Tuesday, May 23, 2006

Symmetry Thesis

Over at Marginal Revolution, Tyler Cowen posts this:

The symmetry thesis: A given person likes (loves) you as much as you like (love) him or her.

I have encountered many apparent refutations of the symmetry thesis, but with time most have turned out to be spurious. I find the symmetry thesis a surprisingly strong predictor of human behavior and inclination.

I have to say I don't get it. He seems to be suggesting that an exogenous increase in how much I like you will prompt a symmetric increase in how much you like me. Certainly, if I like you more I may be willing to do more to make sure you like me, but does this always occur? If I try, am I always successful? Does the relationship return to symmetry? Let's bust open our tool kit and see if we can figure this out.

Recall that how much I like/love you is a function of two things -- the total product of our relationship, how that product is allocated through negotiation/bargaining (and this is heavily affected by what I might expect from choosing the next best option). I ultimately like/love people who, relative to the other available options, provide me with the highest levels of utility. Typically, this involves matching with someone who you combine well with (i.e., you produce alot together) and with whom it is easy to divide the product of the relationship (i.e., there are low bargaining costs).

So let's assume that there is some random increase in how much person A likes person B. I can think of a variety of examples where this might happen, but when it happens do we observe a symmetric increase in B's feelings for A? I don't think this is necessarily true. A and B's ability to achieve symmetry depends on A's ability to get B to like him an equal amount. This requires that A know what to do to affect B's feelings toward him and have the resources to successfully do this. Neither of these things should be taken as given.

For instance, assume that A and B start in a symmetric relationship. Now, imagine a situation where A needs help and B provides it. How will this affect the relationship between A and B? It seems pretty clear that A's regard for B should increase, but it is not obvious that B's regard for A will move symmetrically. In one scenario, B enjoys giving what A required (i.e., providing this assistance is not a cost but a benefit). If the amount that B enjoys giving equals the amount the A appreciates receiving, then the relationship is all square. However, if the amount that B enjoys giving is less than how much A appreciated the help or if (as we expect to usually be the case) providing the assistance to A was actually costly to B, then A needs to "compensate" B in order to re-establish symmetry. Finally, there is the very weird case where the opportunity to help made B like A more than receiving the help increased A's fondness for B. In this case, A needs to actually insult B in some way to re-establish symmetry (this may be what happens in many abusive relationships).

Do we think that A and B will return to the symmetric position? Some might, but many will not because relationship prices are not clearly marked. The return to symmetry requires that A know what B expects in return and that A is able to provide this. If A asked for the favor thinking that it would "cost" less than Y but B agreed to it expecting to be compensated at greater than X (note that this process is further complicated by the fact that relationships frequently don't use tit for tat compensation but rather elaborate subtle exchanges over long periods of time), it is not hard to end up in a situation where Y is less than X. Now, instead of B liking A more, B is disappointed, upset, insulted and likes A less. (This might lead A to like B less, but I don’t think this is the path to symmetry Cowen had in mind.)

Further, in some cases, it is nearly impossible for A and B to achieve symmetry. Imagine that B saved A’s life. A may really like B, but A likely cannot ever transfer enough to B to provoke B to feel the same was toward A.

Ultimately, while how much A likes B is an important determinant of how much B likes A, I do not think that A liking B is sufficient for B to have reciprocal feelings toward A. B may provide A with lots of surplus, but there are still barriers to A’s ability to ensure that B feels the same way. Fixed aspects of A may prevent A from producing things that B values highly (e.g., B may want someone who looks a certain way or is of a certain ethnic or religious background). Similarly, A may face a binding resource constraint and may not be able to transfer any more of his relationship surplus to his partner because he cannot afford what his partner wants. Or, as in the case above, A may not be able to figure out the right mix of stuff to provide before B gives up on him.

Finally (on a slightly different note), it is possible that the local friendship/mate markets are skewed. Particularly in the mating market, if there are not equal numbers of available men and women of appropriate quality, we actually expect to observe asymmetric relationships. Those in short supply face strong outside options and, as such, should be able to extract more than their share of the relationship product. So, outside options also an affect relationship symmetry.

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