Political intolerance and dating pt. 2: Chemistry

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• Part 1

Women lean left. Men lean right. Will this be a problem for future marriages in Sweden?

In the previous post, we applied a model from computer science to see if it would be possible to match together all young men and women in Sweden, without political awkwardness. Answer: almost. But love isn't computer science. Love is chemistry. So, let's make a chemical model instead. 

The Idea

Forget political parties for a minute. The process by which (heterosexual) men and women form and break up relationships can be seen as two reactants forming a product molecule in a solution:

The reaction goes both ways: in equilibrium new products are formed as fast as old ones are breaking up. The key variable in this process is the equilibrium constant*. The equilibrium constant is:



The brackets mean concentrations. What value does K have in real life if A=single women, B=single men and AB=couple? Let's be fairly optimistic and say that with all other variables that affect this except politics, 80% of people will be in a long term relationship at equilibrium. About 80% of all women become mothers at some point during their life, so that's where I get that from. Then A=0.1, B=0.1, and AB=0.4 (since a couple counts as one in chemistry). Therefore, K=40.

*The speed by which the solution converges to the equilibrium is reached is also very important, but here we will just assume that all processes are in equilibrium (though of course life happens before   the asymptote, quote Taleb). 

The Model

We will use the same binary political tolerance model as before, so as to limit the number of assumptions, and make this model comparable to the previous one. The matrix of political tolerance for dating:

Binary tolerance model. Green: "fine, I can live with your views". Yellow: at least one partner says "we're going to have a problem here". Note that the model doesn't assume whether the intolerance goes both ways, as long as I can imagine at least one direction of intolerance. Therefore, the matrix is necessarily symmetric. 

The motivation for using binary tolerance rather than ranges or rankings or something is that I want to limit the number of design parameters in order to limit the impact of my own biases here. The motivation for assuming intolerance between V and {C, L} is that L's election campaign in 2018 was "anti-extremist", which is crypto for working against both SD and V. So the people who voted L a year and a half ago apparently did not have a problem with that. And C is a lot like L. 

Another motivation for using a binary tolerance model rather than something more granular is the assumption that value questions come up quite early during dating, and if the values do not match then chances of going forward are not good. If the values do approximately match however, then it should be possible to reconcile political difference in good faith, and other variables are more important to whether the relationship will hold.

For each politically feasible couple, we get a reaction formula, such as:



for Center women and Social democrat men. This gives us the equilibrium equation:



Where K is the equilibrium constant, assuming no political troubles.
The variables in this model are the concentrations at equilibrium. So there will be one variable for each "single" type, such as Cw, and one for each "couple" type, such as CwSm. We need to preserve the total number of people of course, which gives us the equations like:



Where P is the total concentration of that group, out of both men and women. In the case of Center women, P(Cw) = 16.8% / 2 = 8.4%.

Now we have one equation per single type, and one per couple type, which means one per variable, so the model should be fully constrained. Might exist some satisfying solutions involving negative concentrations, but we can easily constrain concentrations to be in the interval [0, 1]. 

This can be implemented as a quadratically constrained program (QCP) with a trivial objective (no optimization, we're just looking for a solution).


The model solves beautifully with Couenne [1][2] in about 100 ms.

Results

So, what does the equilibrium look like? Starting with a non-political match rate of 80% we get:

Equilibrium matching pattern using the "chemical" model. Line width in the middle is proportional to the commonness of that couple. Singles are not shown. 

So the political intolerance increases the number of equilibrium singles from 20% to 31.2%. Who gets left out?

V, women   57.1%
MP, women  41.8%
S, women   26.4%
C, women   26.0%
L, women   26.0%
M, women   14.8%
KD, women  15.4%
SD, women  17.0%

V, men     19.3%
MP, men    15.9%
S, men     14.8%
C, men     24.7%
L, men     24.7%
M, men     24.7%
KD, men    32.5%
SD, men    50.8%

Discussion

Wow! Let's analyze. Remember the baseline number of singles is 20%, assuming no politics. Some groups actually go under 20% here, the left leaning men and the right leaning women. So being atypical for your gender can increase one's chances. It's good that the incentive is towards reducing the divide! 

The groups on the edges do much worse. Over 50% singles, wow... I'm looking at it and like: are the assumptions reasonable here? Could it really be that people in these groups will spend on average half their adult life alone? It's a sad outlook. What will be the consequence of this, if true? More inter-national marriages is an obvious one: if one can't find a partner with matching values within the "Swedish" population, then can try to find a foreigner. There are plenty of women with more conservative views in Eastern and Central Europe, but where are the foreign men that are as left leaning as Swedish women? 

When I started this analysis, I expected dire results for the SD men, not being able to find a partner. My take away from this is that there must also be a lot of frustration from V women who cannot find a partner with their values, either. 

Alternative Parameter Values

What happens to matchings if we change our assumptions about equilibrium singles without the political dimension? Assuming a future moral / economic situation like Japan with 50% equilibrium singles, we get:

V, women   80.8%
MP, women  72.0%
S, women   58.6%
C, women   59.6%
L, women   59.6%
M, women   47.7%
KD, women  49.8%
SD, women  53.8%

V, men     59.4%
MP, men    51.6%
S, men     48.0%
C, men     58.1%
L, men     58.1%
M, men     56.2%
KD, men    63.9%
SD, men    76.4%

This scenario has a total of 62.4% equilibrium singles.
What about a much more optimistic moral and economic scenario? (morally favourable, in the sense that it incentivises marriages). Let's consider a world like 1950's American suburbia, with only 2% equilibrium singles:

V, women   24.7%
MP, women  8.1%
S, women   2.8%
C, women   2.3%
L, women   2.3%
M, women   0.5%
KD, women  0.5%
SD, women  0.6%

V, men     0.6%
MP, men    0.5%
S, men     0.5%
C, men     2.6%
L, men     2.6%
M, men     3.3%
KD, men    5.8%
SD, men    19.4%

This scenario has 7.6% equilibrium singles. We see that even in this scenario that is very optimistic with regards to matching, people at the edges still spend a lot of time alone!

References

[1] Couenne, a free open source MINLP solver https://github.com/coin-or/Couenne
[2] I use Couenne by wrapping Pyomo http://www.pyomo.org/