Given the payoff matrices constructed last time, I constructed decision matrices for several sets of parameters. I constructed tables for each type of payoff--prosocial, fiscal, and offspring quality--and reverse ranked each outcome within the table. For example, the offspring with the highest quality had the highest numeric rank in the offspring quality chart. I created a summary chart where the ranks for each payoff were added after being multiplied by a weighting parameter to allow for analysis of the priorities for each player.
The "basic" table looks like this:
(Note: Parameters for each partner are expressed as [P, G, $] and the coefficients for each value [x, y, z] are in the same order.)
| Combined by Ranks | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Male Options | |||||||||||
| Marry (2) | Marry (3) | Separate | Abandon | Pay | |||||||
| F,M | F,M | F,M | F,M | F,M | |||||||
| Female Options | Marry (2) | 3.0, 3.0 | |||||||||
| Marry (3) | 3.3, 3.3 | ||||||||||
| Separate | 1.7, 1.7 | ||||||||||
| Alone | 1.7, 2.0 | 3.0, 1.7 | |||||||||
| Adopt | 3.0, 3.0 | ||||||||||
| Parameters: Female [0.5,0.5,$30,000], Male [0.5,0.5,$30,000], b = .25, c = .5, d = .8, pCON = .25 and xyz = [.33, .33, .33] | |||||||||||
For this parameter set with both partners essentially symmetrical, all three factors (prosociality, genetic, and fiscal) of equivalent value, a positive synergy value [b], 50% child support expectation [c], and female access to 80% of the offspring's allocated resources [d], the best responses for both sexes are identical--that of marriage with offspring. With the assumption both partners will elect the best outcome for themselves, this set of parameters rewards the cultural ideal.
However, in this culture, many women do not earn as much as men. Let's consider the modified model taking this into account:
| Combined by Ranks | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Male Options | |||||||||||
| Marry (2) | Marry (3) | Separate | Abandon | Pay | |||||||
| F,M | F,M | F,M | F,M | F,M | |||||||
| Female Options | Marry (2) | 4.0, 2.7 | |||||||||
| Marry (3) | 3.7, 3.3 | ||||||||||
| Separate | 1.3, 2.0 | ||||||||||
| Alone | 1.3, 2.3 | 2.7, 2.0 | |||||||||
| Adopt | 2.7, 3.3 | ||||||||||
| Parameters: Female [0.5,0.5,$20,000], Male [0.5,0.5,$30,000], b = .25, c = .5, d = .8, pCON = .25 and xyz = [.33, .33, .33] | |||||||||||
By reducing the woman's income by a third, the dynamics of the model change with no other parameter modification. Although the marriage is still the top choice--both marriage with children or without--for the woman, the man's values change. His top two outcomes are now marriage with children or having a child out of wedlock and encouraging the woman to adopt it out (although the actual adoption is not primarily his decision). In general though, the best response he can influence directly is to marry the woman, or--if she chooses not to marry--encourage adoption.
Going further down the economic rabbit hole for women, dropping her income completely produces this result:
| Combined by Ranks | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Male Options | |||||||||||
| Marry (2) | Marry (3) | Separate | Abandon | Pay | |||||||
| F,M | F,M | F,M | F,M | F,M | |||||||
| Female Options | Marry (2) | 4.0, 2.7 | |||||||||
| Marry (3) | 4.7, 3.3 | ||||||||||
| Separate | 1.3, 2.0 | ||||||||||
| Alone | 1.3, 2.3 | 2.3, 2.0 | |||||||||
| Adopt | 2.7, 3.3 | ||||||||||
| Parameters: Female [0.5,0.5,$1], Male [0.5,0.5,$30,000], b = .25, c = .5, d = .8, pCON = .25 and xyz = [.33, .33, .33] | |||||||||||
The greatest change when the woman doesn't have an income is actually the switch between marrying without children and married with children. This is probably driven by the [d] parameter where a mother controls the allocation of resources allocated to the offspring. The payoff for the man is likewise to be married with children in this scenario.
The original premise by Geraldo was oriented primarily toward "people of color". Beyond the above scenarios, for some ethnic groups, women have more income than the available males. By switching the economic advantage to women:
| Combined by Ranks | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Male Options | |||||||||||
| Marry (2) | Marry (3) | Separate | Abandon | Pay | |||||||
| F,M | F,M | F,M | F,M | F,M | |||||||
| Female Options | Marry (2) | 2.7, 4.0 | |||||||||
| Marry (3) | 3.3, 3.3 | ||||||||||
| Separate | 2.3, 1.7 | ||||||||||
| Alone | 2.0, 2.0 | 2.3, 1.7 | |||||||||
| Adopt | 3.7, 3.0 | ||||||||||
| Parameters: Female [0.5,0.5,$30,000], Male [0.5,0.5,$20,000], b = .25, c = .5, d = .8, pCON = .25 and xyz = [.33, .33, .33] | |||||||||||
This predicts the most opportune choice for men is a marriage without children--well above his other options. For the woman, the best option is suggested to be adoption as a single mother. This asymmetric combination and the second-choice symmetry on marriage with children may parallel some of the marriage/relationship issues in the general media. The stereotype regarding women focused on having kids as the first priority and primary reason for marriage compared to men's focus on living together and dodging kids is suggested by these outcomes. Additionally, the tendency in some circles for successful, single moms to have their parents raise their children--essentially, adoption without the legality--when a marriage isn't chosen is suggested as well.
Altering the conception risk (pCON) with all other parameters the same in this situation only exchanges the first and second choices for women from adoption to marriage with children, suggesting a Nash equilibrium on marriage with children. However, if the man is either unwilling to or unable to marry, the most effective response given the parameters remains for him to push for adoption.
With Geraldo's focus on "people of color" and the assumption social benefits may not be as much a driving factor in minority populations, I considered decreased effect of social motivation for marriage. By exchanging the value of the [x] parameter for a zero and adjust the other two upward evenly, we can eliminate the effect of prosociality as a motive for marriage. Additionally, we return to symmetrical estimates of fiscal resources initially to produce this outcome:
| Combined by Ranks | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Male Options | |||||||||||
| Marry (2) | Marry (3) | Separate | Abandon | Pay | |||||||
| F,M | F,M | F,M | F,M | F,M | |||||||
| Female Options | Marry (2) | 2.0, 2.0 | |||||||||
| Marry (3) | 2.5, 2.5 | ||||||||||
| Separate | 2.0, 2.0 | ||||||||||
| Alone | 2.0, 2.5 | 4.0, 2.0 | |||||||||
| Adopt | 4.0, 4.0 | ||||||||||
| Parameters: Female [0.5,0.5,$30,000], Male [0.5,0.5,$30,000], b = .25, c = .5, d = .8, pCON = .25 and xyz = [0, .5, .5] | |||||||||||
For the male, it's the same old story for non-marriage options: adoption is better than abandoning is better than paying. The only effect of Geraldo's suggestion would be for men--if women don't choose to adopt--to choose between paying or just not getting a woman pregnant. If a man could persuade a woman to marry and have his child, that would also be a decent choice but he's directly restricted from the high payoff outcome of adoption.
For the woman, however, the two highest payoffs are to adopt out her child or to force the man to pay. This actually includes all values of [c] (the ratio of support the man pays for his child) from 24% to 100%. By altering the ratios of income, this advantage kicks in when he earns just more than half her income up until the man makes about 150% of of her income (at which point it pays her to marry him.)
Additionally, when the man's income is less than 50% of hers, this model predicts it's a higher payoff to be abandoned. This is most likely due to the [d] parameter and the proportion of the her income directed at the baby.
This dynamic--the preference for "baby daddy's" as abandonment is shifted to paying--over marriage appears in popular culture. Because of the ability of women to more directly manipulate the probability of conception through deceptive means and (through abortion or adoption) shift the situation toward this outcome without male cooperation, the only effective male response is to manipulate the probability of conception themselves through partner selection of non-reproductive partners, avoiding sexual activities risking conception, or to simply not engage with women.
Additionally--because of the effect of prosociality and relative income--this produces a highly competitive situation for men and explains the degree of focus on male-male competition and money possession--though not use--in men of color. In essence, it's not what they do with the money, it's the effects it has on female decision making that they are after.
Because this is a one-off model, an iterative effect isn't directly considered. The dynamic of preferring a "baby daddy" over a married partner when prosocial benefits are not a priority or unavailable are somewhat obvious. Because bigamy is proscribed in this culture, exploiting the system of child support is possible because multiple offspring from different fathers are legally possible whereas multiple husbands are not. Additionally, a woman may accrue additional resources from the child support exploit and select a husband which could provide prosocial benefits. The adoption options and a single marriage do not allow this accumulation of additional resources.
Another effect that's probable in an iterative model would be the restriction on male decisions based on resource drain from child support and the creation of non-marriable men in this fashion. If this effects partner choice, it can quickly lock out any opportunity for marriage as a future option for these men. A similar effect on women could occur if men's partner choice is affected by a woman's election of child support as a previous strategy.
Stabilizing dynamics
The effects of prosociality appear to buffer much of the fiscal resource focus when prosociality is a priority. A general resistance to adoption may also be a stabilizing factor but isn't directly addressed in this model. Although adoption is inferred to mean a legal adoption, "adopting out" an offspring to one's close relatives may also be inferred and would have a more interesting dynamic as it is not as absolute as a "legal" adoption. This flexibility may be a point for future exploration.
Fiscal resources are both stabilizing and destabilizing in this model. In general, greater relative male resources increases the value of marriage with children for females in this model. This is primarily because of the proportion of shared resources in marriage and access to the allocation of resources for the off-spring. Additionally, in a hypothetical iterative model, marriage as a tool for avoidance of resource sharing outside the family unit would also serve to stabilize marriage as a strategy.
For males, however, higher fiscal income ratios increase the value of the adoption strategy. Another variation--not discussed above--of "adoption" may be extra-pair coupling or cuckolding of other men. In function, this is a form of adoption. When prosocial benefits are a priority, this strategy has the same estimated benefit for the male as marriage when his income is higher than his wife's, but is usually higher when prosocial benefits aren't considered. This option gains favor because of the low fiscal cost and decent (assumed) prosocial benefit to the infant in the new family.
Conclusion: The better solution
The better solution to Geraldo's suggestion is simple: prosocial benefits and more income for men. The added prosocial benefits--measured in social connection, familial connection, and simple social network access--rewards those who choose to have kids (or, at least, not avoid having them) and restricts the benefits of the child support exploit suggested above.
Added social welfare benefits--which could be inferred in the model as part of the woman's direct income reinforce the child support exploit, but only when it's directed at either the woman or offspring (assuming the mother manages the funds). Allocated to men, you might change the dynamic of the system to increase the potential value of marriage. The problem with building marriages isn't so much the amount of the money as who is receiving it in the family dynamic.
The direct impact of women's decisions--primarily in birth control use, abortion decisions, and the option to adopt--put her in a pivotal decision-making role in this system. Through partner choice and conscious or unconscious manipulation of her conception risk, she creates the situation surrounding the whole system. Within the system, she can effectively drive the options into almost any set of choices with little direct male influence while his only (current) option to assert direct control over the situation is to abandon her.
The removal of the abandonment strategy creates an antagonistic system for males where the highest value options accessible to them are to avoid conception. This creates the long-term effect of these men avoiding the more stable and potentially beneficial outcomes--such as marriage--and selects for only those men who are able to produce enough prosocial and fiscal benefits so as to "coerce" women into cooperation and therefore gain access to high payoff strategies.
The effects of abandonment--at least in the model--really depend on women's resources relative to men's. At certain levels, it becomes more beneficial for women and offspring to be abandoned, especially if this independence opens the possibility for a more stable, more supportive future relationship. Essentially, the costs of child support from a low-income father become more costly than the benefits over time.
I think Geraldo's solution of mandatory paternity testing is dangerous to the long-term survival of "families of color" or families of any sort. The better solution is social integration and building strong, useful social networks in these populations that pay more when you're partnered.
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