Game Theory and Mormon History

So let’s think about Zion as a prisoner’s dilemma (PD). Over the course of nineteenth century Mormon history you see a succession of attempts to create an ideal community based on cooperation and some degree of self-sacrifice. Hence, you have the law of consecration in Missouri (and to a lesser extent Ohio) followed by various collective enterprises in the Great Basin. Under a simplified game theoretic explanation of Mormon history, these successive attempts to create Zion represent differing solutions to the PD.

A PD is a game in which two people are faced with a choice: they can either cooperate or defect. The highest joint payout comes in they both cooperate. However, if one party defects while the other party cooperates, then the defecting party realizes a greater personal gain and the cooperating party gets shafted. However, if both parties defect then they both lose, but less than if they are the schmoe who cooperates when the other guy defects. Clear? In a PD the best thing to do if you want to maximize your pay offs, is to defect. This is called the dominant strategy.

The PD is a pretty useful little concept. It allows you to think about all sorts of cooperative interactions. For example, Hobbes’s argument about the state of nature is basically a kind of proto-statement of the PD. Everyone has an incentive to defect from cooperation and we are all left with a life that is nasty brutish and short. Indeed, virtually any cooperative endeavor where one person has an opportunity to take advantage of another person’s trust can be thought of as a PD. Hence, Zion, if you will, is a PD.

Now there are a couple of standard solutions to the PD. First, you can create enforceable contracts. Both parties agree to cooperate and then some third party will sanction any party who reneges on the agreement and defects. Second, if the players play the PD game several times, then they can retaliate against defectors in the next game. Here is how it works. A and B are in a PD. A always cooperates, unless B defects. If B defects, then the next round A will defect. In the third round, A will cooperate. B does the same thing. This tit-for-tat strategy results in a long term equilibrium of cooperation. A closely related solution to the PD is reputation. If A can observe the way that B plays the game, then B has an incentive not to be known as a defector because no one will cooperate with him. A third solution to the PD is ideological. One instills beliefs about the evil of defection independent of the immediate payout from defection in an attempt to constrain behavior. Finally, one can solve the PD by simply raising the costs of defection, so that anyone who defects will sanctioned or will have to incur some other major cost.

OK, back to Mormon history. As it turns out, the 19th century Mormons pursued all of these strategies. The first two strategies that they used in Missouri and Ohio were basically legal and ideological. They tried to structure the cooperative aspects of Zion as legally enforceable agreements that would solve the problem of defection. The courts, however, were almost universally hostile to these attempts and as a result, contract enforcement proved an ineffective solution to the Zion PD. The other attempted solution to the PD was ideological. Joseph and others taught that the failure to cooperate was sinful, etc. This also proved inadequate (as attested to by the rebukes of the saints sinfulness contained in the Doctrine & Covenants).

The move to Utah, however, change the nature of the game and made the PD more manageable, at least for a time. First, the size (small) and isolation of Mormon communities in the West meant that people were of necessity repeat players with one another. As a result, the tit for tat strategies and reputational effects mitigated against defection. Second, isolation dramatically increased the costs of defection, because it was very difficult to go elsewhere to avoid the social ostracism and the like resulting from defection.

One would therefore expect that as the cost of transportation (and hence isolation) decreased and the population increased that the PD problems would become more acute. One would respond to the declining effectiveness of the geographic solution to the PD by increased reliance on law and ideology to solve the problem. And this is what we observe. With the railroad and the influx of people into Utah, the older cooperative systems began to break down. Church leaders, especially BY, responded with increased sermonizing on the importance of cooperation and new legal forms (co-operative joint stock companies) designed to make defection more difficult.

17 comments for “Game Theory and Mormon History”

1. greenfrog
June 14, 2005 at 6:36 pm

This sheds an interesting perspective on the timing and content of the Church’s Proclamation on the Economy.

Thanks.

2. john fowles
June 14, 2005 at 7:30 pm

I agree that the PD model is very useful in looking at the United Order and cooperative experiments of the early Saints. It also shows the social entropy, so to speak, of the telestial social order where we do indeed live in Hobbes’s world and the PD is our subconscious approach to these types of economic configurations, and perhaps even to relationships in general. As you noted, the best joint outcome is when both players cooperate. Both players would cooperate in such an endeavor, out of their own free will, if they were removed from the Hobbesian world. To use LDS terminology, it would take, perhaps, at least a terrestrial world to allow both parties to set aside the suspicion and desire to maximize their own individual benefit, which is done by defecting (because they can’t count on the other person to cooperate). In other words, in a world in which the nature of men and women is presumed to be fundamentally evil (that is, our current world) and our institutions and world is structured around that principle (see e.g. U.S. Constitution; see also Federalist 10 & 51), defection is the way to go–no way around it. If the foundational premises are altered, however, so that the nature of mankind is not fundamential greed and evil but rather Christian virture (i.e. the Millenium), then defection loses its appeal because of the mutual trust that the new nature of things entails.

In the telestial, Hobbesian world, therefore, some kind of outside enforcement is needed to achieve the mutual cooperation because it will not–it cannot–happen by itself. This will be, as you noted, either institutional enforcement (the law) or perhaps ideological coercion (religious dogma). Neither of these has thus far survived the other external factors that you observe in the decline of these United Orders in the LDS experience. And they have failed miserably in the totalitarian experiments of every single Marxist state that has thus far existed. That is because, in the case of the latter, the foundational premises remained the same and were even strengthened through the criminalization or ridicule of religion. In the case of the former, it appears that religious belief, while salvatory on a personal level in the sense that it invites an individual to improve him or herself in virtue, has not been sufficient to overcome the suspicion of the other that causes defection. In other words, does being Christlike in the Hobbesian world require allowing the other side to defect on you while you try to cooperate out of Christlike motives? I would say it probably does, but who among us is strong enough to ignore the natural man within and defect to maximize our own utility (or should I say minimize our own loss), even while at the same time trying to follow the precepts of the Gospel?

3. Daylan Darby
June 14, 2005 at 9:52 pm

God bless the free market…

June 14, 2005 at 10:52 pm

Of course, if the problems facing the United Order were purely those of the prisoner’s dilemma, it would have been a lot more successful than it was.

5. June 15, 2005 at 10:13 am

There are lots of ways of thinking about this, but one way to look at it is that the PD arises because individuals do not sufficiently value the happiness of other people. In a word, they are selfish. If one does value the happiness of others, then your gain from defection is obliterated by the loss of the other person, and so it is no longer a gain. A fair chunk of the behavioral implications of the gospel can be summed up in the counsel that we should:

1. care about other’s utility (be selfless) and
2. not discount the future (be patient)

6. john fowles
June 15, 2005 at 11:38 am

Frank, I am tempted to think that “trust” is more central than “selflessness.” You can be selfless and care about the good and welfare of others but still defect in the PD because you simply cannot trust that the other will also cooperate, thus causing you to minimize your losses by defecting rather than establishing the highest joint utility. It isn’t really a matter of lack of charity or caring.

However, we do have successful examples of cooperation in the PD. In every instance, it was a product of the type of homogeneity that is often decried as somehow inherently bad in our present society. The homogeneity of which I speak is that societies that have succeeded in achieving joint cooperation in the PD model (Enoch, Fourth Nephi) were homogeneously of one mind about their temporal existence. Their shared and sincere faith in Christ was the common thread binding them together and allowing them to break free of the Hobbesian world and enter a type of terrestrial existence where each individual, it seems, could trust that the other individuals in the society would also cooperate out of their own volition, and not because of outside coercion of any kind. That kind of absolute trust, I imagine, also freed all the people from other anxious endeavors common to our telestial existence.

7. Nate Oman
June 15, 2005 at 11:49 am

John Fowles: If A actually values B’s utility as his own, then he will cooperate when B defects. Indeed, since this is the situation in which B’s payout is highest, if A is interested in maximizing B’s payoff he will want B to defect when he cooperates. Yet this somehow seems wrong to me. Hence, I would question Frank’s idea that the gospel should always be thought of as striving to create interpresonal utility functions.

BTW, ideology, as used in my post, was not meant to be pajoritive or refer to religious dogma or some other “bad” form of religion. I was trying — no doubt unsuccessfully — to use it the way that Douglas North and others in the New Institutional Economics use it, namely as a way of describing endogenous shifts in preferences that shift behavior in the same way as exogenous shifts in incentives.

8. john fowles
June 15, 2005 at 12:14 pm

Nate, that’s one reason why I prefer to say “minimize losses” when describing motivations for defection because it orients the focus away from selfishness (but does not deny the role of selfishness in the process) and emphasizes that the root of the problem is lack of common striving–people not being capable, as a group, to be “of one mind” in their Christian living.

Do you think that the homogeneity that I mentioned could have led to some of the more successful UO attempts rather than some of the rational external factors that you mentioned as enabling Deseret-era PD cooperation? On this aspect you wrote

The move to Utah, however, change the nature of the game and made the PD more manageable, at least for a time. First, the size (small) and isolation of Mormon communities in the West meant that people were of necessity repeat players with one another. As a result, the tit for tat strategies and reputational effects mitigated against defection. Second, isolation dramatically increased the costs of defection, because it was very difficult to go elsewhere to avoid the social ostracism and the like resulting from defection.

I agree with you on this. Speaking of factors that changed the cost-benefit analysis in the PD is helpful and useful. But, rather than the slightly cynical (though logical and understandable, given certain foundational premises) identification of the threat of ostracism or reciprocity as enabling factors, perhaps it was much simpler although less economically quantifiable: the Saints gathered in religiously homogeneous communities, commissioned from the center (by Brigham Young), and were thus freed, through their common participation in a divinely sanctioned mission and through being “of one mind” in this mission based on their faith in the Restored Gospel of Jesus Christ, from the distrust of “the other” which could be seen as the reason for defection in the PD. Gradually, however, because of the telestial world in which we live, the natural man began to take over again and people lost their sense of “being of one mind,” which began causing people to defect again rather than cooperate. It happened eventually in Fourth Nephi too, although it took much longer there than in the Deseret communities.

9. Mike McBride
June 15, 2005 at 12:31 pm

Couldn’t pass this one up since I’m a game theorist.

Thanks for summarizing these key points, Nate. This is standard game theory. I just taught all of this to my undergrads two weeks ago in my lectures on repeated games–not in the context of the Law of Consecration, of course. I also brought all this up (this time in the context of communitarian practices) some weeks ago in our grad student/young married Church History institute class here at UC Irvine. I think it really helps us understand the difficulties in implementing the Law of Consecration or other cooperative practices.

As a side note in support of Nate’s comments, I mention that the Church courts often operated as the de facto courts of the land in the UT Territory. Even non-LDS would often come to LDS bishops to settle cases. A number of federally appointed Territorial leaders would just not stay in UT for various reasons, and so the LDS were basically left to run themselves, which, of course, they would have largely done even if the Territorial leaders stayed. But this just couldn’t last as more non-LDS lived in the UT Territory (as Nate mentioned), and as Federal persecution intensified later in the century. The persecution focused on polygamy but also sought to end Mormon political and economic hegemony and practices, which were seen as “un-American” (which is how many LDS would view the practices today!).

As a second side note, the last couple decades have seen the proliferation of “Behavioral Game Theory” which tries to understand, among other things, the powerful social and psychological factors at work in real life “games.” A nice recent but expensive book is Camerer, _Behavioral Game Theory_, Princeton Univ Press. One of the key lessons of this work is that social and psychological factors (such as ideology) can greatly influence behavior in such situations as the PD game. But they are just one of the many competing factors.

Can’t wait for the next game theoretic spin on Mormonism. There’s still so much to be said…

10. Nate Oman
June 15, 2005 at 12:38 pm

John: I suspect that you are right that homogeneity and trust played an important role. My question is whether or not we can come up with a sharper explanation for their decline than the “take over of the terrestial world.” I am not necessarily dismissing your theological claim, but I am suggesting that thinking about the concete solutions to the PD embedded in the mid-19th century Mormon commonwealth helps us to understand which changes caused those solutions to breakdown.

11. Nate Oman
June 15, 2005 at 12:49 pm

Mike: Thanks for commenting. I am curious as to what you see as being other possiblities for game theory an Mormon studies? You might also be interested in these posts:

12. Mike McBride
June 16, 2005 at 4:01 am

Nate: I actually commented on your “Why Aren’t There More Economists…” post. In fact, I commented that applying basic game theory to understand the attempts at implementing the Law of Consecration is a topic I’d consider “low-hanging fruit.” Your comments give a nice glimpse of how interesting such analysis can be.

Other applications of game theory to Mormonism? Let me give just two examples. (I must postpone my book until after getting tenured.)

TENSION IN A GLOBAL CHURCH
Sociologists of religion often talk about a denomination’s “tension” with its surrounding environment as one of its key characteristics, eg, behavioral requirements imposed on members prevent them from engaging in many aspects of social behavior in their city. This tension makes maintaining membership costly, but also serves to screen out those not willing to make sacrifices. Some degree of tension thus helps maintain a membership with high committment levels. Mormons in Missouri and Nauvoo eventually both existed in a state of high tension. Moving to UT led to a reduction in tension, but even that increased with increasing contact with outsiders. Put one way, the transition period 1890-1930 consisted of a reduction of tension between LDS and non-LDS. Today, LDS in UT exist in a lower level of tension than LDS in CA, which is lower than in NY, which is lower than in England, which is lower than in Germany and Japan, and so on.
While some degree of tension is necessary, what is the optimal level? Any answer must use some form of game theory since the optimum depends on the strategic interaction between the Church and other denomninations in the particular religious market, and between the Church and current and potential members. Moreover, the optimal tension in UT is different than the optimum tension in Bulgaria. This raises natural questions about how the Church can maintain some degree of unity and commonality while still adapting optimally to various locations. This topic is both theoretically interesting and relevant practically.
BTW, the religion literature on tension has largely ignored the strategic elements so fundamental in understanding cross-denominational tension. There are only a few papers on it (actually, I have a couple papers on it; please excuse the plug).

SIGNALLING, WHITE SHIRTS, AND CHURCH NORMS
Why do men wear white shirts to Church? Sure they’re encouraged to do so, and some may just think they look good. But wearing white shirts and adhering to other ultimately trivial Church norms can serve an important function of signalling to other Church members one’s committment to the Church.
Members live and function in a Church replete with incomplete information–which is game theory speak for a lack of information about certain characteristics of the individuals you interact with. Eg, you don’t know if the other person is nice or mean. If I know you’re mean, I will choose to not interact with you, but I will if I know you’re nice. If I don’t know, I might choose to not interact if I think you’re very likely to be mean, which means I may miss a good opportunity to interact if you are in actually nice.
So how do people respond to these settings? Send me a signal. If the signal is too costly for mean people to undertake, and if I observe the signal, then I know you’re nice, so I interact with you. Notice that you’re worse off than if you didn’t have to send the signal. But while this is not the best overall, it is the best outcome for a world with incomplete info.
Abiding Church norms sends signals. “She’ll be RS Pres someday” because her behavior signals her commitment. Same for a guy you think might be the next Bp. Church leaders are also aware of these signals. Of course, this system only works if the signals are generally informative. In real life, signals are imperfect. A few mean people might be able to send them cheaply and deceive me (“he’s picking up chairs because he’s bucking for a different calling”). Or some nice people may find certain signals too costly (“the best Mormon in the ward doesn’t shave”). Also, a person might unwittingly send a signal (“he wears white because he likes white not because the Church leader said to”).
Overall, this system is quite complex and far from perfect since we often misinterpret others’ behavior. The brain must make so many judgements in situations characterized by incomplete info, so it just uses whatever info it has and often makes incorrect inferences. We must strive to rely less on imperfect signals by getting to know others and by following the Spirit. This is one of then many reasons why limiting congregation sizes is so important. The repeated interaction encouraged by limited sizes allows people’s characterstics to be revealed. However, even that cannot fully reveal characterstics. As long as there’s some incomplete info, there will be an important role for signals, and the signal itself is often quite arbitrary, eg, blue shirts might be the signal on planet X. (How norms form and persist is another application of game theory.) I think we should understand it for what it is without being overly critical. Though imperfect, signals serve an important purpose.

Much more to say on each of these, but I’ll stop here. I commend all who read this far. Other applications must wait for another time…

13. Brian G
June 16, 2005 at 4:17 am

Mike McBride finally throws his hat into the ring.

14. Ty
June 16, 2005 at 11:19 am

Most importantly, in Zion the contracts are incomplete since it is difficult, if not impossible to observe whether our neighbor is consecrating his all.

But the previous posts are right in that the only way to solve the PD (tragedy of the commons) is by changing the game and having utilities where cheating is not the dominant strategy.

John F.–the situation you describe is called “turning the other cheek”

This is my first post, by the way…

15. June 18, 2005 at 1:36 pm

Complete threadjack, but I’ve been curious why some of the sexual abuse victims of Jeffs, et al., have not sued him under RICO — seems that taking all the land away (like they did to the neo-KKK types in Idaho) would effectively kill the group and stop most of the issues.

16. June 18, 2005 at 1:41 pm
17. June 20, 2005 at 8:20 pm

http://www.aom.pace.edu/cmd/game.htm

Is an older collection of links from the AOM site I was the web master for.