The mathematics of throuples, old age and loneliness.
A powerful advantage that throuples could have in old age and survivorship.
INTRODUCTION
Whether Gays could exist in relationships with more than two people, couples, is a current question. This essay does not discuss whether it is possible or not, but discusses how it could be advantageous in one aspect.
In the development of new things, one reason to make the effort is that there are advantages if the new thing can be realized successfully. Also, individuals are more likely to give a new possibility of realizing something if they are aware that there might be advantages both small and large.
This essay does a simplified analysis to show that a throuple has a significant advantage is avoiding being left alone in latter life when one partner dies.
It might be that only a small fraction of the Gay community can successfully have a throuple, but that then is a small fraction of the Gay community that has realized an advantage. It might be when a small fraction has realized advantages there will be a greater effort by others to gain the same advantage, but even if not, the Gay community can use and needs every advantage that it can find.
SIMPLIFIED MATHEMATICS
To properly do a full analysis it would require setting up a model with numerical analysis of triple integrals. I am not going to do that and who would understand it besides me and some analysts.
It is important that the advantage be explained in as simple terms as possible, but I also want some basic numerical answer to show that there is a very significant advantage.
Consider that a couple might have one member live to be 76 and the other 84. The surviving spouse would be living alone for eight years. Consider, the same pair is actually a member of a throuple, and that the 3rd member making up the throuple lives to be 81. Then the last surviving spouse is living alone for only three years.
Also, for the couple, one-half the couple ends up alone and for the throuple, only one-third ends up alone and for a much shorter time.
So how can we get some guesstimate/estimate of the advantage without integral calculus.
Let’s divide life spans into three levels, Age 1, Age 2, Age 3, and score the possibilities of the number of steps that the surviving spouse is by himself.
For the following, we have two spouses, A and B, and they have the following possibilities. (3X3 = 9). We will assume each of the Ages is equally likely as a life span. The average score is the score divided by the number of partners.
In Case 1, both A and B passed away at Age 1. The score is 0, and Avg. score is 0.
In Case 2, spouse A passed away at Age 1, and Spouse B passed away at Age 2, and so the score is 1, and divided by the two members of the group, the average score is 0.5
The average outcome would the sum of the scores, 8, divided by the number of possibilities which is 9, giving 8/9 = 0.8889, and divided by the number of persons in the relationship, 4/9, 0.444.
What happens when we add Mr. C. to the possibilities? In some cases C will pass away in the same Age as the current last surviving spouse, but in other cases A & B might have passed away in Age 1 and C will live to Age 3.
Intuitively you might assume that there is some advantage, but is it a little or a lot?
So to know the advantage we need to evaluate all 27 possibilities of A,B, and C being distributed in Age1, Age2, and Age 3. (3X3X3=27). That is why this model is simplified. If we had five divisions of ages it would require 125 combinations evaluated.
The following are the 27 possibilities. Again, we are assuming the Ages are equally probable.
One important difference in the two tables is that the average score here is the score divided by three.
Not only is the amount of the loneliness less by a third (0.67 vesus 0.89), that is the amount of loneliness is only two-thirds of the couple, the loneliness is divided among three, not two people so the average loneliness is half, (0.22 versus 0.44).
A throuple can expect half the loneliness in old age.
Let’s explain it in another way.
Imagine three couples, they could be two throuples.
The three couples with an average possible score of 8/9ths, could be two couples with an average possible score of 6/9th.
The ratio would be [3 X (8/9)]/[2 X (6/9)] = [(24/9)]/[(12/9)] = (24/12) = 0.5.
That is the loneliness of three couples could be two less lonely throuples.
Caregiving and survivorship
Consider that with a throuple, that situation where the surviving spouse has only himself to rely on is cut in half. Further with a throuple, for a significant period of time, there are two people to care for one ill spouse.
For one third of the time, when one spouse passes away, there remains a couple to comfort each other.
These both would be advantages in other situations where a spouse in a throuple was lost to disease or an accident outside of old age.
SUMMARY
There are other advantages of a throuple over a couple in old age. Financially, there are three retirement benefits possible to live on, and the estates of two of the three are there to help the last surviving member.
This essay is to address just one aspect of a throuple versus a couple. As for relations involving more than three, such as quadruples etc., there would be even more advantages.
This essay is also to show that throuples need to be examined for their material benefits and social benefits for their members versus that of couples by quantitative means, if only in simplified ways like this.
Throuples may offer Gays very significant advantages in living.
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