Fair division in homeowner association fees

I received a great email from Hector regarding game theory:

Hi Presh. I enjoy your blog a lot, and recently a situation arose where I think game theory could be applied, so I thought I’d send you an email to see if you have any opinion on it.

Here in Mexico, “private” neighborhoods are common, which means that the neighborhood is closed to any outsiders, and there’s a guard controlling access and taking care of security. All the neighbors are charged a monthly fee to pay for the guards salary and any extras that might be needed in the neighborhood, such as supplies for the guards, common improvements, etc.

The amount of the fees is decided by a council formed form neighbors. I own a house in one such neighborhood, but I don’t live there and probably won’t live there in the near future, yet the neighbors expect everyone to pay the monthly fee. Since the neighborhood is new, almost half the houses are uninhabited at this moment, so the decision that everyone would pay the fee was taken mostly by the current neighbors. I assume that the other houses will be occupied soon, as it’s a small neighborhood and all the houses have already been sold.

I’ve asked to a couple of friends who live in similar places and they tell me that in their cases, it was decided that people would only start paying after moving into the house, as prior to that, they had not much need for security.

So, on one hand, the neighbors expect me to pay the monthly fee, and on the other hand, I don’t think it’s fair to pay it as the house is empty and I won’t be living there anytime soon. But, I have to consider that I might live there some day, and I wouldn’t want the neighbors to think ill of me.

So, I’m thinking that I might be able to negotiate some partial fee, until I move in there.

What do you think?

My thoughts

(I replied to Hector with a few thoughts. Later I elaborated and here is my current thinking.)

This is a great question–thanks for asking Hector. The topic falls under what is called coalitional or “cooperative” game theory.

The question is: what is the fair division of the fees? How might one negotiate a lower fee?

Fair division is interesting because depends both on game theory and on social customs. As such, there are few universal answers. But there are some methods in fair division which are more popular than others. Three of the fair division methods I’ve discussed before are splitting evenly, proportional division, and equal division of the contested sum. Let’s discuss how these methods might be applicable.

Splitting evenly means simply divide the fees across all houses. The logic here is that it is the house, not the property value or residence, that matters. The arguments for splitting evenly are that its simple to implement and its a forced equality in that everyone pays the same. The arguments against are that its unfair to low-end users (as is your case), and also that splitting evenly can lead to a type of tragedy of the commons where costs are inflated for all. For instance, in the case of splitting the bill at restaurants, a group of three economists have demonstrated an even split leads to inefficient ordering and negative externalities for all.

Another method commonly used is proportional division. Proportional division means each party should pay relative to their contribution to cost (or their size of benefit). In a neighborhood, bigger houses might cost more to monitor and also they receive a larger benefit from security. So a proportional division might translate to homeowners paying neighborhood fees relative to their property values or plot size.

Proportional division is good because it assesses fees relative to costs imposed, and consequently parties will not inflate costs as in the splitting evenly system. The problem with proportional division is that it requires everyone to agree on a valuation system. Also, if it is hard to track payments (like when collecting money in a large restaurant group), some parties are likely to underpay. The shortfall is usually covered by the group evenly.

A final method worth discussing is equal division of the contested sum. This fair division method was first discussed over 2,000 years ago in the Jewish Talmud. It’s an interesting method that depends on splitting the disputed sum or the gains of negotiation. (See a detailed explanation in how game theory solved a religious mystery)

Here is a simplified example where equal division could be applied to a homeowner setting. Suppose that an inhabited house would cost $100 to maintain and secure whereas an uninhabited house would cost $50. But if both ordered together, they could negotiate a reduced fee of $120. Both can gain from cooperation, but how should the cost be split?

A first approach might be to split the cost evenly at $60 a piece. But this solution is not appealing, as the owner of the uninhabited house has to pay more than if he negotiated alone. Another method could be proportional division of the cost. In this case, the split would equate to a cost of $80 for the inhabited home and $40 for the uninhabited home. This is reasonable, though one can see the savings are uneven. The cost for the inhabited home falls by $20 versus the cost for the uninhabited home falls by only $10.

So another way to approach the situation is to split the savings equally. First, we need to calculate the savings from joint negotiation. We can see that if each owner went alone, it would cost a total of $150 as opposed to $120 in joint negotiation. This means there is a potential of $30 in savings from cooperation.  Accordingly, if each party gets half of the savings, then each should get $15 back. This means the costs would be $85 for the inhabited home and $35 for the uninhabited home. This is one application of equal division of the contested sum. Notice the result is close to proportional division though not exactly the same.

So after saying all of this, which method seems best? I leave it for you to judge, but I will mention the custom in my area. The closest analogy in my state is homeowner association fees or condo association fees. These fees cover costs like maintaining common lawns, amenities like pools and gyms, repairs, and so on. These fees are generally split evenly to the dismay of many residents.

And that is why I am anxiously awaiting an association that proposes an equal division of the contested sum

Discussion questions

1. Why do you think homeowner association fees are often split evenly?

2. Naturally homeowner association fees increase over time to reflect inflation and other cost increases. Why else might homeowner association fees increase? See the following: HOA fees rising in California.

3. During a bad economy, would you expect homeowner association fees to rise or fall? How might this change if costs were shared differently? See: fees on the rise and adverse selection example.