Some people may find this fascinating, and others may dismiss it as mathematical mumbo-jumbo. That's fine; most people treat the issue of unrestricted marriage from a purely emotional standpoint, and if you're one of those people then I don't expect a discussion based on mere logic to have much of an impact.
The Marriage Problem is defined as follows: two equal-sized sets of people, male and female, need to form pairs. It's easy to do -- pairings can be done completely randomly, and as long as each man gets assigned to one woman, you're done. The problem is that when these people have preferences as to who they get paired up with, the situation gets much more complicated.
For example, if M1 gets assigned to W1, but would prefer to be with W2, he will leave W1 if W2 is willing to pair up with him -- that is, if W2 prefers M1 over whoever her current mate is. As far as M1 is concerned, he is willing to leave his mate for another woman as long as there is a woman who he prefers over his mate, and that woman also prefers M1 over her mate. Got it?
A stable marriage is a set of matchings between these men and women such that, for any given man, there is no woman he prefers over his mate that also prefers him over her mate. The man may prefer other women over his mate, but as long as they don't want him it doesn't matter; he won't leave his mate if he doesn't have anyone else to go to.
As it turns out, it's pretty easy to form stable marriages. Essentially, you let all the pairings swap back and forth, and eventually an equilibrium state will be reached such that no one wants to change. That's an intuitive result, but it wasn't easy to prove that it works under every possible set of preferences. That is, no matter how convoluted the preferences of the two groups of people may be, there is guaranteed to be at least one stable marriage that will match the men to the women and not lead to any more swapping.
Among humans, we typically refer to this as "dating". People get to know each other and try each other out, and eventually commit. Unlike the mathematical model, the sets of men and women are not really finite; there's always a chance that you'll meet someone new that you haven't considered before, and you may prefer her to your wife, and she may be willing to take you. Nevertheless, stable marriages are theoretically guaranteed as long as the initial conditions are met.
The crucial initial condition is that there are two sets of people, and that no individual is willing to be matched with another individual in the same set. This is called a "binary partition" (divided in two), and without it the entire proof falls apart. In fact -- except in a few very specific instances with carefully crafted sets of preferences -- it's impossible to form a stable marriage among a single set of people.
[I tried to write a simple illustration of why, but you'll have to read the proofs yourself, I think. I've tried to keep this whole post as simple as possible, and I hope that hasn't led me to omit any important details.]
Homosexuality eliminates the two groups we normally deal with (men and women) and lumps everyone together into a single group. Without getting caught up on the terminology of "marriage", it has been mathematically proven that homosexual pairings are less stable than heterosexual pairings, wholly and simply due to the mate preferences of the people involved. Individual humans aren't as rigid as mathematical models, of course, but the aggregate behavior of real humans will closely match what is predicted by theory.
So the obvious conclusion is that homosexual pairings (or marriage) should not be allowed, since it disrupts the ability of heterosexuals to form stable marriages. It took me a while to figure out why this was complete bollocks when applied to real life.
One problem is that in real life, even in a simple set containing only hetero men and women, some marriages will dissolve *even if the people in it have no hope of forming new marriages*. Two people may be married who are so incompatible that they decide (or at least one of them decides) that they hate each other, and get divorced. All the other marriages are stable, and neither of the divorcées will be able to find anyone who prefers them over their current mate.
Realistically, there will be more than one of such pairings, and as a result, there will still be divorces and marital instability *even if there are no homosexuals*. The conclusion fails, whether or not there are homosexuals in the mix, because the heteros will not necessarily remain in the marriage, even if they have no other mating options.
Another problem is the assumption that the number of men and women is equal. This isn't true to begin with, but if we're going to recklessly assume it is, then we can similarly assume that the number of male-male and female-female pairings would leave an equal number of hetero males and females who could still pair off just fine (since, presumably, none of the heterosexuals would desire the homosexuals to be their mates -- or even if they did, none of the homosexuals would return the favor, meaning that the heteros would be stuck in whatever stable marriages they desired).
Then there's the question of what you'd propose we do even if real life did remotely resemble this situation. Oppress all homosexuals (for most of whom it is not a choice to be homosexual) in some way, by denying them the ability to couple with others? Exile them? Execute them? This is an interesting mathematical exercise, but it bears virtually no relation to reality.
You miss the most important problem with the model: in real life, preferences change over time.
People may not have a choice as to who they are attracted to sexually, but they have a choice as to how they express it. That's not particularly relevant to this discussion, however.
As I said, the model does not project directly onto reality. However, insofar as it deals with aggregate behavior, it's quite valid. Real life is far more fuzzy than any model, but that doesn't mean that the models are useless. You ignore friction when you're learning physics, but that doesn't mean the simple models are useless -- just that they aren't wholly accurate. Similarly, this model gives us some insight as to why homosexual relationships tend to be less stable than heterosexual relationships (which is pretty well established statistically, whether the multiplier is 2 or 10).
Also, I think "compatability" is a myth. I suspect we have entirely different views on marriage that are much lower level than the topic at hand.
I didn't express an opinion as to how the conclusions of this model should be applied to real life, I merely pointed them out because I think they're pretty interesting. There aren't many such clear-cut cases where human behavior can be simulated mathematically.
You honestly expect me to believe you had no ulterior motive in posting this article? As if your previously expressed views on homosexual marriage don't exist? That's a pretty disingenuous position to take.
They may have a "choice" as to how they express it, but you and other "traditional marriage" advocates insist that they not express it at all. So you're not really giving them much of a choice. For someone who thinks that competition and choice are such important economic factors, you seem to recant that belief all too often when it comes to social mores. Are you afraid to compete with homosexual women for mates?
If I wasn't aware of your political and social beliefs, I certainly wouldn't read anything into this article beside your interest in mathematics. Alas, I am aware.
Also, your claim that "homosexual relationships tend to be less stable than heterosexual relationships" links to a page that says that homosexuals are more *promiscuous* than heterosexuals. This doesn't mean their relationships are unstable; it means they are less likely to have a relationship and more likely to have casual sex. One obvious reason that went unmentioned (assuming the statistics are accurate) was this: Since two gay men can't get each other pregnant, there's less risk in having multiple sexual partners. You're not going to leave a string of babies behind if you have a bunch of sex in one night.
STDs are still an issue, as well, but that's true for both genders. Anyway, you ignored the point that the homosexual men and homosexual women can, in theory, be completely removed from the two sets of men and women. We end up with four sets: straight men, straight women, gay men, and gay women. The gay men only group with each other, as do the gay women. The straight men and straight women couple with each other. There's no interplay between the gay groups and the straight groups. Ergo, the gay groups don't affect the mating capabilities of the straight groups.
Realistically, as you pointed out, it's far more complex, but as a *useful* simulation of real-world behaviors (let alone as any kind of support or justification for political action), it's absurdly useless, no more interesting than as a mathematical diversion.
Bah, I just wrote a long response to this, but then Mozilla crashed. IE never does that to me anymore. Maybe I'll respond in the morning. Main points:
1. I never said gay relationships interfere with straight relationships. You said that. My point was simply that this model can explain why they are less stable, which seems pretty cut and dry.
2. My goal in everything is to try to lead people to God. Free market principles are often the best way to promote a society in which this is possible, and that's why I'm almost always against restrictive laws. However, allowing gay marriage or civil unions would create a positive right and force everyone in society to bear an addition burden. It's not a freedom issue, from my perspective. Civilly recognized marriage is not a right, and like voting needs to be carefully weighed. I have weighed the issue, and I don't think that recognizing gay marriages or civil unions would be in the best interests of society, considering my goal of bringing people to God.
Homosexuals are gay!
What theory would you use to explain why homosexuals have so much trouble making their relationships monogamous?