Guest post by Paul Burnham

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What Conditions Might Generate a Social Preference for Polygyny?

Introduction

During the occasional discussions of polygyny in Church literature and on the Bloggernacle, I see two competing narratives—a religious narrative and a romantic narrative. In the religious narrative, God’s will must always prevail and on occasion His will has been that polygyny be practiced. In the romantic narrative, pair-bonding is the most important feature of marriage and polygyny is antithetical to true pair-bonding, making it unthinkable under any circumstances. But I think there is a third narrative—what I call a quasi-Darwinian narrative that eschews both religion and romance. That narrative views marriage, whether monogamous or polygamous, solely as an effort to maximize one’s genetic legacy (i.e., number of descendants).[1] As I see it, both the religious and romantic narratives are selective subsets of the quasi-Darwinian narrative. The former is designed to further the pro-polygyny interests of elite men, and the latter is designed to further the anti-polygyny interests of elite women. Both narratives ignore the interests of non-elite men and women, which, it turns out, are not the same as those of the elites of the same sex. I propose to rectify that.

To do so, I propose to perform a set of simulations to see how the full quasi-Darwinian narrative would play out under different scenarios. In these simulations, religion and romance are disregarded. Both men and women have only one goal—to maximize their number of descendants. However, marriage decisions in these simulations are entirely female driven. Men are assumed to have different levels of suitability as a father (which I refer to as their “value” or “resources”) and women can select the one they want—even if that man has already been selected by somebody else.

The goal of the exercise is to generate two types of results:

1. To identify which women would choose to be plural wives if such were allowed, and
2. To identify conditions under which a majority of the adult population would be better off if polygyny were allowed.

Underlying the analysis are assumptions that (a) reproduction occurs only within marriage, and (b) marriage is subject to regulation—whether by a government, a religion, or nonreligious cultural traditions—and that such regulation can only be imposed with the consent of those being regulated. Without such regulation, the second type of result is irrelevant, and one could expect polygyny to effectively occur under any circumstances in which even one woman would find it to her advantage to be a man’s secondary partner.

Details and Assumptions

The data used for these simulations are entirely synthetic.[2] All relevant characteristics of both men and women are reduced to a single number which allows me to rank them and, in the case of men, place a value on them. This has the advantage of providing unambiguous results. A disadvantage is that it is easy to inadvertently predetermine the results by selecting a particular method of synthesizing the data.

Universal Assumptions

To mitigate that disadvantage, I create different scenarios under which to perform the simulations. All those scenarios involve changing the assumptions about men. The following assumptions about women apply in each scenario:

1. Eighteen women are ranked by their inherent ability to maximize their number of descendants, whether through greater fertility (always nonzero) or superior mothering/providing skills (however broadly you want to define those). The rankings are known to and accepted by all parties.
2. Women choose their husbands in order of their rank—that is, the highest-ranking woman gets first choice, and the lowest-ranking woman chooses last. Men have no say in marriage decisions.
3. Women always choose the husband who can provide the most resources to their children, after factoring in the number of other wives with whom those resources must be equally divided. Children’s survival rates are implicitly a function of both their mother’s and father’s resources, but only the latter enters into a woman’s marriage choice.
4. A first wife has no power to veto the marriage of her husband to additional wives if those women choose to be plural wives to her husband. (Allowing first wives a veto would render the exercise trivial—polygyny would simply never happen.) A first wife can, however, reconsider her own choice if additional wives insert themselves. Such reconsideration must wait until all women have made their initial choice.[3]
5. There are no synergies among sister wives. Each wife’s children benefit solely from their own mother’s resources and her share of the father’s resources.

Also unchanging among scenarios are the rules for determining when polygyny is socially preferred to monogamy. For women, the question is complicated. As part of the simulation, I consider the full value associated with a woman’s husband under monogamy and compare it to the value they would receive from their husband (not necessarily the same man) under polygyny, when they may only receive a portion of his total value. The system generating the highest value for a woman determines how she would vote.

I evaluate men’s preference for a polygamous or monogamous system solely in terms of the number and ranks of the wives they would end up with. If a polygamous system gave them multiple wives, they would prefer that system. If it left them unmarried, they would prefer a monogamous system. If they ended up with a single wife under polygyny, then their vote would be determined by comparing the ranks of the wives under each system. I sum the value of the quantity (19 – rank) over all their wives under each system to determine their votes.

The Distribution of Men’s Value

Men’s value may derive from the quality of time spent directly with the children (“fathering skills”) and/or the level of outside support (in the form of food, shelter, clothing, etc) that they can provide (“providing skills”).[4] I test four basic distributions of men’s value. Each distribution represents a different mix between fathering skills and providing skills. One should interpret the most skewed distributions as placing more weight on the providing aspect than on the fathering aspect.  The basic distributions, in order of skewness (most skewed to least), are as follows:

1. The “nonlinear inverse rank” (NIR) distribution. Values equal the square of (19 – rank) and range from 324 (18²) for the highest-ranked man to 1 for the lowest-ranked man (little more than a sperm donor). This distribution tracks most closely to the empirically observed distribution of income, which can be considered a proxy for “providing skills”.
2. The “inverse rank” (IR) distribution. Values range linearly from 18 for the highest-ranked man to 1 for the lowest (still just a sperm donor).
3. The “normal” distribution. Instead of a linear distribution, the values are clustered around 9.5 with a standard deviation of 4. This is an alternative to the IR scenario that tracks more closely with empirical evidence that the distributions of many attributes that one could consider proxies for fathering skills tend to resemble a normal distribution (or bell curve) more than a linear distribution.
4. The “equal” distribution in which all men have the same value. This is not a realistic distribution of either providing skills or fathering skills but is included to illustrate the implications of that extreme when there is a surplus of women.

I also consider a variation on the two inverse rank distributions in which the lowest-ranked men are more competitive in terms of their skills. They are as follows:

1. The “modified nonlinear inverse rank” (MNIR) distribution. Values equal the square of (35 – rank) such that the highest-ranked man has a value of four times that of the lowest-ranked man. Reducing the ratio of highest value to lowest value from 324:1 (under the NIR distribution) to 4:1 (under the MNIR distribution) implies a significant degree of policy-driven income redistribution (e.g., a highly progressive income tax coupled with a generous earned income credit). Such a radical policy would seem politically implausible, but I include it for illustrative purposes.
2. The “modified inverse rank” (MIR) distribution. Values equal (35 – rank) such that the highest-ranked man has a value (34) double that of the lowest-ranked man (17). This distribution is included to document the most unequal conditions under which polygyny would attract zero votes.

Table 1 illustrates the six distributions by showing the values of the 1^st, 7^th, and 12^th ranked men relative to that of the 18^th-ranked man (normalized to 1).

 

Table 1: Men’s Relative Values by Distribution Type
	NIR		IR		Normal		Equal		MNIR		MIR
Value of…
1st-ranked man	324		18		17.2		1		4.00		2.00
7th-ranked man	144		12		11.3		1		2.71		1.65
12th-ranked man	49		7		8.0		1		1.83		1.35
18th-ranked man	1		1		1.0		1		1.00		1.00

 

The Balance of the Population between the Sexes

The base assumption is that of a population that is balanced in terms of sex. Such an assumption is appealing because it approximates the modern world and eliminates one of the primary justifications for historical polygyny.[5] But I think it is useful to determine just how valid the historical justification was. To do that, I repeat the simulations twice, in each case using a population of 18 women and 12 men. In the first case, I eliminate the six lowest-ranked men; in the other case, I eliminate the six highest-ranked men. Finally, I briefly discuss the possibility of polyandry when there is a surplus of men.

Results with a balanced population

In a monogamous system, every woman would choose the husband of the same rank as herself, regardless of how the men’s resources are distributed. That result serves as the baseline against which the results in a polygamous system are compared under each of the six distributions of male value.

I focus with the inverse rank distribution because its results are the easiest to explain of all the simulations in which polygyny is chosen by some women.

Inverse rank distribution

Under this distribution, the top ten women would choose the man of corresponding rank to be their husband. Of the remaining eight women, six would choose to become plural wives of the six highest-ranked men; each of the other two would choose to be the only wife of a man ranked higher than herself. The left side of Table 2 lists the women from 1 to 18 and shows the rank of the man each would select. The right side of Table 2 lists the men from 1 to 18 and shows which women would select them.

This result is stable—the higher-ranked women could not do better by changing their choices.[6] The implications for men are that the six highest-ranked men would have two wives, the six lowest-ranked men would have no wives and the six in the middle would have one wife.

It is immediately obvious that the six highest-ranked men would be better off under polygyny because they would have multiple wives and could therefore expect more children. It is equally obvious that the six lowest-ranked men would be worse off under polygyny because they would have no wives or children at all. Of the middle six, four would end up with the same wife they would get under monogamy; the other two would end up with a lower-ranked wife than they would get under monogamy. Thus, men would cast 6 votes in favor or polygyny and 8 votes in favor of monogamy. The other 4 would be indifferent.

 

Table 2: Results in a Polygamous System Under the Inverse Rank Distribution of Men’s Values
By Women’s Rank			By Men’s Rank
Women’s rank	Husband’s rank		Men’s rank	Rank of first wife	Rank of second wife
1	1		1	1	11
2	2		2	2	12
3	3		3	3	14
4	4		4	4	15
5	5		5	5	17
6	6		6	6	18
7	7		7	7	None
8	8		8	8	None
9	9		9	9	None
10	10		10	10	None
11	1		11	13	None
12	2		12	16	None
13	11		13	None	None
14	3		14	None	None
15	4		15	None	None
16	12		16	None	None
17	5		17	None	None
18	6		18	None	None

 

For women, the results are the opposite. The six highest-ranked women would be worse off under polygyny because they would only benefit from half of their husband’s resources. The women choosing to become second wives would be better off because half of the resources of their high-ranking husbands is still more than the resources of the lower-ranking husband they would get under monogamy. Four of the remaining six women would get the same husband they would get under monogamy; the other two would prefer polygyny even though they would not be plural wives because they would end up with higher-ranked husbands than they would under monogamy. Thus, women would cast 8 votes in favor of polygyny and 6 votes in favor of monogamy. The other 4 would be indifferent.

Overall, the vote would be a 14-14 tie. What is interesting, however, is that more votes for a monogamous system would come from men than from women.

Other distributions

Table A-1 shows the results under all six distributions of men’s values with a balanced population. It shows that none of the distributions results in polygyny being the socially preferred system. Furthermore, it shows that support for polygyny is not a monotonic function of the inequality of men’s values. Polygyny gets no support under the most equal distributions—that is, when the value of the lowest-ranked man is at least half that of the highest-ranked man. Similarly, monogamy is the socially preferred system when the distribution of men’s values is the most unequal because the concentration of value attracts a concentration of wives in a polygamous system and leaves more men without wives and therefore in favor of a monogamous system. In the middle, the interests of men and women exactly offset each other and result in tie votes. Under any distribution in which polygyny would be preferred by anybody, more women would support it than men.

Results with a surplus of women

These simulations removed six men from the population, leaving a surplus of women. In a monogamous system, the top 12 women would choose the husband with the closest rank to her own—1 through 12 if the bottom six men are removed and 7 through 18 if the top six are removed. In either case, the bottom six women would remain unmarried. That result serves as the baseline against which the results in a polygamous system are compared under each of the six male value distributions and removal rules (that is, bottom six or top six).

Inverse rank distribution

Removing even a single male from the exercise has major implications for the social preference for polygyny. The simplest results to understand are those for the IR distribution in which the vote between polygyny and monogamy was a tie when the population was balanced. The absence of the lowest-ranked male has implications only for the lowest-ranked woman, who would remain unmarried under monogamy. Clearly, she would prefer polygyny to remaining unmarried, but she also preferred polygyny when the population was balanced so her vote would not change. This scenario does, however, remove one male vote for monogamy, which breaks the tie and makes polygyny the socially preferred system. The removal of all six of the lowest-ranked men who would remain unmarried under polygyny in the balanced population scenario would not change any woman’s vote but would eliminate six male votes for monogamy and thereby shift the social preference even further in favor of polygyny.

Would the social preference be different if it were the highest-ranked men (who supported polygyny when the population was balanced) who were removed instead of the lowest-ranked men? Not actually that much. A simulation using the IR distribution but removing the six highest-ranked men yielded the following results:

• The top six remaining men (originally 7 through 12, who were indifferent when the population was balanced) would now get multiple wives (three, in cases of 7 through 9) and would switch their votes to polygyny. The next three (13 through 15, who would remain unmarried if the population were balanced) would get one wife who ranks higher than the wife they would get under monogamy, so they would also switch to favoring polygyny. Only the bottom three would continue to favor monogamy as that is the only system in which they would get a wife. Thus, 9 men would vote for polygyny and 3 for monogamy—none would be indifferent.
• The top six women, who would favor monogamy if the population were balanced, would continue to favor monogamy. The seventh-ranked woman would get the same husband under either system, just as she would if the population were balanced. Of the bottom eleven, nine would choose to become plural wives of higher-ranked men. Seven of them would thereby improve their access to male resources and would vote for polygyny. However, two of them (ranked 8 and 9) would move up only one rank. The half-share of resources they would get are less than the full share of the lower-ranked husband’s resources they would get under monogamy (which were claimed by higher-ranked women under polygyny). The two who would not choose to become plural wives (ranked 13 and 16) would not get husbands at all under monogamy and so prefer polygyny. Thus, 9 women would vote for polygyny, 8 would vote for monogamy and 1 would be indifferent.
• The overall vote when the top six men are removed would be 18 votes for polygyny and 11 for monogamy with 1 indifferent. That contrasts with 14 votes for polygyny and 8 votes for monogamy with 8 indifferent when the bottom six men are removed.

Other distributions

Table A-2 shows the results under all six scenarios when the bottom six men are removed from the population. Table A-3 shows the results when the top six men are removed. The results in the two parts are different, but not dramatically so. What is dramatic is that all scenarios in both parts in which women outnumber men show polygyny as the socially preferred system. Furthermore, that result is driven by women–under none of the scenarios do a majority of women prefer a monogamous system.[7] That is the inevitable consequence of potentially denying the bottom six women any possibility of reproducing.

A Brief Note on Polyandry

The fact that a surplus of women shifts the social preference in the direction of polygyny raises the question of whether a surplus of men might shift the social preference in favor of polyandry. The answer, given the assumptions that apply in the rest of the analysis, is no. If there is an equal distribution of men’s value, women would be indifferent between monogamy and polyandry. If there is any variation at all in men’s values, however, they would prefer monogamy.

Consider a population with 17 women and 18 men. The 17 women would pick the top 17 men as their husbands whether or not polyandry is allowed. The bottom-ranked man would prefer polyandry, but the man with whom he would share a wife would prefer monogamy (the remaining men being indifferent), so their votes would offset. But their votes are irrelevant, because no woman would pick the lowest-ranked man to be a second husband. Unlike polygyny, which allows a man to have more children, polyandry does not allow a woman to bear more children. It just means that some of her children would be limited to the resources of her lower-ranked husband. With monogamy, all of her children would benefit from the resources of her higher-ranked husband.[8] Thus, when there is a surplus of men, monogamy provides all women with the highest possible value from their husbands.

 

 

	Table A-1: Simulation Results with a Balanced Population
			NIR		IR		Normal		Equal		MNIR		MIR
	Number of …
		women choosing polygyny…
		as 2nd wife		6		6		4		0		5		0
		as 3rd wife		3		0		0		0		0		0
		as 4th wife		0		0		0		0		0		0
		as 5th wife		0		0		0		0		0		0
		men voting for monogamy		12		8		7		0		8		0
		men voting for polygyny		6		6		4		0		5		0
		indifferent men		0		4		7		18		5		18
		women voting for monogamy		8		6		4		18		5		17
		women voting for polygyny		10		8		7		0		8		0
		indifferent women		0		4		7		0		5		1
		total votes for monogamy		20		14		11		18		13		17
		total votes for polygyny		16		14		11		0		13		0

 

 

	Table A-2: Simulation Results with a Surplus of Women (Men ranked 1-12 survive)
			NIR		IR		Normal		Equal		MNIR		MIR
	Number of …
		women choosing polygyny…
		as 2nd wife		6		6		6		6		6		6
		as 3rd wife		3		0		0		0		0		0
		as 4th wife		0		0		0		0		0		0
		as 5th wife		0		0		0		0		0		0
		men voting for monogamy		6		2		1		0		2		0
		men voting for polygyny		6		6		6		6		6		6
		indifferent men		0		4		5		6		4		6
		women voting for monogamy		8		6		6		6		6		6
		women voting for polygyny		10		8		7		6		8		6
		indifferent women		0		4		5		6		4		6
		total votes for monogamy		14		8		7		6		8		6
		total votes for polygyny		16		14		13		12		14		12

 

 

	Table A-3: Simulation Results with a Surplus of Women (Men ranked 7-18 survive)
			NIR		IR		Normal		Equal		MNIR		MIR
	Number of …
		women choosing polygyny…
		as 2nd wife		5		6		7		6		6		6
		as 3rd wife		3		3		1		0		0		0
		as 4th wife		2		0		0		0		0		0
		as 5th wife		1		0		0		0		0		0
		men voting for monogamy		7		3		3		0		3		0
		men voting for polygyny		5		9		7		6		6		6
		indifferent men		0		0		2		6		3		6
		women voting for monogamy		7		8		8		6		6		6
		women voting for polygyny		11		9		8		6		9		6
		indifferent women		0		1		2		6		3		6
		total votes for monogamy		14		11		11		6		9		6
		total votes for polygyny		16		18		15		12		15		12

 

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Footnotes

[1] A truly Darwinian narrative would not make the connection between “genetic legacy” (which belongs only to the gene itself) and the number of descendants of any particular organism incorporating that gene–hence, my “quasi” qualification.

[2] Given the “maximize the number of descendants” goal, I synthesize only fertile, heterosexual, nonadulterous, and nonabusive people. The absence of other types of people is not to ignore their existence—it is solely to uncomplicate the analysis.

[3] This assumption turns out to be a mere formality. In no scenario did any women reconsider their initial choice. It is possible that allowing first wives to reconsider immediately upon another woman choosing to be a plural wife to their husband would result in actual reconsiderations, but that is a complication that will have to wait for another paper.

[4] Men’s value can be viewed as a function of their age or not. I did not create any distributions that track well with age and the results are easier to interpret if one implicitly assumes that all men are the same age and have the same life expectancy. To the extent that women’s ages differ, that is factored into their rank.

[5] Between the ages of 18 and 44, men outnumber women in the United States. The overall surplus of women exists only at higher ages, when the women in question are beyond child-bearing years.

[6] One can imagine highly ranked women trying to game the system by becoming a second wife to a lower-ranked man in hopes that that man’s first wife will reconsider her choice and become the only wife of an even lower-ranked man. Such gamesmanship is too complicated for me to model so I can’t say whether it would work.

[7] That conclusion would not necessarily hold if the surplus of men were not as large. For example, the scenarios in which polygyny wins by two votes would yield a tie if only two men were eliminated and a win for monogamy if only one man were eliminated.

[8] Just as I assume no synergies among sister wives, I assume no synergies among “brother husbands”. The children of each benefit only from their own father’s resources.