negative, we can easily see that the relevant speed of execution could be positive or negative. Naturally, a positive speed will ultimately lead to an outcome of no war and vice versa for a negative speed.

Which of the cases that we examined before will actually occur is going to depend on the individual values of P and C, and potential prediction thus becomes an ultimately subjective matter. However, the model provides a relatively plausible framework from which one can begin to think empirically.

Middle Play:

The sustainment of war lends itself to some interesting analysis as well. Once a war has begun, it is essentially like any other body in motion; it will continue to move unless acted upon by an outside force, be that force friction, or simply the stopping power of an endpoint. In that same way, a moving object representative of the continuation of war experiences friction in the form of occurrences that act against the preferences of the participating agents. Let's look into this interpretation with more detail:

What are the factors that allow a war to continue? Wars are generally fought until all sides are either defeated, victorious, or satisfied with the status quo (in other words, can be no better off). Let’s first take the case of two actors to make clearest the points about to be presented (one of these actors will naturally be the United States). The decision whether or not to continue a war for an individual nation can be briefly and generally modeled in the following way:

Sunk Costs + Expected Value(Future Costs) - Acquired Benefits - Expected Value(Future Benefits) (2)

Note that, in this equation, the references to value and costs are an aggregate of the personal benefits and costs (of all a nation's constituents) that accrue as a result of a victory or a defeat. If this equation is greater than 0, the nation has no rational reason to continue warfare. If it is less than 0, it would be irrational to stop warfare. This makes 0 the turning point at which the war becomes no longer worth it to the individual nation, and thus an ideal point at which to quit the theater of action. But just because one of the two nations decides it would be rational to quit the war, does not necessarily mean that the war is over. Even if a nation surrenders or retreats from the theater of action, the opposing nation can continue to harass the now weakened retreating nation’s troops and motherland, further adding to that retreating nation’s costs.

The opposing nation would choose to do this in the case that the expected benefits for continuing war with a now defensive-minded nation still exceed the expected costs. Because this is the case and because retreating naturally increases the probability that costs of greater value will be incurred, the cost of retreat/surrender must also be taken into account when deciding whether to continue a war. It can be incorporated into the model as an addition to the expected value of future benefits (since not paying a retreat cost is one of the benefits of staying in a war):

Sunk Costs + Expected Value(Future Costs) - Acquired Benefits - Expected Value(Future Benefits) - Expected Value(Retreat/Surrender Costs) (3)

From this updated model, we can quickly see that if the retreat costs are particularly high, a nation that would otherwise have already surrendered may continue to fight. It is also important to note that the variables involved in this model are very dynamic, constantly oscillating as the tide of the war changes and new information becomes available to the warring parties. For example, the costs of continuing a war may outstrip the benefits before a pivotal battle, while the opposite may be true following the battle. The question remains as to how long a nation should wait to update its information before making a decision based on that information. This is a subtle art, and cannot be definitively answered. Past experiences and expertise would help in narrowing the margin of luck on this point.

To this end, we can see that, at least according to our simple model, a war will be over when the model is equal to 0 for all parties involved. So far, however, our model has taken only the most rational, altruistic assumptions into account, specifically the assumptions that would make the country the best off (by maximizing the aggregate sum of utilities). As we all know, countries are not run this way, but rather by human beings, who make decisions based not only on what is best for the aggregate, but also on what's best for themselves. In terms of the incentive model that we have already presented, this simply means that war-time agents maximize their personal utility function as well as the national utility function.

Another factor to consider is that wars usually become the biggest news within the respective countries perpetuating those wars. As such, a relatively free nation’s citizens and politicians have ample opportunity to form opinions and perceptions about the war, and as the Vietnam War has taught us, these public perceptions are not trivial to success. In the United States, a war that is popular with the public can continue to be fought despite producing great loss to the country, and a war that is unpopular could be brought to an end despite actually being quite beneficial (although this is unlikely).

Why is this so? The main reason has to do with the fact that the United States is a democratic country, and therefore our leaders are, for the most part, elected. If the public is unhappy with a war and the politicians are the agents (as we discussed earlier) who ultimately start and end wars, it becomes rather simple to predict who will and who will not be re-elected. Although politicians do care about the state of their country, as human beings, they also care about their own status and positions. As such, there is a point at which they will no longer be willing to benefit the country in exchange for their own well-being. Most of the time, it is likely that an equilibrium will be established between these two not necessarily mutually-exclusive forces (altruism and selfishness). We should then find a place for all these aforementioned constructs in our model:

Sunk Costs + (1-(Selflessness of Congress/Presidents))*(Expected Value(Future Costs)) - Acquired Benefits - (Selflessness of Congress/Presidents)*(Expected Value(Future Benefits)) - Expected Value(Retreat/Surrender Costs) - Popular Perception (4)

In the case that popular perception is negative, it would add to our costs, and vice versa for the positive case. The selflessness of the current Congress and president will also function the same way as expected by theory: the “Selflessness of Congress/Presidents” term is a number between 0 and 1 that represents the percentage of the war-time decisions that political agents make which service to maximize national utility instead of personal utility. Thus, as would be predicted, a higher such percentage would amplify the expected values and downplay the expected costs of the war.

It should also be noted that this model is robust to mixed strategies, in which instead of total war or full retreat, a nation cuts the size of expenses geared towards war if the cost is too high (though this carries with it the diminution of the probability of victory), or increases its commitment if the potential benefits at the time are particularly great.

End Game:

So suppose the war has come to an end, with one of two (for conciseness) outcomes. Either the United States has been defeated, or it has claimed victory. What are the political/economic consequences of each resolution?

Victory:

In the case of a United States victory (and ceasefire, since we assume the war ends when all participating nations will no longer reap benefits from continuing warfare, even after victory), a peace treaty will most likely be negotiated, with the U.S. almost certainly receiving large rewards. The negotiations of a peace treaty are in themselves an interesting game to consider and deserve a paper of their own, but we will nevertheless examine them briefly here.

Since the United States was the victor, its representatives will have the upper hand in peace treaty negotiations. What does it really mean to have the upper hand in this situation? Technically speaking, since the United States won the war, it can lay siege to the entire opposing nation if it so desired. However, with that action, like with every action, comes a cost (global outrage, sanctions, etc). Thus, it is also helpful to think about these negotiations in terms of costs and benefits, much like the way we thought about the opening and middle play of the war. Rationally speaking, both parties of the negotiation should continue to negotiate until the benefits they reap equal the costs of doing so. As the victor, the United States will have much larger potential benefits and much smaller potential costs than the losing party. We can write a simple model as such:

Expected Negotiation Benefits(U.S.) - Expected Negotiation Costs(U.S.) = Expected Negotiation Benefits(Losing Party) - Expected Negotiation Costs(Losing Party) = 0 where Expected Negotiation Benefits(U.S.) > Expected Negotiation Benefits(Losing Party) and Expected Negotiation Costs(U.S.) < Expected Negotiation Costs(Losing Party) (5)

Once again, we must remember to keep in mind that negotiations are not being conducted by machines, but by humans, who have their own personal utility curves. However, given the most likely very public nature of peace treaty negotiations, it is highly unlikely that delegates will start to split hairs for provisions that would benefit them directly, as this would generate social costs (in terms of public criticism) that would far outweigh any of the potential benefits. Similarly, politicians (including the president) who negotiate a favorable contract for the U.S. could expect to reap the rewards of the public’s satisfaction come next term’s election days. This fact should provide incentive enough for altruism.

Defeat:

In the case of a United States defeat, much of the above model is simply reversed. The main point to be made is that, assuming the integrity of the homeland is preserved following the defeat, the politicians and the president that facilitated the war will be held responsible for its failure. One way for these politicians to redeem themselves even a bit would be to negotiate a favorable peace treaty for the United States (as favorable as possible under the circumstances). However, it is still very likely that major overhauls will be made to the governmental representation.

Of course, there are many shades of grey as far as what is considered a victory or a defeat (the Vietnam and Korean wars are still being debated regarding this point, for example), and these same shades of grey provide for the myriad of mixed strategies that enrich the above model.

Conclusion:

There were many points touched on in this paper, and there are several theoretical conclusions that may be drawn from those points. We have looked carefully at how the decisions involved in beginning, continuing, and ending war belong in the hands of a very small group of people. We also examined how the decisions that are made by this select group of people are based partly on what is best for the nation, and partly on what is best for them. The factors constituting what is best for the nation and what is best for them are constrained by the natural interplay between the executive and legislative branches, which often involves a lot of pandering and/or message sending. Without understanding how politicians try to maximize both of these utility functions within the constraints of these separation of powers relationships, the study of the motivations behind warfare will quickly fall apart.

Politicians are often accused of their callousness towards the preservation of human life during times of war, but we have seen that although selfishness is a decision-making factor, it is hardly the only one. The potential benefits that come from being an incumbent following a war-time victory provide strong incentive to think in terms of national benefit rather than personal benefit. A politician will seek to appropriate his personal utility gains and the national utility gains in such a way as to keep the personal gains equal to the personal costs, like any rational agent would.

This works to produce a functioning government because, being a member of his own nation, part of the politician’s personal gains and losses are composed of national gains and losses. Benefiting and hurting the nation will thus be realized in that politician’s personal gains and losses by way of re-election opportunities, standards of living, etc.

In order for actors to be able to make rational decisions, the cost of human life must in some way be quantified to allow for proper marginal utility comparisons. As such, given the prevailing valuations of human life, war can, at least theoretically, sometimes be the answer, as hinted at by the fact that so many have transpired throughout history. The reason for this will ultimately boil down to the idea that a warring nation does not seek to maximize peace or human life, but the total utility of that nation.

Bibliography:

1. Full text of the War Powers Resolution (50 U.S.C 1541–1548)

2. Greenwald, Glen (June 25, 2011). "Congress vs. the president on war powers". Salon.

3. Henderson, Phillip G. (2000). The presidency then and now. Rowman & Littlefield. p. 51.

4. Laver, Michael. “Legislatures and Parliaments in Comparative Context.” Oxford Handbook of Political Economy. Ed. Barry R Weingast & Donald A Wittman. Oxford University Press, 2006. 1-16.

5. Lithwick, Dahlia, "Wrestling Over War Powers", Newsweek, July 12, 2008

6. Rumsfeld, Donald, Known and Unknown: A Memoir, Penguin, 2011. Cf. especially Chapter 1

7. De Figueiredo Jr., R J P, T Jacobi, and B R Weingast. “The new separation-of-powers approach to American politics.” The Oxford Handbook of Political Economy. Ed. B R Weingast & D A Wittman. Oxford University Press, 2006. 199-222. Print.

8. Berdal, M. and Keen, D. (1997) Violence and Economic Agendas in Civil Wars: Some Policy Implications Millennium: Journal of International Studies 26(3): 795-818.

9. Stewart, F. (1993) War and Underdevelopment: Can Economic Analysis Help Reduce the Costs? Journal of International Development 5(4): 357-380

10. Rubin, B.R. (1999) The Political Economy of War and Peace in Afghanistan. Council on Foreign Relations, New York

Evolution and Utility Maximization: A Synthesis

In the previous article, I touched on the theory regarding the relationship between our evolution and utility maximization. In this one, I'd like to present this theory in a more concrete manner.

Evolution is driven by what we today call the "survival of the fittest", which implies that those who are most well adapted to their environment are those that are able to persist and pass on their genes to their offspring. But this only answers part of the question. If evolution is driven by the survival of the fittest, what drives the desire to not only live on, but for those who possess superior faculties, to dominate those of lesser ability? To make it worth their while, fitter individuals must receive something for their troubles. This is where the concept of utility maximization enters the play.

All rational individuals seek to maximize their utility for as long a time period as their foresight allows them. Some individuals are naturally more short-sighted than others, so they seek to maximize only their short-term utility, while others think and optimize further ahead. Additionally, if we think of each individual's utility function as consisting of a very large number of differently weighted variables, we realize that everybody's variables and weights will be as diverse as the individuals themselves.

The vast differences in all these utility functions are precisely what drive the evolutionary mechanism. Everybody ultimately does what grants them the most utility within the time period that they can reasonably assess. If those actions that maximize their utility also happen to coincide with the actions required to survive and reproduce in their specific environment, then those individuals could be considered to be fit in the Darwinian sense. In that same sense, it can almost be said that for every environment, there exists a form of utility function that fares best. The closer a person's function comes to this, the better off he'll be within that setting. The genes of these individuals are what are eventually passed down from generation to generation.

To some degree, this interpretation is similar to Adam Smith's "Invisible Hand". Each individual only does what is natural for him to gain the greatest amount of utility, not necessarily thinking about survival, evolution, or the larger scope of humanity. However, arising from this interaction of everybody doing what is best for themselves, comes the very battle for survival that Darwin had envisioned. As Smith's invisible hand guided everybody to make the decisions that benefited total welfare, solely by making the decisions that best benefited themselves, so does the evolutionary invisible hand extract and pass down the most successful genes solely through each individual's personal utility maximizing actions.

An Evolutionary Explanation for the Success of Capitalism and the Failure of Communism

"Nothing in Biology Makes Sense Except in the Light of Evolution" reads the title of the famous essay by Theodosius Dobzhansky. So too it is with many other things, including, to some degree, forms of government. So what is it that makes capitalism so much more conducive to our origins as human beings?

The history of the world is scattered with the remarkable life stories of great men and women. It is even said by some (and debated by others) that these remarkable individuals are the very catalysts of said history. Even if this is not 100% the case, it would be hard to argue that these individuals did not have a very large effect on the state of society as it is today. Furthermore, the fact that we remember only these key individuals from the past implies that we are not all the same, and that individual ability has always had a large role in the order of things.

Let's go further back now, to the very beginning. It was true then, as it is today, that evolutionarily speaking, the main priority of the species is to spread and multiply. That being said, back then, as well as now, there were individuals who possessed higher capabilities than others, be those mental or physical in nature. These individuals would often come out on top in various engagements, and thus be the ones to either survive, or at least to carry on the species via reproduction. Why would these individuals choose to do this? Sometimes they probably wouldn't choose and would instead be chosen (perhaps by being challenged by another individual), but other times these individuals were seeking to maximize their utility. Thus enters Darwin's theory of natural selection, by which time and nature filter the quality of the genes passed down from generation to generation.

By this reasoning, we can then see that, evolutionarily speaking, it makes no sense for all individuals to be equal. If all individuals considered themselves equal and shared equally all resources, a lack of intellect, strength, etc., would no longer be a disadvantage. This would cause all genes, even the most pernicious amongst them, to be continuously passed down from era to era, as no punishment or survival mechanism exists to weed out the least capable. This is clearly not beneficial for the species, and what isn't beneficial for the species goes against the dynamics of evolution.

Capitalism, on the other hand, plays right into the hand of what nature expects. In capitalism (at least when it is without flagrant free market failures), any man can become wildly successful if he is only so able. A capitalist is restricted only by his desire and competency. What is this but a 21^st century example of the survival of the fittest environment I mentioned earlier? Those of higher capabilities attain more success and thus gain a greater probability of surviving and passing on their genes. They are compensated for going out of their way to do this by reaping all the rewards that come from being successful, thus enhancing their utilities.

Communism, by its core beliefs, stifles the human instincts that have been bestowed on us by our cave dwelling ancestors . We are an instinctively competitive species, for that is the process by which we purify our gene pool. It is our way of establishing quality control, and capitalism builds around this framework very cleanly. Thus, for all its altruistic pretensions, it turns out that communism is in fact much more oppressive to us than capitalism could ever be.