Volume 11, Issue 4 - April 2013

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VOLUME 11, ISSUE 4: STUDENT SPOTLIGHT

Optimization Models as an Advanced Dispute Resolution Tool

Timothy R. Watson*

I.  Introduction

Optimization is an important concept in the field of engineering, particularly in the increasingly important field of systems engineering.  Optimization allows an engineer to study a problem and determine the best (or optimal) result, thus it has been defined as “the act of obtaining the best result under the given circumstances.”[1]  Optimization has provided seemingly endless applications.  From manufacturing design, to computer programming, to biological research, nearly every field imaginable utilizes optimization to achieve results that human beings could not otherwise achieve.[2]  With so many different fields benefitting from optimization, it is not surprising that researchers have sought to apply optimization techniques to alternative dispute resolution (ADR).[3]

Applying optimization techniques is a unique form of ADR research.  Rather than focusing on better ways for people to facilitate dispute resolution, optimization-driven ADR will seek to better utilize a combination of math, science, and technology to provide dispute resolution.  While moving too quickly into an automated, less human-involved approach to ADR may raise some legitimate concerns, the potential that optimization offers is enough to suggest that future developments of dispute resolution should attempt to learn and benefit from optimization techniques.  Increased use of optimization presents an opportunity for efficient and effective dispute resolution beyond what a person alone can provide.  Furthermore, using optimization models as a tool can aid negotiation, mediation, and arbitration processes.

Section II will provide a brief overview of optimization, including the history, techniques, and benefits.  Then, Section III will discuss basic concepts of dispute resolution system design in order to establish a framework on which optimization principles may be applied.  Finally, Section IV will explain how optimization can be used in dispute resolution, present a hypothetical dispute optimization model, examine existing uses of optimization techniques in dispute resolution, and attempt to weigh the benefits and costs that are likely to arise from such applications.  This paper concludes that although existing uses of optimization in dispute resolution are not perfect, the potential benefits show optimization models will play a critical role in the future of dispute resolution.

II. An Introduction to Optimization

While optimization is most effective at a highly technical level, often taught in graduate level engineering courses, this section will simplify the basic concepts of optimization into terms not requiring a mathematical background.  Part A provides background as to what an optimization model is and describes fields that utilize such models.  Part B lists the steps involved in creating an optimization model.  Part C then discusses the benefits that can result from creating and applying an optimization model.

A.  Background and Existing Applications of Optimization Models

An optimization model is a type of “problem-solving method;” a specific way for determining the potential solutions for a given problem.[4]  The model consists of a set of mathematical formulas; it is a mathematical representation of a real world situation.  By using a mathematical representation, a decisionmaker may be able to understand the actual problem better and thus reach a better solution.[5]  Because anything that can be represented algebraically can be made into an optimization model, optimization has been applied to a large variety of fields.[6]  In fact, the spread of optimization to an increased number of disciplines, each with different situations and concerns, has been responsible for many theoretical and methodological developments.[7]

The first, and possibly best-known, application of optimization is in operations and planning.[8]  This use of optimization evolved from the need for a more effective military strategy.[9]  During World War II, the British military relied on mathematicians for solving resource problems in a scientific manner.[10]  These mathematicians developed mathematical methods to create better and more efficient deployment strategies for scarce resources such as troops and supplies.[11]  These wartime developments have been credited as leading to modern mathematical and optimization techniques, such as linear programming.[12]

Another early application of optimization is commonly known as “the diet problem.”[13]  The diet problem was to fulfill a person’s daily nutritional requirements using the cheapest possible combination of food.[14]  The problem was solved by George Dantzig, who created a theory for solving for the maximization of a linear function subject to linear inequality constraints.[15]  Dantzig’s theories greatly expanded linear programming and paved the way for engineers to apply optimization techniques to other fields.[16]

Expanding from its military origins and Dantzig’s theories, optimization spread to the field of operations research.[17]  Common operations applications include: cost planning, inventory control, and strategizing to maximize profit in the presence of a competitor.[18]  Many effective computer algorithms are also based on optimization methods.[19]  Examples include artificial intelligence, and—most important to modern society—algorithms that power online search engines.[20]  Optimization has even been utilized to better understand how diseases, such as diabetes and cancer, affect the body and thus, how they can be treated.[21]  Other biological applications of optimization of included inferring gene regulatory networks and protein interaction networks.[22]  In sum, optimization has played a key role in running businesses, understanding the human body, strategizing in wartime, and even planning people’s diets.

B.  How an Optimization Model is Created

As stated in the previous part, an optimization model is a mathematical representation of a real world problem.  Thus, theoretically anyone can create an optimization model by simply determining mathematical relationships from real world events.  While different types of optimization models exist,[23] all models share some general characteristics.  The following are the general steps involved in creating an optimization model.  Parts 1 through 3 explain how the parameters of the model are determined.  Parts 4 and 5 explain how to solve the model.  Parts 6 and 7 describe various forms of optimization models.

1.  Creating the Objective Function

Logically, the first step in developing a model of a problem is identifying what the problem is to be solved.  Identifying the problem to be solved is known as creating the “objective function.”[24]  Creating an objective function is based on the idea that “the benefit desired in any practical situation can be expressed as a function of certain decision variables.”[25]  In most optimization problems, the decisionmaker is seeking to either maximize or minimize the objective function.[26]  A common example of an objective function in a business optimization model is profit.  With profit, the business  seeks to maximize their objective function.  Another example could be manufacturing time.  For time, the business is more likely to want to minimize their objective function.  For the conceptually simpler example of maximizing profit, the objective function would be: Maximize P, where P equals profit.  Determining the objective function should be the easiest step, as it is simply what problem the decisionmaker wishes to solve.

2.  Identifying Variables

Once the objective function to be solved is identified, all factors affecting the objective function must be determined, along with their relationship to each other.  These factors are the “variables” in the model.  Variables are controlled by the decisionmaker, and altering the variables will change the outcome of the model.[27]  Thus, the goal of the decisionmaker is to change the variables in a way that will achieve the desired maximum or minimum objective function.  To understand what variables are, consider the example of maximizing profit: every product sold effects profit, thus each different type of product could be represented by a variable.  If product A makes two dollars per product sold and product B makes three dollars per product sold, an equation could be made stating: 2A + 3B = P.  While many variables will be easily identifiable, more complex problems, such as those arising in nature, may have hidden variables that will not be noticed without an advanced understanding of the problem.

3.  Establishing Constraints

The ability to modify the variables in a problem is often limited by a set of “constraints.”  A constraint is a limit on how variables can interact, existing when only certain values of variables are possible.[28]  Constraints may also be referred to as the “parameters” of the objective function.  Each constraint adds additional equations to the optimization model.  In the profit example, if only ten total products can be sold, a constraint of A + B ≤ 10 (the sum of A and B must be less than or equal to ten) would be added to the model.

Once constraints are established, the model is complete and ready to be solved.  The complete profit model would thus be:

Maximize:       P = 2A + 3B

Subject to:       A + B ≤ 10

4. Determining All Feasible Solutions to the Problem

After the problem has been formulated mathematically, the next step is to determine possible solutions.  A potential solution is any combination of variables that will equal the objective function; however, where constraints exist, not all potential solutions will be achievable in real life.  Therefore, determining “feasible solutions”–any combinations of variables that will satisfy the constraints of the problem–is more important than simply determining potential solutions.[29]  In the profit example, because the goal is maximizing profit, a simple solution would be to make an infinite amount of product A and product B, thus resulting in an infinite profit.  However, real life problems are seldom unconstrained, and companies cannot simply sell infinite products.  If the constraint applied above is applied, a solution is only feasible if ten or less total products are sold.

5.  Selecting the Optimal Solution

From the list of feasible solutions, one can identify an “optimal solution,” the solution that minimizes or maximizes the objective function.[30]  For the profit example, a constraint stated that only ten total products could be sold.  Since product B is sold for one dollar more than product A, selling ten of product B will result in the business’s maximum profit of thirty dollars.  While the optimal answer for the profit example can quickly be found by trial and error, most optimization applications are much more complex.[31]  Thus, a wide variety of algorithms exists to solve for the optimal solution, many of which can only be efficiently applied through use of a computer program.[32] However, understanding the means of solving optimization models is not necessary for the purposes of this paper.

6.  Multi-Criteria Decisionmaking

Step one described determining the objective function (or issue to be solved for) in a problem.  But, in most real life problems the decisionmaker will be faced with more than one, often conflicting, objective functions.  Rarely will a problem be as simple as the profit example provided.  For these more complex problems, the technique commonly referred to as “multi-criteria” (or “multi-objective”) decisionmaking may be applied.  Multi-criteria decisionmaking is the process of using an optimization model to solve for multiple objective functions.[33]  For example, if the business seeking to maximize profits also wanted to do so while minimizing production times of their products.  If product B takes longer to manufacture than product A, but B is sold for more than A, the two goals are conflicting.  This situation creates an added step and requires the decisionmaker to assign preferences to each objective.  Preferences are assigned as a percentage, or fraction, where the total cannot exceed one hundred percent, or one.[34]  Thus, an example of preferences would be assigning a 75% preference to maximizing profit and a 25% preference to minimizing time.

Formulation of a multi-criteria model is the same as an ordinary model until the solution step.  Once all feasible solutions are determined, the decisionmaker applies preferences for the various factors considered to find the best possible solution.  In order to do this, a new objective function is created, where the previous functions are the variables.  Thus, in this example, the multi-criteria decisionmaking objective function would be maximize U = .75P + .25T, where P equals the profit maximizing objective function and T equals the time minimizing objective function.    As independent objective functions, P and T may be subject to different variables and constraints.  Thus, multi-criteria decisionmaking provides a means to combine these different goals to achieve a single optimal solution.  The percentages being multiplied against the variables equal the weight assigned to the preferences.[35]  Each combination of assigned preferences will provide an optimal solution; thus, changing preferences allows a range of optimal solutions to be seen.  Note that before the multi-criteria decisionmaking objective function can be solved, the independent objective functions must be normalized by using mathematical algorithms beyond the scope of this paper.[36]

7.  Various Types of Optimization Models

While the basic steps described above for formulating models are the same, the type of models that can be developed range in complexity.  The reason different types of models exist is because no one type can solve all optimization problems efficiently.[37]  The first classification of models is static versus dynamic models.  A static model involves set variables, variables that do not change over time.[38]  Slightly more complex are dynamic models, which involve variables that do change over time and require decisions to be made over a period of time, rather than at once.[39]  The profit example above was static, however, if it were modified to list different prices each month of the year, it would be dynamic.

Another classification of models is integer versus noninteger models.  An integer model only allows integers, or whole numbers, to be used as variables.[40]  Conversely, a noninteger model allows variables to be both integers and fractions.[41]  While many people would find working with integers easier than fractions, an integer model is actually more complex than a noninteger model due to the additional limits placed on potential variables.[42]  The profit example was an integer model, assuming that a fraction of a product cannot be sold.

The final classification of models is likely the most mathematically complex, yet possibly the most important to developing a quality model.  This classification is linear versus nonlinear models.  In a simple linear model, variables are multiplied by constraints and added together to determine the objective function.[43]  The math required to solve linear models is no more than basic algebra, therefore most models could be solved as effectively (though not as quickly) by hand as by computer.  Nonlinear models however may involve more than multiplying and adding variables, often involving variables being manipulated exponentially.[44]  Solving these problems often involves application of calculus and differential equations.  The profit model was an example of a linear model.

C.  Benefits of Utilizing Optimization

One benefit to optimization is efficiency.  Though various optimization methods have existed for many years, the field has grown in recent years due to the rapid growth in computer capabilities.[45]  This has allowed for more advanced techniques to be developed, making it possible to solve larger and more complex problems in a matter of seconds.  Presently, the complexity involved in optimization algorithms means that many such algorithms are designed to be implemented by a computer.[46]  Several computer programs exist for implementing optimization models.[47]  Alternatively, a model could be created as its own computer program.[48]

An additional core benefit of optimization is effectiveness.  By providing every feasible solution to a given problem, optimization allows engineers to determine the best solution in design problems.  Advanced techniques allow engineers to consider many goals at once and use assigned preferences to determine an optimal solution from the list of feasible solutions.  This is a more effective means of problem solving, as it ensures that every possible solution is considered.  Because optimization provides both an efficient and effective means of solving problems, many of its methods are worth exploring in the dispute resolution context.

III. Overview of Dispute Resolution Design

To understand why optimization can improve dispute resolution, it is important to understand a few points about dispute resolution design.  Dispute system design is the attempt to coordinate resources, processes, and capabilities to best achieve a specified objective.[49]  An effective dispute resolution system goes beyond a specific dispute in order to take a broad look at a range of conflicts to determine how to best address these over time.[50]  This section will briefly discuss basic principles and goals in designing effective techniques for the three major areas of Alternative Dispute Resolution (“ADR”): negotiation, mediation, and arbitration.

A.  Negotiation

Negotiation is a consensual procedure where parties aim to reach an agreement.[51]  It serves as the foundation for dispute resolution, as at its core it can be thought of as parties communicating to reach a settlement.[52]  Negotiation models range from adversarial and competitive at one end of the spectrum, to collaborative and problem-solving at the other, with various combinations in between.[53]

Some forms of negotiation theory have already attempted to utilize some of the same principles as optimization.  The “Full, Open, Truthful Exchange” (FOTE) manner of negotiating involves creating an efficient frontier of possible negotiation outcomes.[54]  The FOTE method is described as a form of deal-making rather than dispute settling.[55]  This step is similar to determining all feasible solutions, as described in Section II(B)(4).  The FOTE theory also maintains that each party has a “Best Alternative to a Negotiated Agreement” (BATNA),[56] which the party hopes to leave the negotiation having achieved.  Each party’s BATNA would be its optimal solution, as described in II(B)(5).  From this landscape, parties will hopefully converge on the solution that best balances their individual BATNAs.

Because negotiation is a procedure only involving the parties to the dispute, it provides the best opportunity to apply optimization to dispute resolution.  An optimization model can serve as a tool that both parties use in order to reach the fairest solution.  As negotiations are non-binding, the potential drawbacks to using such a model are less than with other forms of dispute resolution.

B.  Mediation

Like negotiation, mediation is also a consensual procedure, where a third party attempts to facilitate an agreement between disputants.[57]  The goals of the mediator include: reducing hostility between parties, creating an agreement of what obligations each party will assume, and creating a method for ensuring obligations are carried out.[58]  Mediation ideally ends in a win-win result for the parties.[59]  However, mediation has many theories including: facilitative, transformative, understanding, narrative, and eclectic.[60]  While the specifics of these various forms of mediation are beyond the scope of this article, it is worth noting their existence as evidence that there is no one “correct” form of administering mediation.

As mediation can be thought of as a form of negotiation facilitated by a third party, the potential applications of optimization in mediation are as great as in negotiation.  However, because mediation utilizes a third party as a facilitator, an issue that does not exist in negotiation arises—whether an optimization model can serve as the facilitator, or whether it should merely exist as a tool for the facilitator.  This issue will be addressed further in Section IV(A).  An existing attempt at applying optimization to mediation will be described in Section IV(C).

C.  Arbitration

Arbitration has been defined as “an adversarial procedure in which an independent third party decides the case.”[61]  Of the traditional ADR methods, arbitration most closely resembles litigation.[62]  The arbitration process often provides parties the ability to guide the format through selecting rules, procedures, who the decisionmaker will be, and whether or not the decision will be binding.[63]

Due to its potentially binding nature, arbitration appears to be the area of ADR least likely to accept use of optimization.  As with mediation, an optimization model could theoretically serve either as a tool used by an arbitrator or as the actual arbitrator to the dispute.  However, skepticism over the fairness and accuracy of such model could prevent parties from consenting to such arbitration, and, depending on the conflict involved, laws and regulations may prevent certain uses of an optimization model.

IV.  Potential Application of Engineering Optimization as Dispute Resolution

Optimization can potentially provide a better form of dispute resolution.  Part A discusses how an optimization model would be created to solve dispute resolution problems.  Part B discusses how the optimization model could be effectively implemented.  Existing attempts at applying optimization to dispute resolution are examined in Part C to see whether or not there is room for improvement and what lessons can be learned.  Part D then discusses the benefits of applying optimization to dispute resolution. Finally, Part E examines the potential downside to creating a dispute resolution optimization model and why such model will likely be met with skepticism and will struggle to gain widespread acceptance.

A.  Creating an Optimization Model for Dispute Resolution Problems

While an optimization model may provide a more effective solution to a dispute, such an outcome can only be achieved if the model is properly created.  There are two steps to using a dispute model: first, establishing the parameters of the dispute and second, solving for the optimal solution.  After both steps are explained, a hypothetical dispute model is described.

1.  Establishing the Parameters

As described in II(B)(1)-(3), the key to developing a model is identifying the objective function to be solved,[64] the variables effecting the issue,[65] and any constraints that exist on potential solutions.[66]  Accurately identifying these parameters of the model is crucial to creating a useful model.  Establishing the parameters is the most important and challenging part of creating an optimization model because failure to identify a variable or constraint could lead to a solution being provided that is not actually feasible.[67]  In the dispute resolution context, inaccurate parameters could result in a model that prejudicially favors one party over the other.[68]  Thus, steps should be taken to ensure that the given parameters accurately reflect the dispute.

Because the parties are in the best position to determine the factors affecting their dispute, effective brainstorming between parties is needed to identify the objectives, parameters, and preferences of the dispute.[69]  While the parties have the capability of recognizing and agreeing to these variables on their own, parties in a dispute may not always be willing to act in a cooperative manner, and may try to ensure only factors favorable to their position are considered.  The use of mediators may be needed to help foster brainstorming in more challenging areas.[70]

Furthermore, not all factors and issues are easily quantified into numbers,  a problem especially likely in the complex disputes.  Mediators may not be able to translate disputes into mathematical relationships. After a situation is disclosed, it may be necessary to meet with an engineer who would have such ability.  Accordingly, the process for creating a dispute resolution optimization model would ideally involve three actors: (1) the parties to the dispute, (2) a mediator who helps the parties identify and agree upon all of the variables affecting the dispute, and (3) a person with technical knowledge who can translate the issues into an optimization model.

2.  Solving the Model

Once the parameters for dispute model have been determined, a list of feasible solutions can be developed.[71]  From the feasible solutions, the model can be solved for the optimal solution.[72]  If the dispute model involves multi-criteria decisionmaking, the parties will have to provide preferences.[73]

In order to use optimization in an arbitration setting, a separate objective function could be developed for each party to represent its interest.  The arbitrator could use a multi-criteria decisionmaking objective function to weigh the parties’ interests together to create an optimal solution to the entire dispute.  If the arbitrator decides the parties are equal in the dispute, the weights assigned to each party’s objective function would be the same.  However, if the arbitrator decides the parties should not equally share in the outcome, higher weight could be given to the more deserving party.[74]

3.  A Hypothetical Example

Imagine a divorce dispute between a husband (“H”) and a wife (“W”).  First, the parameters of the dispute must be identified.  As divorces disputes typically involve the distribution of common assets, an objective function could be the wife’s settlement.  As W is likely to want the largest settlement possible, her objective function should be maximized.[75]  To develop the objective function to solve for this settlement, the variables effecting the settlement must all be listed.  For simplicity, three will be considered here: weekly alimony payments, the value of the property settlement, and the days per week she gets custody of her children.  Thus, W’s objective function could be to maximize the sum of the alimony payments and the property settlement.  While custody of one’s children is undoubtedly an important consideration in a divorce settlement, custody will not be considered as part of this example’s objective function for simplicity’s sake.[76]  W’s objective function would thus be to maximize S = A + P, where S is the wife’s settlement, A is her weekly alimony payments, and P is her property settlement.

The next step is to identify how the variables interact to form constraints.  First, say the weekly alimony payments are limited to what H can pay, which is one thousand dollars.  Next, the value of the property to be divided is also one thousand dollars.  Finally, the parties agree that H should see his children at least twice a week, so the maximum number of days per week W can have custody is five.  With only these constraints and W seeking to maximize her settlement, she would choose one thousand dollars in alimony and a one thousand dollar property settlement.  Therefore, W would have an optimal solution of two thousand dollars.

A divorce dispute would rarely have constraints as simple as the ones above, and, as there are two sides to a dispute, H would not likely agree to a settlement where he has to pay the full amount he can afford to W.  Two possibilities exist for including H’s point of view in the model.  As previously described, one approach would be to use a multi-criteria decisionmaking objective function to weigh the husband’s interests against the wife’s interests.[77]  A second approach would be implementing H’s preferences as constraints on W’s variables.[78]  If H wants to maximize the days he has custody of the children, a restrain could be that for each day W gets custody, fifty dollars are subtracted from the property settlement.  Likewise, if H is unwilling to pay the maximum property settlement and the maximum alimony, the parties could agree to subtract one percent of the property settlement from the weekly alimony payment.  The parties may also agree that the children need to be cared for, thus five dollars are added to the alimony for each day that the wife has custody.  Finally, because the husband is to pay the wife, not vise-versa, the alimony, property settlement, and days of custody must all be greater than or equal to zero.  There, the complete optimization model for the dispute would be:

Maximize: S = A + P
Subject to: D ≤ 5
P ≤ 1,000 – 50*D
A ≤ 1,000 – .01*P + 5*D
A, P, D ≥ 0

where D is the days per week W gets custody of the children, and the other variables are as described above.  Solving this model, the optimal solution would be for W to never have custody of the children, receive a property settlement of $1000, a weekly alimony of $900, for a total settlement of $1,900.[79]

In the model above, W is only concerned with maximizing her settlement.  Because the value of her settlement is lower for each day she has custody of the children, her optimal solution is to never have custody.  While some people may choose more money over time with their children, others would likely accept less money in order to have custody.  Such conflicting goals can be considered by the model through use of a multi-criteria decisionmaking objective function.  The objective function would be to maximize U = w1*S + w2*D, where S is the settlement objective function, D is the custody objective function, and w1 and w2 are the weights assigned to each.[80]  Assuming that custody is limited to whole days, not partial days, and that the constraint of H having custody at least two days still applies, there are six feasible solutions to the dispute, as shown in the table below.[81]

D 0 1 2 3 4 5
S $1,900 $1,865 $1,830 $1,795 $1,760 $1,725

W’s optimal solution will now depend on the weights assigned to D and S.  If one hundred percent of the weight is placed on the settlement, the optimal solution will still be to have no custody and a $1,900 settlement.[82]  If W places one hundred percent of the weight on having custody, the optimal solution will be to have custody for five days and receive a $1,725 settlement.[83]  If equal weight is given to custody and the settlement, any of the six feasible solutions would be optimal.[84]  In an actual dispute, a party may be likely to assign weights to objectives they determine are more likely to result.[85]

B.  Development of a Means to Implement Dispute Resolution Optimization Models

Even if effective optimization models are created for dispute resolution situations, models in their abstract form will not provide a benefit to the field unless they can be implemented efficiently.  Due to the efficiency and ability of computers to solve mathematical functions quicker than humans, the development of a computer program or system is likely the best way to implement a dispute resolution optimization model.  While existing computer programs allow implementation of optimization models,[86] such programs are not likely designed with lawyers, mediators, or arbitrators in mind, thus the learning curve may dissuade people from using them to resolve disputes.  A better option would be to design a system specifically for use in dispute resolution.  Development of such a system would require a collaborative effort between engineers or computer programmers who have the technical capabilities of creating the system, and lawyers or mediators who have the understanding of the issues and variables affecting the dispute.

Even if a computer program implementing a dispute model is effectively designed, a program with application limited to the specific dispute may not be of widespread or practical use.  As most mediators likely do not wish to act as engineers, and vice versa, a system where collaboration between the two is necessary for every dispute is not a practical means of dispute resolution.  However, as more complex optimization algorithms are developed, the potential for a model that is able to learn from particular disputes and effectively adapt to handle other disputes is quite feasible.

Likewise, an optimization model may be seen as a limited form of dispute resolution because it lacks the behavioral analytical capabilities of a human negotiator.[87]  However, with the development of more advanced artificial intelligence techniques, a computer may be able to learn from and respond to human emotions.  While people employed in the ADR field may argue they provide a service that cannot be duplicated by machines, to think that artificial intelligence will not be eventually be applied to dispute resolution is “unrealistic.”[88]  Until that day, however, the implementation of optimization models in dispute resolution will best be served as a collaborative effort between people familiar with optimization principles and people familiar with the form of dispute resolution being implemented.  Thus, rather than considering if or how optimization can replace dispute resolution, the current focus should be on how optimization techniques can be used as another tool to more effectively and efficiently resolve disputes.

C.  Existing Attempts to Utilize Optimization in Dispute Resolution

Over the past decade, the first steps in applying optimization to dispute resolution have been taken.  Most of these steps have come in the form of “online dispute resolution” programs, with over sixty such programs being offered by 2002.[89]  While some of these programs have existed for over ten years, it is not yet clear whether they are fully accepted as an effective form of dispute resolution.[90]  Additional existing forms of dispute resolution optimization include software based mediation and negotiation support systems.

1.  Online Settlement Programs

The simplest example of using optimization in dispute resolution is an online settlement program.  Many of these programs serve as communication tools, allowing parties in a dispute to submit “blind bids,” from which the computer program determines whether or not a settlement has been achieved.[91]  While a blind bidding system on its own does not represent optimization, more complex programs that add to the system by attempting to account for every possible solution do.  One such example is the “Smartsettle” program.[92]  Unlike many early blind bid websites, Smartsettle is capable of handling multi-party disputes.[93]  Smartsettle implements an optimization method by using a party’s preferences and constraints to generate optimal solutions.[94]  Smartsettle’s goal is to allow each party in a dispute to be better prepared for and supported during the negotiation process.[95]

Despite being an initial attempt to provide the general public dispute optimization, the Smartsettle program has been described as not mirroring “ways in which individuals use technology in their daily lives.”[96]  Having a complicated interface effectively reduces the appeal of such software and does not fulfill the goal of efficiency.  While Smartsettle represents a step in the right direction, there is much room for further development.

2.  Software Based Mediation

In the late 1990s, a group of researchers attempted to create a web-based negotiation system using optimization techniques.[97]  Originally titled “One Accord,” the system was designed to negotiate settlements, including monetary and nonmonetary considerations, over the internet, with the goal of taking negotiators “beyond win-win.”[98]  The system first requires that each disputed issue be submitted; it then allows each party to enter its preferences for the dispute.[99]  The One Accord program uses optimization-based techniques while still requiring a facilitator.[100]  The program requires parties to agree to all existing interests and issues, and the facilitator develops a model based on the provided information.[101]  The facilitator also works with each party individually to assign weights and preferences to the potential outcomes.[102]  Based on the parties’ weights, potential settlements are eliminated, and after each round where no consensus is reached, parties are able to adjust their preferences.[103]  When two parties select the same settlement, the program attempts to make any changes that will maximize benefits for both parties within their specified constraints.[104]

3.  Negotiation Support Systems

A theory of negotiation has been put forward that uses artificial intelligence and game theory as means of implementing optimization principles.[105]  A “negotiation support system” proposes a solution to a conflict based on available information.[106]  These involve combining dialogical reasoning tools with game theory.[107]  Early uses of negotiation support systems ranged from serving as a tool for helping legal experts settle product liability cases to helping insurance claim adjusters evaluate asbestos exposure claims.[108]  An application called Family_Winner uses a game theory and a form of multi-criteria decisionmaking called the Analytical Hierarchy Process to help resolve family law disputes.[109]  The support system uses algorithms to create importance variables based on the parties’ preferences to aid negotiations.[110]

One problem with a pure negotiation support system is that parties may have to assign weights to an issue before discussing the issue, as a party’s preferences may change throughout the course of a dialogue.[111]  Negotiation support systems have also been criticized for focusing only on the parties’ interests, while ignoring issues of justice and power.[112]  Thus, while existing negotiation support systems may be effective at solving disputes in commerce or family life where interests are the main concern,[113] the systems may not yet be effective in areas such as criminal law, where other factors, such as justice and policy concerns, should be taken into consideration.[114]

D.  Benefits of a Dispute Resolution Optimization Model

As described in Section II(C), the main benefits of optimization are increased effectiveness and efficiency, both of which can provide value to the dispute resolution field.  Improving effectiveness ensures that the solution to a dispute is one that is best for both parties.  Increasing efficiency can lead to cheaper costs, allowing more people to have access to effective dispute resolution.  Additionally, use of optimization may provide an incentive for parties to take a results-oriented approach to solving disputes rather than an adversarial approach.

1.  More Effective Problem Solving

The main benefit to developing an optimization model for dispute resolution is the ability to establish every possible solution to problem, thus creating a higher likelihood the problem is solved in the most effective way.  While a dispute over a single yes or no issue only has two possible outcomes, most real life disputes are more complex and involve many issues and sub-issues. A dispute with ten distinct yes or no issues has one thousand twenty four possible outcomes.[115]  Parties attempting to resolve a dispute would undoubtedly dislike spending the time and money needed to list and consider over one thousand outcomes.  However, by developing an optimization model, a computer could quickly print a list of every feasible solution and recommend an optimal result.

Using more advanced optimization methods will allow parties to find a more efficient solution where one is not immediately visible.  Multi-criteria decisionmaking can be used to allow parties to consider independent elements of a dispute simultaneously by assigning preferences, thus weighing the elements against each other.[116]

2.  Cost Efficiency

Optimization offers the field of dispute resolution yet another major benefit: cost savings.  This is a very important benefit because a long dispute can be expensive in time, energy, and money.[117]  A desire to reduce cost is already apparent in many applications of ADR, where technology is gaining a larger role.  A computerized optimization model can manipulate data with speed and accuracy far beyond what a mediator could do individually.[118]

Technology has often led to society having access to resources that were previously unaffordable.  Optimization models have the potential to provide effective dispute resolutions to people who are unable to afford lawyers or mediators.  By having a computer program capable of analyzing the dispute and providing the possible solutions, a dispute facilitator may be able to resolve disputes in a lesser amount of time, thereby reducing parties’ fees.  Also, while  current optimization models do not appear to be a complete replacement for using trained professionals,[119] some would argue that existing applications can provide dispute resolution on their own and at a cheaper price to the parties.[120]

3.  Results Based Dispute Resolution

Optimization can enhance dispute resolution by providing  a results oriented approach.  When parties simply agree on the issues and factors involved, the focus for both sides becomes reaching a result.  Optimization’s bottom-line approach can help prevent parties from posturing, a common problem that can result in tension and parties taking positions further away from a compromise in ordinary negotiations.[121]  Provided the model is fairly designed and implemented, concerns that the solutions offered are biased or arbitrarily determined should also be alleviated.  Use of optimization models supports the idea of “principled negotiation,” the idea that negotiations work best by removing the people’s emotions from the dispute.[122]

Dispute resolution has been described as “multi-party, multi-attribute decisionmaking under uncertainty.”[123]  In a complex dispute, a third party may have an issue that only effects one aspect of the main dispute but is nonetheless necessary to solve in order to find a solution.  Multi-criteria decisionmaking can provide a framework for solving such complex problems.[124]  A multi-criteria objective function could be created, allowing the different issues to be weighed against each other, providing the possibility to examine every feasible solution to the entire dispute.[125]  By approaching a dispute as an optimization problem, dispute resolution professionals can develop an analytic model that better identifies potential solutions and ultimately selects the solution that is best for all parties.

E.  Potential Drawbacks and Resistance to Implementing Optimization as Dispute Resolution

While there are many advantages to applying optimization to dispute resolution, these must be weighed against the potential drawbacks.  The drawbacks represent potential roadblocks in developing the field, including: the need for quality in implementation, societal concerns that may need to be addressed by laws or regulations, and the existence of patents as a barrier to further innovation.

1.  Need to Provide a Quality Form of Dispute Resolution

The biggest concern with using optimization as dispute resolution is the need for certainty and confidence in dispute resolution methods.  Dispute resolution methods need certainty and public confidence before gaining wide acceptance.[126]  The potential for fraud and deception in creating and manipulating optimization models may exist.  If implemented online, strong security measures are needed to protect the information being exchanged.  Additionally, a strict computer method for applying dispute resolution will not be able to account for factors such as body language, which a human mediator or arbitrator could see.[127]

No matter how optimal a settlement is for both sides to a conflict, the terms of the settlement are meaningless without the ability to enforce them.  Consider what might happen if a settlement reached using an online dispute resolution program is not recognized by a court when enforcement is sought.[128]  This is especially true of international disputes.  While the use of optimization in dispute resolution can help improve online dispute resolution between parties on opposite sides of the world, a party is unlikely to want to travel to collect their share of the settlement.  So, without a means of enforcing the result, the money spent resolving the dispute may be wasted.

The use of optimization in dispute resolution also needs to be appropriately priced.  In order to gain wide acceptance as a dispute resolution tool, optimization should be widely utilized.  The best way of achieving wide use is through frequent, low cost disputes.  In order to allow the public to gain value from using optimization dispute resolution, optimization must be offered at a low cost.

2.  Regulatory and Social Policy Concerns Over Optimization of Dispute Resolutions

The second major concern with using optimization as dispute resolution is the potential policy and regulatory implications.  Policy and regulation may be needed to ensure that optimization is being properly applied.  Risks involved may be too great to allow use in arbitration.  Difficult questions arise, such as: What standard of review (and by whom) would be used if a party disputed the result? Does the lack of review suggest that an optimization model can only be used as a tool to provide non-binding solutions?

Using optimization in dispute resolution complicates the public acceptance issue.  One of the main issues that ADR faces in general is gaining acceptance that can only be achieved through public awareness and education on ADR methods.[129]  When optimization is added to the ADR process, the public will not only need to be educated about what ADR is, but also what optimization is.  People are likely to be suspicious of having a computer-implemented algorithm make important decisions for them, so there needs to be a way of effectively communicating that the program is fair and accurate.  However, while dispute resolution methods that heavily rely on technology may receive skepticism now, society may grow more trusting of technology as it begins relying more and more on the internet and computers as integral parts of day-to-day life.[130]

Privacy may also be a greater concern with an optimization based dispute resolution system than with other forms of ADR.  As described in Part IV, optimization is most effective when implemented by a computer program.  However, while the use of a computer can provide a better, more cost efficient result, it also creates a greater capacity to store and transfer personal information.  Computers can “store and manipulate data with speed and accuracy unknown to a mediator using only her head and a pad of paper.”[131]  Thus, a computer model created for a negotiation would, at minimum, have the particular issues and preferences of the parties and possibly include personal information as well.  Depending on who is implementing the model, privacy protections such as attorney-client privilege or arbitration confidentiality may not be present.  A company that develops dispute resolution optimization software has the potential to track users’ information and share it with parties who users would not want to see it.  In the worst possible scenarios, collected personal information could be used to steal a person’s identity or gain access to other personal sites such as emails or bank accounts.[132]

3.  Patentability as a Limit on the Potential of Optimization in Dispute Resolution?

As optimization arises from engineering, applying it presents an issue not likely found in other areas of dispute resolution: patentability.  Some forms of optimization, such as the Smartsettle program, are patented.[133]  Unlike other forms of ADR, optimization is best performed on a computer.[134]  While most new ADR techniques are shared through articles and taught at conferences, people taking the time to develop an effective optimization model for dispute resolution may seek to patent their methods, thus restricting the ability for widespread benefit.  Many such patents have already been granted.[135]  The U.S. Patent and Trademark Office even has a subclass of patents specifically for alternative dispute resolution.[136]  Such patents could be problematic to developing further uses of optimization in dispute resolution, as a patent provides “the right to exclude others from making, using, offering for sale, or selling the invention.”[137]  A person who patents a form of dispute resolution optimization may be able to prevent others from using the same concept, not only preventing the method from reaching the public, but also potentially preventing research that is within the claims of the patent.

Despite the hurdle patents may pose, dispute resolution optimization is worth pursuing for a few reasons.  First, it is unclear whether allowing patents on computer-based forms of dispute resolution will be the exception or the rule.[138]  Second, the benefits provided to society by a successful form of dispute resolution optimization outweigh the associated research costs, even if a patent cannot be granted.  Finally, if patents do become more frequent, they should provide additional incentive to develop the best forms of dispute resolution optimization because  the value of obtaining such a successful patent could be quite high.

V.  Conclusion

As the capabilities of computers and computer programs have grown, the ability to develop optimization models capable of effectively and efficiently solving problems has dramatically increased.  With many businesses and industries already relying on such models to make decisions, development of a means for using optimization models to resolve everyday problems is a natural evolution.  Development of dispute resolution optimization models has many potential benefits.  Optimization models may achieve results that more efficiently balance the conflicting desires of the disputing parties.  The models may provide the parties with assurance that the suggested solution is the best possible solution, not a solution decided arbitrarily or with bias, and not a solution favoring one side more than the other.  Finally, development and acceptance of dispute resolution optimization models may reduce costs associated with hiring lawyers and mediators, and may assist in providing a fair and effective means of dispute resolution without a large economic burden.

Optimization models can potentially serve all areas of ADR.  Models can be used to negotiate between parties with or without guidance of a mediator.  Knowing a settlement will be reached by such models may foster a more collaborative approach between the parties.  Finally, multi-criteria decisionmaking optimization models can provide a valuable tool to arbitrators.

Though the use of optimization models does have drawbacks, the risks can be minimized through effective implementation.  Currently, optimization models can best be applied as a tool for, rather than a replacement of, dispute resolution.  People have already taken the first steps in developing this new field with computerized mediation and negotiation programs.  While these initial attempts have not seemed to gain widespread acceptance for various reasons, many of the issues may be solved as technology continues to evolve.  As the potential for an efficient and effective means of dispute resolution exists, it would be a mistake not to continue to push the bounds of creating dispute resolution optimization models.  Yes, using optimization techniques to solve disputes may sound like a pioneering idea, but society cannot forget that there was a time when using such optimization to wage war and figure out how the human body works also seemed impossible, yet optimization has successfully been applied to those two instances. Imagine what optimization can do for the field of dispute resolution.

 


*J.D. Candidate, May 2013, The Ohio State University Michael E. Moritz College of Law.  This article is dedicated to the late Daniel C. Watson, because I would not have gained the knowledge to write it without his encouragement and guidance.

[1] Singiresu S. Rao, Engineering Optimization: Theory and Practice 1 (4th ed. 2009).

[2] See infra Section II(A).

[3] See infra Section IV(C).

[4] Thomas H. Athey, Systematic Systems Approach: An Integrated Method for Solving Systems Problems 2 (1982).

[5] Wayne L. Winston & Munirpallam Venkataramanan, Introduction to Mathematical Programming 1 (4th ed. 2003).

[6] Athey, supra note 4, at 2.

[7] Vira Chankong & Yacov Y. Haimes, Multiobjective Decision Making:  Theory and Methodology 3 (1983).

[8] A Ravindran, K.M. Ragsdell, & G.V. Reklaitis, Engineering Optimization: Methods and Applications 15 (2d ed. 2006).

[9] Rao, supra note 1, at 1.

[10] Id.

[11] Id.

[12] Id.

[13] Julio R. Banga, Optimization in Computational Systems Biology, 2 BMC Systems Biology 47, 47 (2008).

[14] Id.

[15] Andre Briend, Nicole Darmon, Elaine Ferguson, & Juergen G. Erhardt, Linear Programming: A Mathematical Tool for Analyzing and Optimizing Children’s Diets During the Complementary Feeding Period, 36 J. of Pediatric Gastroenterology & Nutrition 12, 13 (2003).

[16] Id.

[17] Winston & Venkataramanan, supra note 5, at 1.

[18] Rao, supra note 1, at 5.

[19] Ravindran, Ragsdell, & Reklaitis, supra note 8, at 1.

[20] Stuart Russel & Peter Norvig, Artificial Intelligence: A Modern Approach 59 (2d ed. 2003).

[21] G. Fousteri, J. R. Chan, Y. Zheng, C. Whiting, A. Dave, D. Bresson, M. Croft, & M. von Herrath, Virtual Optimization of Nasal Insulin Therapy Predicts Immunization Frequency to Be Crucial for Diabetes Protection, 59 Diabetes 3148 (2010).

[22] See Banga, supra note 13.

[23] See infra Section II(B)(5).

[24] Joseph C. Hartman, Engineering Economics and the Decision Making Process (2007).

[25] Rao, supra note 1, at 1.

[26] Winston & Venkataramanan, supra note 5, at 2.  Although there are other potential objective functions beyond maximizing and minimizing, for simplicity in the purposes of this paper, only these two options will be considered.

[27] Id.

[28] Id.

[29] Id. at 3.

[30] Winston & Venkataramanan, supra note 5, at 3.

[31] See id. at 894–912 (providing various case studies where optimization can be applied).

[32] Id. at 1.

[33] Edwin K.P. Chong & Stanislaw H. Zak, An Introduction to Optimization 541-42 (3d ed. 2008).

[34] Id.

[35] Note that when formulating the model, weights are expressed as decimals or fractions rather than percentages.

[36] For a list of normalization algorithms, see Zenonas Turkis, Edmundas Kazimieras Zavadskas, & Friedel Peldschus, Multi-criteria Optimization System for Decision Making in Construction Design and Management, 61 Engineering Economics 7, 9 (2009).

[37] Rao, supra note 1, at 1.

[38] Winston & Venkataramanan, supra note 5, at 4.

[39] Id.

[40] Id.

[41] Id.

[42] Id.

[43] Winston & Venkataramanan, supra note 5, at 4.

[44] Id.

[45] Chong & Zak, supra note 33, at xiii.  While optimization has its roots in early mathematical theories of Newton and Lagrange, it did not become an effective resource until it could be implemented by computers.   Rao, supra note 1, at 3.

[46] Ravindran, Ragsdell, & Reklaitis, supra note 8, at 1.

[47] Microsoft Excel can solve simple optimization models using the Solver add-in.  See Introduction to Optimization with the Excel Solver Tool, available at http://office.microsoft.com/en-us/excel-help/introduction-to-optimization-with-the-excel-solver-tool-HA001124595.aspx (last visited Apr. 11, 2013).  Another existing program is LINGO, optimization modeling software that can solve linear, nonlinear, and integer models.  See LINGO 13.0- Optimization Modeling Software for Linear, Nonlinear, and Integer Programming, Lindo Systems Inc., http://www.lindo.com/index.php?option=com_content&view=article&id=2&Itemid=10 (last visited Apr. 6, 2013).

[48] MATLAB, a mathematical programming environment, has an optimization toolbox that allows users to add preprogrammed optimization algorithms to their programs.  See Optimization Toolbox 6.0, The MathWorks Inc., (2011), available at http://www.mathworks.com/products/optimization/ (last visited Apr. 6, 2013).  See also An Overview of LINDO API, Lindo Systems Inc., http://www.lindo.com/index.php?option=com_content&view=article&id=1&Itemid=9 (last visited Apr. 6, 2013) (LINDO API allows optimization solvers to be implemented into custom built programs).

[49] Cathy A. Costantino, Second Generation Organizational Conflict Management Systems Design: A Practitioner’s Perspective on Emerging Issues, 14 Harv. Negot. L. Rev. 81, 82 (2009).

[50] Peter Robinson, Arthur Pearlson, & Bernard Mayer, DyADS: Encouraging “Dynamic Adaptive Dispute Systems” in the Organized Workplace, 10 Harv. Negot. L. Rev. 339, 344 (2005).

[51] Amo R. Lodder & John Zeleznikow, Developing an Online Dispute Resolution Environment: Dialogue Tools and Negotiation Support Systems in a Three-Step Model, 10 Harv. Negot. L. Rev. 287, 296 (2005).

[52] Amy S. Moeves & Scott C. Moeves, Two Roads Diverged: A Tale of Technology and Alternative Dispute Resolution, 12 Wm. & Mary Bill of Rts. J. 843, 845 (2004).

[53] Carrie Menkel-Meadow, Are There Systemic Ethics Issues in Dispute System Design? And What We Should [Not] Do About It: Lessons from International and Domestic Fronts, 14 Harv. Negot. L. Rev. 195, 196 (2009).

[54] Howard Raiffa, John Richardson & David Metcalfe, Negotiation Analysis: The Science and Art of Collaborative Decision Making 247 (2002).

[55] Id. at 2.

[56] Id. at 110.

[57] Lodder & Zeleznikow, supra note 51.

[58] Id.

[59] Id. at 297.

[60] Menkel-Meadow, supra note 53.

[61] Lodder & Zeleznikow, supra note 51, at 296.

[62] Moeves & Moeves, supra note 52, at 845.

[63] Id.

[64] See supra Section II(B)(1).

[65] See supra Section II(B)(2).

[66] See supra Section II(B)(3).

[67] An example where an infeasible solution may arise is a land dispute.  If two parties seek to divide a parcel of land, their options are limited by the boundaries of that parcel.  However, if the parties do not accurately know the boundaries, one party may agree to a settlement providing land beyond the boundaries of the disputed parcel.  As the parties have no right to divide land beyond the disputed parcel, such a settlement would be an infeasible solution to the dispute.

[68] Such prejudice can be seen in a dispute where A is seeking money from B.  Provided A is only interested in a damages award that B will actually pay, he is unlikely to seek more money than B actually has.  Thus, the amount of money B has provides a constraint in resolving their dispute.  However, if B falsely portrays his money as less than he actually has, the constraint will be incorrect, and the model would be prejudicial against A.

[69] Lenden Webb, Note & Comment, Brainstorming Meets Online Dispute Resolution, 15 Am. Rev. Int’l Arb. 337, 337 (2004).

[70] Id.

[71] See supra Section II(B)(4).

[72] See supra Section II(B)(5).

[73] See supra Section II(B)(6).

[74] For example, in a divorce dispute, if the husband is found to be more blameworthy than the wife, an arbitrator could assign a seventy-five percent weight to the wife’s objective function and only twenty-five percent weight to the husband’s, rather than assigning fifty percent to each.

[75] As explained in Section II(B)(1), an objective function can either be maximized or minimized depending on what the model is solving.

[76] Unlike alimony or property settlements, custody cannot easily be converted into a monetary value; however, in order to include custody in the objective function, a mathematical relationship between custody and money received would need to be found.  This could be accomplished by assigning a monetary value to a day of custody, however, not all parties will want to quantify time with their children monetarily.  A better approach is to apply multi-criteria decision making, as is demonstrated above.

[77] See supra note 61.  If H and W could not agree to weigh their interests equally, an arbitrator or agreed upon third party would need to step in to assign weights.

[78] The parties would have to agree on such constraints.  Thus, while using a multi-criteria decision making approach may require an arbitrator or other third party, the constraint approach may require a mediator or agreed upon third party to facilitate negotiations.

[79] These values were computed by implementing the model using Microsoft Excel Solver.

[80] As explained in Section II(B)(6), the sum of the weights must equal one hundred percent.

[81] The values were also computed using Microsoft Excel Solver.  Because only six feasible solutions existed, they could be easily listed here.  However, in a more complex dispute, the number of solutions would be much greater and may not be as easily listed.

[82] This solution was reached by normalizing the values of D and S using Weitendorf’s linear normalization method.  See Turkis et al., supra note 36.  The objective function was then solved using Microsoft Excel.

[83] See id.

[84] See id.  In the example, assigning more than fifty percent to either objective function will result in the same optimal solution as assigning one hundred percent to that objective function.  This is due to the simplicity of the dispute provided; in most real life disputes, a range of optimal solutions would exist depending on the assigned weights.  For an example of a typical multi-criteria optimization problem outside the dispute resolution context, see generally Turkis et al., supra note 36.

[85] Lodder & Zeleznikow, supra note 51, at 310 (suggesting a husband in a divorce proceeding who feels his chance of retaining primary custody of the children is low may assign a lower weight to custody).

[86] See supra notes 34–35 and accompanying text.

[87] Gregory Todd Jones, Designing Heuristics: Hybrid Computational Models for the Negotiation of Complex Contracts 167, 168, in Rethinking Negotiation Teaching: Innovations for Context and Culture (2009).

[88] David Allen Larson, Artificial Intelligence: Robots, Avatars, and the Demise of the Human Mediator, 25 Ohio St. J. on Disp. Resol. 105, 163 (2010).

[89] Benjamin G. Davis, Franklin G. Snyder, Kay Elkins Elliott, Peter B. Manzo, Alan Gaitenby, & David Allen Larson, The First International Competition for Online Dispute Resolution: Is this Big, Different and New?, 19 J. Int’l. Arb. 379, 379 (2002).

[90] See David Allen Larson, “Brother, Can You Spare a Dime?” Technology Can Reduce Dispute Resolution Costs When Times Are Tough and Improve Outcomes, 11 Nev. L.J. 523, 559 (2011) (stating that computer dispute resolution programs will not gain widespread acceptance unless they are presented in a manner that is easily to use and understand); Rafal Morek, The Regulatory Framework for Online Dispute Resolution: A Critical View, 38 U. Tol. L. Rev. 163, 192 (2006) (concluding that online dispute resolution has yet to find success due to the flaws in its regulatory framework); But see Joseph W. Goodman, The Pros and Cons of Online Dispute Resolution: An Assessment of Cyber-Mediation Websites, 2003 Duke L. & Tech Rev. 4 (2003) (finding that more complex forms of online mediation have yet to achieve commercial success, but predicting that they will become more popular as the technology involved continues to advance).

[91] Lucille M. Ponte, Throwing Bad Money After Bad: Can Online Dispute Resolution (ODR) Really Deliver the Goods for the Unhappy Internet Shopper?, 3 Tul. J. Tech. & Intell. Prop. 55, 68 (2001).

[92] See Smartsettle, www.smartsettle.com (last visited Apr. 6, 2013).

[93] Moeves & Moeves, supra note 52, at 852.

[94] Lodder & Zeleznikow, supra note 51, at 297.

[95] Id. at 299.

[96] Larson, supra note 90, at 542.

[97] Ernest M. Thiessen & Joseph P. McMahon, Beyond Win-Win in Cyberspace, 15 Ohio St. J. on Disp. Resol. 643, 643 (2000).

[98] Id. at 643.

[99] Computer-Based Method and Apparatus for Interactive Computer-Assisted Negotiations, U.S. Patent No. 5,495,412 (filed Jul. 15, 1994) (issued Feb. 27, 1996).

[100] Ponte, supra note 91, at 73.

[101] Id.

[102] Id. at 73.

[103] Id. at 74.

[104] Id. at 74.

[105] Lodder & Zeleznikow, supra note 51, at 313.

[106] Id. at 289–90.

[107] See id.  For background on dialogical reasoning, see generally Arno R. Lodder & Aimee Herczog, DiaLaw: A Dialogical Framework for Modeling Legal Reasoning, 5 Int’l Conf. on Artificial Intelligence & L. 146, 146–55 (1995).  For background on game theory in negotiation, see generally Emilia Bellucci & John Zeleznikow, Representations of Decision-making Support in Negotiation, 10 J. of Decision Systems 449, 449–79 (2001)

[108] Lodder & Zeleznikow, supra note 51, at 311.

[109] Id. at 310–15.  See also John Zeleznikow & Andrew Stranieri, The Split-up System: Integrating Neural Networks and Rule-Based Reasoning in the Legal Domain, 5 Int’l Conf. on Artificial Intelligence & L. 185, 185–94 (1995).  For an explanation of the Analytical Hierarchy Process, see Thomas L. Saaty, How to Make a Decision: The Analytic Hierarchy Process, 24 Interfaces 19, 19–43 (1994).  For a hypothetical similar to the one presented in Section IV(A)(3), see Lodder & Zeleznikow, supra note 51, at 316–23.

[110] Lodder & Zeleznikow, supra note 51, at 323–24.

[111] Id. at 324 (citing a divorce dispute as an example where parties may be better off attempting to find agreement on some issues, then using a negotiation support system to solve the remaining issues).

[112] John Zeleznikow & Andrew Vincent, Providing Decision Support for Negotiation: The Need for Adding Notions of Fairness to Those of Interests, 38 U. Tol. L. Rev. 1199, 1199 (2007).

[113] Id.; Lodder & Zeleznikow, supra note 51, at 325.  But see Zeleznikow & Vincent, supra note 112, at 1239–40 (concluding that negotiation support systems in the family law context also fail to consider issues of power and justice by only accounting for the interests of the parents and not the children).

[114] See generally Zeleznikow & Vincent, supra note 112 (proposing a negotiation system to take power and  justice into account into sentencing negotiations by advising prisoners of their BATNAs).

[115] As shown by basic arithmetic, 2^10 =1024.

[116] See Section II(B)(6).

[117] Thiessen & McMahon, supra note 97, at 644.

[118] Stephen J. Ware & Sarah Rudolph Cole, Introduction: ADR in Cyberspace, 15 Ohio St. J. on Disp. Resol. 589 (2000).

[119] See supra Part IV(B) (arguing current optimization models are best used as a dispute resolution too, not as an alternative form of dispute resolution).

[120] See Joseph W. Goodman, The Pros and Cons of Online Dispute Resolution: An Assessment of Cyber-Mediation Websites, 2003 Duke L. & Tech. Rev. 3 (2003) (examining how simple forms of online dispute resolution, such as settlement programs, have found commercial success).

[121] Moeves & Moeves, supra note 52, at 854.

[122] Lodder & Zeleznikow, supra note 51, at 325–36.  For information on principled negotiations, see Roger Fisher, William Ury & Bruce Patton, Getting to Yes: Negotiating Agreement Without Giving In 17 (1981).

[123] Gregory Todd Jones, Sustainability, Complexity, and the Negotiation of Constraint, 44 Tulsa L. Rev. 29, 44 (2008).

[124] See Section II(B)(6).

[125] See supra Section II(B)(6).

[126] Ralph Morek, The Regulatory Framework for Online Dispute Resolution: A Critical View, 38 U. Tol. L. Rev. 163 (2006).

[127] Moeves & Moeves, supra note 52, at 843.

[128] Ponte, supra note 91, at 88.

[129] Id. at 90.

[130] See generally David Allen Larson, Technology Mediated Dispute Resolution (TMDR): A New Paradigm for ADR, 21 Ohio St. J. on Disp. Resol. 629 (2006) (examining how modern children communicate differently, with a heavier reliance on technology, and predicting that as these children age, they will likewise solve disputes in a different, more technology dependant manner); see also David A. Larson, Online Dispute Resolution: Do You Know Where Your Children Are?, Negotiation J. 199, 203 (2003) (finding that even among teens, there is a trend in younger teens relying on the internet for communication than older teens, with thirty-seven percent of twelve to fourteen year olds stating the internet helps create friendships and almost one fifth of that same age having used an instant message to end a relationship).

[131] Ware & Cole, supra note 118, at 593.

[132] David Allen Larson, Technology Mediated Dispute Resolution (TMDR): Opportunities and Dangers, 38 U. Tol. L. Rev. 213, 237 (2006).

[133] Smartsettle, www.smartsettle.com/home/about-us/ (last visited Apr. 6, 2013).

[134] See supra Section IV(A)-(B).

[135] See, e.g., Computerized Dispute Resolution System and Method, U.S. Patent 7,831,523 (filed Oct. 13, 2006) (issued Nov. 9, 2010); Computerized Transaction Bargaining System, U.S. Patent No. 7,831,480 (filed Oct. 13, 2006) (issued Nov. 9, 2010); Integrated Electronic Marketplace and Online Dispute Resolution System, U.S. Patent No. 7,630,904 (filed Sep. 26, 2003) (issued Dec. 8, 2009); Electronic Dispute Resolution System, U.S. Patent No. 7,630,903 (filed Feb. 15, 2000) (issued Dec. 8, 2009); Computer-Based Method and Apparatus for Interactive Computer-Assisted Negotiations, U.S. Patent No. 5,495,412 (filed Jul. 15, 1994) (issued Feb. 27, 1996).  However, it should be noted that not all such patents are granted, and it is unclear what the ratio of granted to rejected patents is.  See, e.g., Multivariate Blind Bidding Negotiation Support System Rewarding Smallest Last Session Move, U.S. Patent Publication 2009/0099970 (filed Oct. 14, 2008) (abandoned Jun. 21, 2010); Blind Bidding Negotiation Support System for Any Number of Issues, U.S. Patent Publication 2003/0163406 (filed Dec. 20, 2001) (abandoned Sept. 29, 2009); System and Method for Non-Linear Negotiation, U.S. Patent Publication 2004/0148243 (filed Jan. 28, 2003) (abandoned Feb. 26, 2008).

[136] USPTO Class 705/309: Alternate dispute resolution (defined as “[s]ubject matter drawn to a computerized arrangement for the development or maintenance of procedures or processes (e.g., arbitration, reconciliation, mediation, etc.) that are voluntarily adopted to resolve controversies (or to settle disagreements) before taking recourse to legal action (i.e., litigation)).  United States Patent and Trademark Office, www.uspto.gov (last visited Apr. 11, 2013).

[137] 35 U.S.C. 145 (2011).

[138] See supra note 135.

Posted in: Volume 11, Issue 4

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