Wednesday, October 27, 2010

The Normative Economics of Dating

Anyone who's ever been in a longer-term relationship will probably be familiar with the bothersome issue of picking up the bill after a nice meal out.  Who should pay?  What is the most just allocation of the couple's scarce resources?  This is a pretty complex issue, but by breaking it down we can generate some nice rules that simplify the whole question, leaving us free to ponder other mysteries, like what to get our significant other for valentine's day.

Before we can deduce a set of rules, lets take a look at the situation as it exists today.  By comparing the complexity of payment rules with the strength (seriousness, length, etc.) of the relationship, a striking pattern emerges:



Initially, the guy pays.  Sorry dudes, but that's just the way it is.  The upside is that it's simple.  As a relationship gets more serious, it becomes absurd for one person to constantly pay, so some cost-sharing scheme usually emerges.  This middle phase is by far the most complex: how often should each person pay, and what practical method should be used to determine this cost-sharing?  As a relationship matures (cohabitation, marriage, etc.) some form of economic union usually forms, again simplifying the issue.

So what about that middle phase?  For the sake of argument, let's assume the couple wants to split costs 50-50.  It's a huge hassle to split every bill, especially given credit card transactions.  Conversely, keeping a record of all expenses then settling up later is just too weird, and may hinder progress along that x-axis.  Alternating every other meal is dangerous, because the person not paying that day has a huge incentive to spend a lot.  What we need is a rule that's simple and keeps both people uncertain about who's paying.

What we need is expected value.  Here's the rule: every time that pesky bill arrives, flip a coin.  Heads, one person pays the entire bill.  Tails, the opposite person pays the entire bill.  It's incredibly simple, plus nobody knows in advance who's paying, which eliminates the risk of dessert inflation.  Let me head off a possible objection: what if one person gets stuck paying the entire anniversary meal at a really expensive restaurant?  Shrug it off.  The perceived injustice is a fallacy.  The other party has paid for half the meal in a probabilistic sense.  Because each person's expected value (probability of paying multiplied by the amount) is the same every time, this rule is perfectly equitable.  Furthermore, the rule is easily modifiable by using different-sided dice (maybe the guy should pay 60% of the time, because he tends to eat more).

 If you end up paying for three anniversary dinners in a row, don't get discouraged.  Over time, the proportion of money paid by each person should come to reflect the agreed-upon probabilities.

3 comments :

  1. Very thoughtful analysis, and I agree with just about all of your points. However, I think the coin flip solution needs to have a very clear ban on table talk. I can easily see the Doe Eyes Corollary coming into play, i.e., when the coin has decided who pays, but the paying party is able to come up with reasons x, y, and z why they shouldn't pay, and just look too durned cute in the process. If this type of situation emerges, you are right back to the middle of the curve in terms of complexity, because you have reintroduced negotiation and the accompanying awkwardness / hurt feelings.

    My solution: don't date. Or if you do, don't go out to dinner.

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  2. You could probably grow this idea into a book -- lots of interesting potential here -- as long as you continue your research...

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  3. I don't see why more people don't just get separate checks. so easy and no one getting butthurt over paying a check three times in a row! p.s. I like your blog.

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