While I generally agree the most effective environment for raising children is a cooperative, mutually supporting environment, I think his solution has serious risks of unintended and perverse consequences on multiple levels. Ignoring most of the legal issues for the time being, let's talk interpersonal relations.
For argument's sake, let's break the process of having children into a 5-step process model:
The process model starts with mate selection, progresses through sexual activity, results in conception leading into pregnancy, and finally ends in parental responsibility. The assumption in this model--vis-a-vis parental responsibility--is based on a reproductive outcome.
The problem with assuming a reproductive outcome--and one reason for the risk of systematic problems with Geraldo's solution--is the difference between reproductive and prosocial reasons for having sex. Unlike many other primates or other species with a very seasonal and highly telegraphed signal for women's reproductive status, humans and a number of other very social species conceal this and participate in sexual activity at will, even when no children may result. The function--of course--usually revolves around establishing and maintaining social connections.
While a direct connection is somewhat easy to understand--imagine a marriage between two elderly people where no risk of conception exists--indirect connections where the partners are not the "target" of the social connections may also exist. For example, consider a prostitute who employs sex in order to support her family. While the sexual activity is between two partners, the beneficiaries of that activity include others.
These differences (reproductive vs. prosocial) show up in mate selection.
Mate selection
Mate selection feeds the rest of the process. From a choice perspective, we'll consider the basic options to be limited to reproductive or prosocial traits. An obvious and uninteresting option would be to simply not select a mate. By doing this, you terminate the chain effectively. For argument's sake, we won't consider this option.
Another option--for this argument--is the selection of non-reproductive partners [NRP]. In this case, it's a partner who is either of the same sex, physically incapable of conception, or is otherwise impossible to conceive with. This option
The next three options deal with partners who are reproductively capable. The first option is to select a partner based on their prosocial benefits [PRS] at the expense of reproductive value. An example of this may be a partner who is very emotionally supportive, yet has a known genetic defect the other partner may choose to avoid. An additional example may be a significant other of another ethnic group where biracial children would be unacceptable to those involved.
The second option would be a partner selected based on their attractiveness or "good genes" [GDG]. The partner is selected for health and--intentionally or unintentionally--for the potential qualities as a biological parent. Arguably, many flings are based around these traits.
The final option considered will be the combination of the last two. The mate selected will be a combination of both [BOT] "good genes" and prosocial partner. In many cases, this is culturally considered the ideal.
Sexual activity
We will define sexual activity to three options: none [NSX], sexual activity with conception risk [PIV], and sexual activity with no conception risk [NPV]. The no-activity option is--like not selecting a partner--an uninteresting option except as far as it puts sexual relationships at risk. For the analysis, we will only consider it for this reason.
Conception
The only options here fall into two categories: prevention and none [NON]. Within the prevention category, we will consider two possibilities: obvious forms [CDM] and concealed forms [HBC]. The obvious forms include condom use as well as other barrier forms. The concealed forms include those not observable including hormonal birth control, vasectomy, intra-uterine devices, and medical sterilization.
Pregnancy
The only (voluntary) options--in various forms--included here are abortion [ABT] and carrying to term [PRG]. Currently, legally, the only partner able to make this choice is the woman, creating part of the systematic problem discussed later.
Paternal responsibility
This part of the process continues with systematic differences and the options differ. For men, we will consider the following three options: to stay with the mother and contribute [MRY], to not stay but contribute resources [PAY], or to abandon [ABA].
For women, the ability to choose the [PAY] option is essentially ignored for the time being because of the culture we are currently living in. Her options are considered to be adopt the baby out [ADO] which is assumed similar to the male's abandonment but includes the assumption of biparental support in the baby's new living situation, to stay with the father [MRY], or to raise the baby alone [ALO].
To sum up, this is the process with the options:
Payoffs
This is where things start getting complicated. To analyze the choices made and compare them, we need to estimate a few things. First, is the probability of different things happening.
For example, in the process model, we have sexual activity connected to conception. This connection, working backward from pregnancy to mate selection always occurs, but in life--even without using means to avoid conception--is not very likely. Generally, for humans, the probability of a conception is low for penile penetrative sex. This has to be taken into account.
Additionally, we have to estimate the payoffs of each choice. This becomes more complex as many of the choice's pay-offs depend on both the same person's prior decisions--for example, the choice to abort a baby may depend on partner choice--as well as the other partner's decisions--marrying someone who doesn't choose to marry you doesn't work in this culture.
To pull this off, we will have to use variables and consider some decisions in conjunction. First, we will add a few critical qualities to base values off of.
Partner qualities
We will consider three partner qualities. The first two were explicitly mentioned above--prosocial quality [P] and good genes [G]--and will be operationally defined as being a ratio of the ideal. To capture the qualitative nature of these traits, we will code them as values from 0 (absent) -> 1.0 (ideal).
The third quality will be simple resource access. Because this is a quantitative and functionally unbounded on the upper end, we will use a simple scalar value symbolized by [$]. The combined value of a partner will be the set of values [P, G, $].
Relationship/parental/baby quality
The value of the relationship will be measured in the same basic terms--prosociality, biological quality, and resources--where the outcome's value will be a combination of both participating partners. For example, a baby's "quality" would be derived from a combination of the social support available--consider it the "nurture" side of raising a kid--the genetic qualities of both parents--the "nature" side of the equation--as well as the resource availability to the baby and family. Because of the effect of numbers on family, the outcome will also be broken out by number of people in each outcome as well.
The analysis will consider a preferred outcome to be one that has a combined [P x G] as close to 1 as possible and a [$] value that is at least one when it is divided by the number of people in the resulting family (i.e. 3 if both partners elect to marry and keep the baby) and is above an amount defined to be that amount of resources needed to survive. If a baby is not kept, only the partner's individual values will be considered.
Formulaically, outcomes will be described by a one or two sets of values in a [P, G, $, #] format where [#] is the number of people--mother, father, baby--in that set of values.
Forming a payoff matrix
We will now step through the model and construct a payoff matrix. In all cases, [p] will be the probability (from 0 to 1.00) a situation occurs.
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