To a small degree. To a bigger degree, powerful or at least people with extra power can get away with it more often and especially evade consequences.
As to the kind of cheating from the article: They're not tied by material concerns, they can handle the social implications of being found out better, they have a much bigger set of available spouses and/or social time.
Powerful almost always means rich. Rich people who divorce lose out on a richer life, maybe because they pay alimony, maybe because they lose social status, maybe because they just don't get to join finances with another rich person. Cheating is a way to avoid divorce and still get your needs fulfilled. Not a great way, but a way.
It is not useless to research the "obvious", sometimes, the "obvious" can be wrong.
Anyway, the research is about the "why", not a proof that it happens. And their conclusion is that "what determines whether power elicits extradyadic interest is not power perceptions alone but rather the feeling of having a higher mate value than one’s partner". i.e. power => confidence => cheating, not power => cheating directly.
I married into a wealthy-ish family, and this was probably my biggest disappointment. In my anecdotal experience, wealthier individuals lack humanity for others, are quite selfish, and lie through their teeth to make things go their way.
Candidly, I was a centrist before marriage, but I've become a strong advocate for socialism (and against late stage capitalism). The skills you need to be affluent (barring exceptions like FAANG founders) are skills no one should really cultivate.
I've similar anecdotal experience. Generalizing however can be very dangerous so I offer these words with caution.
The most difficult people I've had to deal with throughout my life are those who've had a sense of entitlement. They are greedy and have no shame at exploiting people and they do whatever it takes to achieve their own ends, if that means lying or doing crooked deals then so be it.
Some, I figure, are psychopathic and or have extreme sociopathic tendencies, they have no sense of guilt, and the word 'empathy' is lost on them altogether.
I have difficulty in dealing with such people and I feel ill at ease being around them. What I'm reasonablely good at however is recognizing them early on and that helps when I have to work or communicate with them.
Unfortunately, one of the major problems in the word today is that the drive, ambition and ruthlessness of these people find them in disproportionately high numbers in government, industry and other positions of power, and that has contributed to the growing inequality in the world. As we're now witnessing the smooth functioning of society is being disrupted by their decisions.
Throughout history most societies have never found a way to combat these people effectively, for when in power they use that power to further entrench their positions.
You mention socialism. Take a look at Marx and Engels' work and how that was bastardized by nasty ruthless bastards such as Stalin. Today, the authoritarian rule of Stalin and cohorts is held up and used by those about whom we are talking to taint and discredit any form of socialism or distribution of wealth. They deliberately hold up the outrageous excesses of the likes of Stalin for the very purpose of obtaining power, wealth and control of their own.
Now take the neoliberalism of the late 20th Century, once Breton Woods fell in the 1970s many of these self-centered opportunists reordered the world's economics, and now we have the rich becoming richer and the poor becoming poorer to the extent that the social fabric in many countries is starting to break apart. The middle-class is now fast becoming the new poor.
The problem with these people is that their force of personality, pushiness and lack of consideration for others always puts them in the fore. And it's always been so throughout history.
Tragically, I see no reasonable solution for ways of keeping them in check.
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