do you suppose this is already widely known?

[Paul E Johnson]

June 10, 2002
Paul Johnson address@hidden

Source code available on

http://lark.cc.ukans.edu/~pauljohn/Swarm/MySwarmCode/Marriage

Notes  on Marriage program.

I recently attend a conference on social context ("A Conference on the
Social Context of Politics," Brown University, June 2-4, 2002,
organized by Alan Zuckerman) and a paper by Laura Stoker and M. Kent
Jennings ("Political Similarity and Influence between Husbands and
Wives") struck a chord of curiosity for me.  Stoker and Jennings
observed that, in a panel study of continuously married couples, the
married people seemed to be exerting opinion influence on one
another. Married men and women grew together, and this led to a very
interesting insight on the gender gap: the gap between single men and
women is much greater than the gap between married people.  This was
one hint about the impact of social context in the small (a marriage)
on the politically relevant and important aggregate levels in society.

I suspected that there was a statistical anomaly due to the fact that
some couples were divorced and dropped out of the sample as the years
went through. I suspected that dropout problem would create a spurious
correlation.  Even if individual opinions were changing completely at
random and independently, it seemed to me that married couples would
appear to influence each other because the ones who (randomly) grow
apart would be divorced.  I thought the selection problem would play
havoc with the ability to measure impacts of spouses on one another.

So I set out to build a simulation to find out if I was right. I used
the Swarm template code as a starting point, used a few tricks I
learned through the years working on the Swarm Docs, and assembled
this model in a total of about 8 hours of programming. The model has
some things in common with another project I have done, so I could use
some idioms from that other project. I did not bother to build in a
lot of graphical user interface here.  Also, I have not bothered to
develop a lot of diagnostic information that people might like.  But I
have answered the central question.

Here is the way the model works.  Imagine men and women created as
agents who have an opinion vector with 10 items, each of which is
either 0 or 1.  Women can search through the pool of men. If they can
find a man that disagrees with them on 3 or fewer items, then they
marry. I gave each woman a limited number of attempts to find a
suitable man, searching quite at random among the singles. That leads
to a batch of marriages upon which we can experiment. We can track the
state of "currently married" couples at any given time, and we can also
observe the effect of divorce on the opinion pool of married people.

Where does divorce happen?  Suppose "god" or the TV networks (ha!)
cause a small rate of random change in public opinion. This is a very
small change, and it randomly affects men and women.  The married
people do not persuade one another.  After the random changes occur at
each timestep, the married couples reevaluate. If they have grown
apart, so they now disagree on more than 3 features, they get
divorced.

We can track the overall level of disgreement among married couples.
We can also take a sample of the couples whose marriages last up until
a given instant, and then plot how unhappy they were before.  This
last kind of information is the kind we need to judge the effect found
by Stoker and Jennings.

In the 2 image files, marriage1.png and marriage2.png, that are
distributed with the source code for this program, or on my web page
at http://lark.cc.ukans.edu/~pauljohn/Swarm/MySwarmCode/Marriage, you
can take a look at the model result.  The first one is for a sample
size of 10000 men and 10000 women, and the second is for 30000 of
each.  The second one takes a long time to run, but at the end of the
first simulation, the number of marriages is small enough to make you
wonder if the main result is correct, so I ran it with a bigger batch.
It turns out the result is the same.

Look at the first picture, first row, top left.  That shows the
disagreement level among couples who are married at a given time. Note
that, when you take a sample at each time point, and you ask the
married people how much they disagree with each other, the level of
observed disagreement is almost uniformly falling.  That happens
because some random changes bring people together, while random
changes that cause difference may lead to divorce.  So it appears
marriage causes harmony, but that's a result of selection and
randomness, rather than interpersonal persuasion. How gratifying
to find something I expect!

Here's the big shocker.  The other graphs show disagreement levels for
"panels" of married couples. The first is for couples who last 20
timesteps.  Note the apparently U shaped nature of disagreement levels
observed in continuously married couples. Whether you take a sample
after 20 periods, or 40 periods, or 100 periods, the shape is the
same. The graph of average disagreement levels gets more jagged
because the size of the panel is declining.

I believe these results indicate something extremely useful for
students of persuasion within marriages.  Suppose the null hypothesis
is that husbands and wives do not persuade each other.  This means
that, if we talk to people who are continuously married, and we check
to see if their opinions are changing recently, then the "null
hypothesis" should be that the distance between them is increasing.
That means the effect that Stoker and Jennings found is actually more
important than they (or I) thought.  They were comparing the impact of
spouses on each other with the null hypo of 0 effect, whereas according
to this simulation result, the null effect should be for couples to be
growing apart.

Once you think about the U shaped curve for a while, you start to
figure it is obvious and you should not have expected anything else.
I suppose.

pj
Lawrence, Kansas
--
Paul E. Johnson                       email: address@hidden
Dept. of Political Science            http://lark.cc.ku.edu/~pauljohn
1541 Lilac Lane, Rm 504
University of Kansas                  Office: (785) 864-9086
Lawrence, Kansas 66044-3177           FAX: (785) 864-5700



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