The consequent pay-off matrix for the wives and husbands would be something like this:
If the risks of discovery were lessened by circumstances in some
societies, such as the sheikh being away from the harem for an
extended period, then the wives might risk infidelity. If we further
postulate a principal of strength in numbers, or gender solidarity,
among the wives, then we might find that infidelity would be more
common among the polygynous households. But gender solidarity
faces the collective action difficulty: what if one of the more
ambitious wives reports other wives' infidelities to the sheikh?
If the wives were mutually suspicious we might find, instead,
that infidelity was more common among the relatively autonomous,
Loose Patriarchal Monogamy
Anthropology still debates the origin of monogamy. Gary Becker has suggested that monogamy may have arisen as a means for poor and unattractive men to ensure that they have access to wives.
Since monogamy appeared, however, monogamous societies have varied between relative libertinism and puritanism. Under the looser, libertine patriarchal monogamy, the community, church and state have generally not approved of extra-marital relationships, but not strictly enforced these norms for men. Often there is also an implicit prestige for sexually promiscuous men.
But loose monogamy differs from polygamy in two ways. First, the internalized rewards of non-monogamy (macho prestige) are muted by its official prohibition. Second, men can only exploit the labor power of their one wife, while they must continue to provide material gifts to their mistresses. Mistresses may cost as much to maintain as wives, and are surely more difficult to exploit the labor of. Thus, even loosely observed monogamy sharply reduces the incentive to seek additional, simultaneous mistresses, compared to polygyny.
In general, men will choose to cheat in such a society, to the
extent that they can afford the extra mistresses, and women will
not cheat, to the extent that they face punishment for doing so.
Under puritanism, however, infidelity is more likely to be reported, and if reported severely punished. (Of course, the punishment is still usually more severe for women than men.) In addition, we can assume that the internalization of norms in the puritanical phase is more thorough, displacing some or all of the covert prestige of male promiscuity with guilt and fear. The result is stricter adherence to fidelity by men, and a monogamous equilibrium.
Since the Enlightenment and Industrial Revolution, the growing equality of women has also contributed to the more strict adherence to monogamy. On the one hand, men and women have gradually been treated more equally before the law, and in defending women against domestic battering. On the other hand, women have gained increasing choice in husbands, through "love marriage" and divorce, and increasing economic independence from their husbands. Women thus have both the powers of turning their husbands in to the church or community, if not the law in divorce proceedings, and the power of "exit," as sanctions they can levy against philandering husbands. This female empowerment would create a trend towards either greater male fidelity, or at least greater male care in hiding their infidelity, which would increase its cost, and decrease its demand.
Further Simplifying Assumptions
In order to illustrate the prisoner's dilemma of monogamy I need make a couple more simplifying assumptions:
(1) The first assumption is that the value of a relationship can be summed up in one measure, or rather, that relationships fulfill a unitary dimension of demand. In fact, one of the major rationales for non-monogamy is that different people can fulfill different parts of one's needs, in ways that can't be compared or traded off. For instance, in Spike Lee's She's Gotta Have It, the protagonist has three lovers, one for fun, one for romance, and one for financial stability. But estimating a model for one utility is difficult enough.
(2) A second assumption is that the utility of a monogamous relationship is equivalent for everyone. In reality, people assign different amounts of utility to different combinations of commitment, shared activity and intimacy with different numbers of people. Some people can substitute non-relationship utility for relationship utility, finding their ideal combination to be half a relationship and a full-time hobby or career. We will ignores all these variations and assign everyone a utility of 1.0 for a monogamous relationship.
(3) The third assumption is that while the value of the first full-time relationship is 1.0, each additional simultaneous relationship has declining marginal value. In other words, you are less than ten-times happier when engaged in ten simultaneous relationships.
Obviously, the rate of declining marginal utility is very different for different people. For the voluntarily celibate, the value of even one relationship is less than its cost in time and resources, perhaps because they value the rewards of prayer, art, or politics more. And for some rare individuals, there may even be a multiplier effect from non-monogamy, though this would still face an eventual constraint; philanderers may be three times happier with one mistress, but thirty times happier with ten mistresses. The risks of sexually transmitted disease have added an additional degree of decline for the value of additional relationships.
In my model below I will simply assume that a second relationship is worth only 0.75. With relationships with two single others one receives 1.75. The model will make the simplifying assumption that two simultaneous relationships are as many as these experimenters can deal with.
(4) A fourth assumption is that sexual contracts are reciprocal. Men and women are now subject to the same constraints. Even with relatively gender equality, there are today many situations where powerful partners can enforce fidelity on dependent lovers while they philander. Men and women of great wealth, power or charisma are often able to convince their lovers to remain faithful even if the advantaged person is not. This model, however, will only discuss situations where all partners either agree to monogamy, or consent to one anothers' non-monogamy.
(5) A fifth assumption is that the value of a relationship is reduced if the partner is having another relationship. This is clearly true for most people, because of jealousy and uncertainty. For many, a partner's infidelity reduces the value of a relationship to zero.
But the following model is primarily concerned with libertine sexual experimenters, who do not suffer from jealousy or uncertainty, and receive some degree of satisfaction at the idea that their partner's infidelity frees them to reciprocally engage in infidelity themselves. They do suffer from a loss of some of their partner's time and attention however. The net loss of utility for a libertine with an unfaithful partner is thus assumed to be only a third, rather than 100%.
(6) A sixth assumption is that there is no declining utility of
a relationship over time. Nobody gets bored. Nor does utility
increase with time: nobody becomes attached.
Monogamous Majority and Non-Monogamous Minority in Liberal Society
While about a third of married Americans have experimented with affairs, the majority of American couples see the risks of covert infidelity, in disease, partners' discovery, and so on, to be inferior to its potential benefits. Even affairs rarely continue for any length of time without resolving into monogamy with one partner or the other. The pay-off matrix for most Americans is still essentially that of Figure Three, with monogamy as equilibrium.
But a small minority of every liberal democratic Western society has strongly desired sexual experimentation, and rejected monogamous norms and values. Whether their desires result from anti-monogamous socialization, or from the absence of the suppressive effects of pro-monogamous socialization, they see the rewards of not only covert infidelity, but even reciprocal non-monogamy as greater than its costs. The following model attempts to model the pay-offs that such non-monogamous experimenters might face.
At the beginning, each partner faces a choice. They can choose
monogamy, or choose to also engage in an affair with some single
person. The supply of single people is a critical variable which
we will address later, but for now we assume that there is a ready
supply of single people who are also interested in non-monogamous
relationships. For these non-monogamous experimenters A and B,
their pay-offs having affairs are always better than the pay-offs
remaining in monogamy.
This takes us from box 1 to box 2, where the central couple, A and B, are both having affairs with single others, C and D. But C and D are strategic actors as well, and attempting to maximize their utility. They face the same pay-off matrix as A and B do, under which it never makes sense to have just one lover. So C and D also seek out single lovers, E and F. This takes us from box 2 to box 3.
Again, E and F are rational actors, and they seek out other lovers, moving us to box 4. If actors A through F, in this sub-culture of non-monogamous experimenters, each have two lovers, then A through F are receiving 1.17, which is greater satisfaction than they got under monogamy (1.0).
The first problem is that the people at the ends of these strings are only receiving .66, which is less than they could get in a monogamous relationship. But less us assume an infinitely expanding chain for the moment, and turn to the second problem: everyone receiving 1.17 is aware that they could be receiving 1.75 if their lovers did not have other lovers, and they were the center of two undivided attentions. For A, this situation is box 5A, and for B, 5B. Or at least actors could achieve 1.51, if they only had to share one of their lovers (the "6" boxes). This is where the conditions of the environment become critical.
In order to defect from general non-monogamy (box 4) to a more privileged non-monogamy (boxes 5 or 6), each player must calculate the likelihood of their being able to move from the position they are in to the advantaged position. If there is 100% certainty that they can break off relations with one or both of their lovers and replace them with single lovers, then they will do so, achieving either 1.51 or 1.75. In the case of B, for instance, this would mean moving from box 4, to boxes 2, 5B, or 6B.
The complexity enters here. If everyone has a good chance of finding single others who are willing to engage in non-monogamous relations, then everyone's best strategy is to break off relations with involved others and seek out single others. But if everyone breaks off with involved others, then the environment changes. When no one will maintain a relationship with someone involved with someone else, the greatest number of sustainable partners is one, i.e. monogamy. Neither A nor B can find single others who are willing to be involved with them, since they are already involved with each other, and therefore their subculture reverts eventually to an equilibrium around box 1, monogamy.
This is the prisoner's dilemma. If everybody takes two lovers,
then everybody gets 1.17 (rather than 0 for the singles, and 1.0
for the monogamous). But since everybody can do better if they
are the only one with another lover, then nobody can have two
lovers, and everybody only gets 1.0.
Building Non-Monogamous Equilibria in Liberal Society
There are several "natural" and several "voluntary"
solutions to this prisoner's dilemma. One "natural"
or environmental solution results if it is impossible to find
singles willing to get involved with a non-monogamous situation.
If there is little likelihood of finding two single others to
defect to, a set of non-monogamists who have reached box 4 would
have no incentive to leave it, since the only real alternatives
are monogamy (1.0) or general non-monogamy (1.17).
This set of successful non-monogamists would need to find a solution
for the ends of their relationship chain, those receiving less
than monogamous satisfaction [.66 - 1.51 - 1.17 - 1.17 - 1.51
- .66]. This arrangement would slowly unravel. One solution is
to close the circle at the ends, providing a uniform 1.17. Another
solution is to find individuals who are uniquely attracted to
this limited commitment, such as those who do not have the time
or ability to commit to a monogamous or multiple relationships.
We might imagine a sleepy suburban 1950s Peyton Place, where 99% of all the adults are married. In this situation one's only choice is whether to have an extramarital affair with a married person or not. Column 2 and 3, and Rows 2 and 3, which presume the existence of single people, are simply not available. For the potential non-monogamous experimenter subset of the married couples, the choice is obvious: spouse-swapping, or a small closed circle. As long as the chance of finding singles to connect with is close to 0%, the spouse-swapping arrangement will be equilibrious.
Voluntary agreements can also structure equilibrious non-monogamy. Fear of disease may cause actors to want to set clear boundaries on their partners' contacts: no one may sleep with anyone outside the group. Long-term friendships may have established trust between the partners, making contacts with others more costly and risky. The participants may have arrived at these voluntary agreements through learning from previous affairs that closed circles were the only successful arrangement.
These agreements are probably most common among a closed circle of three, a menage a trois.
The problem is finding partners who will agree to the concept
of menage a trois or group marriage, and to enforcing the
contract. The State does its best to discourage such contracts,
with laws against polygamy and bigamy, and refusing custody and
other rights to such non-traditional families. The community is
usually even less help, heaping buckets of scorn on the sinners,
and rewarding partners who come to their senses and leave the
Achieving Critical Mass
Therefore, those with non-monogamous preferences must organize for collective action, both in order to enforce collective norms governing non-monogamy, and in order to throw off the norms that discourage non-monogamy. Sexual deviance is a local "public good," requiring collective action. From the gnostic "free-love" rebellions of the Middle Ages to the Stonewall riots, the institutionalization of sexual deviance has required the gathering and organization of sexual radicals, who then made deviance safe for less committed experimenters.
If the initial risk-takers are successful, and survive long enough,
they can attain "critical mass." The critical mass number
is the "tipping point" at which the external and internalized
inhibitions reduce to the point that benefits for group members
exceed costs, and membership in the sub-culture is self-sustaining
(Schelling, 1979: 100-110). My argument above is that, while many
sexual radicals have tried to create a self-sustaining non-monogamous
subculture, they were never able to achieve critical mass or sufficient
agreement as to what the rules should be for "normative closure."
Figure Seven: Critical Mass for Non-Monogamy
Occasionally one individual has been able to afford to provide the public good by themselves. For instance, the legalization of divorce was a public good provided by King Henry VIII, making British divorcees a "privileged group" in Olsonian terms (Hardin, 1979:35). Though all British desirous of divorces benefited, only Henry VIII could afford to legalize divorce.
Without such a hegemon, those with non-monogamous preferences are a scattered "latent group," awaiting entrepreneurs willing to risk organizing costs in order to reap later rewards from leadership. For instance, the founder of the Mormon Church, Joseph Smith, can be seen as a public goods entrepreneur, organizing to re-create polygyny, though it ultimately cost his life, and federal troops massed on Utah's border undid his work.
But Mormon polygyny, which was strictly patriarchal, does not really address the possibility of a non-monogamous equilibria in liberal, egalitarian society. Today sexual alternatives face even fewer external and internalized sanctions than they did in the 19th century, and a century of Western sexual libertines have experimented with those alternatives. Yet only one large community is known to have developed a system of egalitarian non-monogamy that lasted more than a few years: the Oneida commune of up-state New York (1837-1879). Oneida may illustrate some of the ironic complexities of attempting contemporary free love.
Oneida was founded by John Humphrey Noyes, a Perfectionist minister who preached "Bible Communism" and rejected both monogamy and polygamy as forms of ownership to be forsaken by the saved. But he also fervently rejected the anarchistic "free love" practices of his contemporary sexual radicals, such as the Fourierists, Owenites and spiritualist feminists who advocated liberalized divorce and promiscuity, and insisted that "complex marriage" could only be practiced within a community under spiritual discipline.
In Oneida, if a man or woman desired a sexual liaison with another member they could petition a community elder to carry a message to the party in question; they were forbidden to ask other communards directly. If the other consented, which was not certain, then the couple could meet several times, but no more; if they developed any feelings of attachment they were immediately separated. If they violated the community's rules, they could be expelled. For the first 17 years of Oneida's existence, men were forbidden to ejaculate, as a contraceptive method and an aid to female sexual pleasure: there were no pregnancies recorded for that period. At its largest, the complex marriage system included about 300 people, and it lasted more than thirty years.
Rosabeth Moss Kanter (1972), in her statistical study of one hundred
19th century communes, correlated sexual systems with the longevity
of the commune, and concluded that the Oneida-type complex marriage
systems, and the celibacy practiced by the Shakers, were correlated
with commune longevity. At the other extreme were communes like
Berlin Heights that attempted to institute "free love"
without strong community controls; these communities were invariably
short-lived. In the end, Oneida's disbanding had nothing to do
with dissatisfaction with the complex marriage system, but rather
grew out of the secularism of the second and third generation
of the community, who were no longer prepared to make the other
sacrifices of communal life; the combination of strong preferences
for sexual variety and a strong commitment to religious
authority proved unique to just one cohort.
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