Few math majors go into law and those who do rarely go into family law. I’m one of the rare family law attorneys who often thinks in mathematical constructs. A question from last night’s “newbies” class demonstrates the benefits of sometimes thinking like a mathematician when practicing family law.
A newbie asked for advice in resolving a family law issue. Her client, the estranged wife in a short-term marriage, didn’t work or file tax returns. Her “dependency” was of no value to her but was of some considerable value to her husband who wanted to claim her on his tax return. She wanted to know how she should handle this dispute and my answer digressed into a discussion of Pareto optimization.
Vilfredo Pareto was an early-20th Century Italian economist who analyzed social change in economic terms. In his view, any proposed change which could leave all actors better off was a change worth making. Such change is labeled “Pareto optimal.” Often changes which make some actors much better off and some slightly worse off can be made Pareto optimal by transferring some of the benefits from the better off to the worse off.
Rather than fighting over whether husband should be entitled to claim her client as a dependent for tax purposes, I suggested she search for a Pareto optimal solution. For tax purposes, the value of wife’s dependency was worth $0.00 to her. However, her dependency had some value to husband as it would increase his tax refund. For math purposes, we can call the value of the increased refund husband would receive from claiming wife as a dependent “x.” Any agreement that allowed husband to claim wife as a dependent for tax purposes in return for husband paying wife some amount between $1.00 and x-minus-one dollars is Pareto optimal in that it leaves both parties better off. An obvious solution is to have husband pay wife ½ x dollars but that solution isn’t required to make the transfer of wife’s dependency to husband Pareto optimal.
By thinking legalistically rather than mathematically, this Newbie prevented resolution of the dispute. The disagreement wasn’t whether wife had the “right” to claim herself as a dependent for tax purposes; it was really about how to allocate the benefits from that right. Analyzed from that perspective, resolution is much easier.
Pareto optimization explains all agreements, including legal settlements. In any area of the law parties only settle a case–as opposed to letting a judge or jury render their verdict–because they have achieved a Pareto optimal result: a result in which each party–balancing the risks, expected rewards and costs of trial–determines that they are better off accepting the settlement then letting a judge or jury decide. Most attorneys spent little actual time trying cases. Rather, the bulk of our time is litigating, which, in mathematical terms, is merely working on convincing the other side that the benefits of proceeding to verdict are lower than the benefits of accepting a settlement. This can be done by “sweetening” the settlement offer or convincing the other side that its expected benefits are lower or its expected risks are greater than previously thought. Attorneys who understand that settlement can only be achieved through Pareto optimization are much more likely to achieve beneficial results for their clients than attorneys who lose sight of this requirement in the pursuit of “justice.”