1. Where can I get more information?
2. What if the goods are not divisible?
3. When exactly should AW be used?
4. All in all, what should I know before I attempt to use AW?
5. Given the simplicity of AW, would we need to hire a lawyer?
6. How will I come up with the point assignments?
7. Will AW work with more than two players?
8. I heard that the AW algorithm is patented; is this true?

Where can I get more information?

You can view the links page for more information.

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What if the goods are not divisible?

Under AW, the only good or issue that must be divided is that on which an equitability adjustment is made. This will not be known in advance but only after the application of AW, so all goods and issues must be considered potentially divisible. In applying AW, probably the biggest problem is identifying a set of separable issues on which points are additive.

If the items being divided are not tangible property but more intangible issues, then the parties should decide before AW is applied what each would obtain if it came out the winner on an issue. Only on the one issue on which an equitability adjustment must be made will a finer breakdown actually be necessary.

This is a situation in which a mediator could play a valuable role. He or she could tell the parties the split on this issue but not which party is the relative winner. Each party, not knowing whether it got the larger or the smaller percentage, would then be motivated to reach a fair-minded agreement. This could mean that one party could win entirely on that issue, or receive all of a good, but in turn it would have to pay the other party an agreed-upon amount.

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When exactly should AW be used?

We suggest that AW first be tried out in negotiations that involve easily specified issues or well-defined goods. Examples might include a dispute within a company over the division of job responsibilities, or the division of marital property in a divorce settlement, as illustrated in the examples page. If the procedure works well in these settings, it might be used in more complex negotiations.

We focused on divorce settlements because of the sheer magnitude of the problem - half of all marriages end in divorce in the United States. AW, in our view, provides a straightforward settlement device that takes due account of the interests of both parties. Since the settlement is not the product of protracted negotiations or court battles, it is likely to lead to a more satisfying and durable outcome as well as foster more civil future relations between the parties, which is especially important if children are involved.

But divorce settlements are not the only domain in which the application of AW seems desirable. In the political arena, negotiations over arms control or border disputes often involve a plethora of issues that AW could help to resolve. In the economic sphere, negotiations between labor and management over a new contract, or between two companies over a merger, are usually sufficiently complex that a point-allocation procedure could, we believe, prove very useful in finding a settlement that mirrors each side's most salient concerns.

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All in all, what should I know before I attempt to use AW?

• AW is easily applied to goods but less easily to issues, in which much negotiation must precede its use. In applying AW to goods in, say, a divorce or estate division, the only real difficulty is in each person's assigning points to the goods. If the items are not physical goods but issues that must be resolved, then the parties need to reach agreement - before the application of AW can even begin - on not only what the issues are but also what winning and losing on each issue means. Because there is no mechanical procedure that can resolve difference at this level, this is the area in which a good deal of hard bargaining is to be expected.

• The packaging of issues is crucial in applying AW, particularly breaking up a single large issue into different parts that are as separable as possible. Thus, if salary is the overriding concern in a labor-management dispute, then there is nothing to trade off against losing on this issue. But often an issue like this can be broken down into components, such as basic hourly or piecework rate, overtime wages, pensions, medical benefits, and the like that the employer and the employee value differently. Hence, "salary" is turned into a compensation package, and its components can be treated as separate issues. Care must be taken in packaging items, however, so as to make them relatively independent of each other. This is to ensure that winning on one does not affect how much one wins on another; otherwise, the summation of points across all items would not be meaningful.
  
  
• Manipulation is sufficiently difficult under AW so as not to be a practical problem. One catch in using AW is that, theoretically, one side can do even better, at the expense of the other side, by capitalizing on its advance knowledge of the other side's allocations. This is not usually a serious practical problem, however, because it is highly unlikely that one side would have the precise information it needs about the other side's allocations to exploit AW in this manner. In fact, although being off by only one point can lead to a relatively poor outcome for both parties, the honest party's sincerity guarantees that it will not envy the disingenuous party. Thus, the incentives to exploit AW will be minimal, with honesty guaranteeing a party at least half its total valuation of all items.

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Given the simplicity of AW, would we need to hire a lawyer in a divorce?

The fact that AW may circumvent litigation that drags on in court and drains husbands and wives of their resources may be a social good, but it will not delight lawyers if it robs them of legal fees. We believe, however, that lawyers can play a valuable role in AW's use by

• helping their clients make their point assignments in a way that reflects their honest estimates of worth, thereby enabling them to obtain better settlements;
• assisting them in predicting possible outcomes, perhaps by anticipating the allocations of the other party and running through various scenarios they might face, so as to reduce certainty.

Of course, it will remain for lawyers and courts to determine what constitutes marital property, to which AW can then be applied.

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How will I come up with the point assignments?

While honesty usually pays, it will not always be a simple matter to come up with point assignments that mirror one's valuations of the different issues. One way to facilitate this task is to have the parties begin by ranking the issues, from most to least important, in terms of their desire to get their way on each.

After the issues have been ranked, the parties face the problem of turning a ranking into point assignments that reflect their intensities of preferences for the different issues. In The Art and Science of Negotiation (1982), decision analyst Howard Raiffa discusses this problem in considerable detail, essentially concluding that a party must carefully weigh how much it would be willing to give up on one issue to obtain more on another.

To come up with point assignments, one option for a party would be to begin by rating the importance of winning on its highest-ranked issue, compared with its next-highest-ranked issue, by specifying a ratio. Continuing down the list, comparing the second-highest-ranked issue with the third-highest-ranked issue, and so on, parties would indicate, in relative terms, an "importance ratio" between adjacent issues.

For example, if there are three issues, and the importance ratios are 2:1 on the first issue relative to the second, and 3:2 on the second issue relative to the third, these will translate into a 6:3:2 proportion over the three issues. Rounding to the nearest integer, the point assignments would be 55, 27, and 18, respectively, on the three issues. A more systematic method for eliciting weightings, pioneered by mathematician Thomas L. Saaty and his associates and called "analytic hierarchy processing," could also be used.

Another option for a party is to begin by assigning points intuitively to items. These assignments could be "tested" by asking whether various 50-point packages represent half the total value. To the extent that they do not, the initial point assignments for items would need to be modified. This process would continue until a party is satisfied that no further adjustments in its allocations of points to each item are necessary.

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Will AW work with more than two players?

When there are more than two parties, there is no procedure that will simultaneously satisfy envy-freeness, efficiency, and equitability (see below for an example). However, it turns out that it is always possible to find an allocation that satisfies two of the three properties: A procedure that gives both efficiency and envy-freeness has been obtained by Dutch mathematicians J.H. Reijnierse and J.A.M. Potters; procedures (called "linear programs") that give both efficiency and equitability have been obtained by American mathematician Stephen J. Willson; and an equal division of each item to the parties gives both equitability and envy-freeness.

The following example, given by J.H. Reijnierse and J.A.M. Potters, demonstrates the impossibility of satisfying all three properties (efficiency, envy-freeness, and equitability). Suppose there are three disputants named Ann, Bob, and Carol and assume that they allocate the following numbers of points to items X, Y, and Z:

The only efficient and equitable allocation turns out to be to give X to Ann, Y to Bob and Z to Carol. Obviously, this 40-40-40 allocation is equitable; it can also be shown to be efficient.

But it is not envy-free, because Ann will envy Bob for getting Y, which Ann considers to be worth 50 points. If we gave Y to Ann and X to Bob while still giving Z to Carol, this allocation would be efficient, but it would be neither equitable (because each player would get a different number of his or her points) nor envy-free (because Bob would envy Ann).

Of course, this three-person hypothetical example does not preclude the possibility that all three properties can be satisfied in a particular situation; it says only that it is not always possible to guarantee their satisfaction when there are more than two parties. The fact that one cannot guarantee the satisfaction of efficiency, envy-freeness, and equitability, however, means that a hard choice might have to be made among them in situations with more than two parties.

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I heard that the AW algorithm is patented, is this true?

Yes, the algorithm was patented in 1999 (patent number 5,983,205).

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