Equitable Partition in Kind?
An interesting problem in property law is how to divide a parcel of land between two parties, each of whom own an undivided share of the whole. Traditionally, there were two ways to go about this: partition in kind and partition by sale. The former involves a judicial fiat that divides the property into equitable shares. The later involves selling the whole of the property and dividing the proceeds (minus costs!) between the parties.
In most jurisdictions, partition by sale has become the default, as judges have found the task of dividing property equitably to be too full of intricacies and nuances particular to the parties. However, it’s worth noting that partition by sale has its own problems - particularly in monopsony situations in which the only interested buyer is the party moving for partition. So both of these approaches have serious drawbacks, and there has been a lot of commentary on the injustices of the system.
It seems to me that there is a better way. There are simple and demonstrably fair methods of physically partitioning a parcel of property so that each party receives a fair share in their own subjective assessment. These methods seems to offer a solution to the problems of fairness in partition in kind, and I am curious as to whether there are any reasons why it shouldn’t be the default method of equitable partition in simpler cases.
The problem is analogous to the math problems known as n-player fair-division problems, which involve finding methods of dividing a good (typically, a cake, occasionally, a pizza) in such a way that each player feels he receives at least 1/nth of the whole.
The most basic case involves splitting Blackacre among A & B, both of whom have an undivided 50% interest. A solution for this is to have A draw a line dividing the property into two equally halves of equal value, and then have B select the “half” that seems more desirable. Logically, A’s portion should subjectively (to A) be half of the property. A’s cooperation is all but ensured by the fact that if A should make an inequitable ‘cut’, it would risk B taking its preferred parcel, leaving A short. Since B gets to choose its “half” it is guaranteed at least a subjective 50%. It’s worth noting that this game is surprisingly resistent to attempts by parties to take unfair advantage of the other parties subjective valuations of particular sub-parcels. See H. Steinhaus, The problem of fair division, Econometrica 16 (1948) 101-104.

Also, a multi-round version of the same game can be employed for different distributions. For example, if A has a 75% interest, and B has a 25% interest, then it can be fairly partitioned in a 2-round game:
Round 1: A draws a line dividing the property in half, B selects a partition for A.
Round 2: B draws a line dividing the remainder of the property, intersecting the original boundary and the line drawn in round 1, A then selects a partition for itself. The result is a win-win situation - two contiguous properties that each party values at more than his respective share:

By adding a handful of extra rounds, you can achieve similar results for virtually any percentage. There are also somewhat more complex games that function the same way for larger numbers of parties. See Robertson and Webb, Cake-Cutting Algorithms: Be Fair If You Can. A K Peters, 1998.
There are a few problems with this approach:
- There are some fractions which cannot be perfectly, although nearly anything can be approximated
- What do we do about high value sections of property whose value is destroyed if they are divided (for example, the old family farmhouse that B lives in)?
- While this approach balances the subjective valuations of the parties, it does not necessarily maximize the overall social utility of the property. So on a fundamental level there is a trade-off between equitable fairness and economic efficiency.



