The math of changing MY mind

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In the first two parts of this series of posts, I looked at a mathematical simulation technique called the Markov chain to explain how the Republican Party positions on at least four key issues have turned 180 degrees in a very brief amount of time. Turnabout is fair play. This post is a brief look at how my own mind was changed, along with the cumulative minds of millions of others, much to the consternation of other millions, on a significant social issue. And the math of change works the same way on me as it does on everybody else.

Like perhaps as many as 90% of Americans, I went through the 1970s, a young adult at the time, vaguely opposed to the legalization and social acceptance of same-sex marriage. I was raised in a time and place where homosexuality was “that which shall not be named,” even though in retrospect I have since learned of the damage that this collective silence had at that time, even on my own family and friends.

The data varies among different studies, but approval of same sex marriage by 1988 in the United States (when I was 37 years old) was only at 11%. [1] By that time, however, my own “world” had expanded, and I counted several LGBTQ people as friends and close business colleagues, and like Barack Obama famously said, my views on the subject “evolved” over time. I can’t tell you exactly where in that period my position changed, but by the time the marriage issue became a more visible part of social conversation, I would have been polled as “accepting.”

And I think that is an important point. For some of us, the “tipping point” may have been clear, but for others it shows up in an after-the-fact realization that, yes, I am now thinking differently. Perhaps our brains resist admitting our past errors until even our “change of mind” is in the past.

The opinions of many other Americans changed during the 1980s, and steadily since, and by, I would assert, a similar, incremental “Markov chain” process, so that by 2017 this approval number stood at 62% in the U.S. People’s views changed “one at a time” as the feared and unfamiliar became the “real people” of “my son,” “my daughter,” or “my good friend.” In the language of the earlier posts on Markov chains, a small, but persistent number of people “defected” to the new position every year, even though a much larger percentage did not change their minds in any given year.

The Markov chain of social acceptance

If “Circle A” in the diagram below represents opposition to same-sex marriage, and “Circle B” is acceptance, then we can see that, from 1988 through to now, there has been some “defection rate” of people shifting to “Circle B” which has, importantly, been greater than the “defection rate back” from “B” to “A”.

Markov Defections

The Pew data referenced below does show a couple of years where the acceptance percentage had slipped a percentage point or two, but it is difficult to parse out whether this a real “net defection back” or rather was, more likely, standard statistical sampling error. I suspect the latter.

The Markov chain spreadsheet referenced in this earlier post can be used to simulate this shift, and you can develop several post hoc mixes of “defection rates” in either direction that come close to reported data. The best fit indicates a low “A to B” defection rate of only about 2% per year early on, but the rate itself appears to have organically grown up to almost a 4% “defection rate” per year over to acceptance by the last decade. [2]

In other words, the odds of you, out of the larger population, changing your mind on this issue was always quite small, but the odds grew a bit stronger every year. And since very few people have “defected back” to the opposition side on this issue in any year, the social “temperature” has gradually changed over to acceptance of same-sex marriage.

Is “normal” just a statistic?

I prefer to look at this issue as one where the enforcement of long-standing social norms has been fighting a losing battle with understanding the nature of biological and statistical “normality.” We all have dozens (and maybe more) of these visible and invisible sex-related characteristics, including adult height (of which I am personally a “deviant” without great social consequence unless I travel by airplane).

The natural variation of people carrying an “XX” chromosome (tagged “female”) creates a normal curve for each of these characteristics that is usually different from, but also greatly overlapping, the normal curves generated by the natural variation of people carrying an “XY” chromosome (tagged “male”). [3] For instance, there are different “normal” curves for adult height for “XX” and “XY” people, but the curves overlap. Many women are taller than many men. So also is the likely case for many (or most) other sex-related characteristics.

Religion historically tags some of these norms as more important than others on moral grounds. The interesting question to me is whether the statistical norms are the cause of long-standing social and religious norms that usually change slowly, if at all, or whether they are sourced in some larger, independent “Truth.” In short, does religion drive culture or does culture drive religion? These days I lean toward the latter.

The best case for the latter is found in the earlier post about the positional changes in the Republican Party over the last two years. Somehow, an American president that fails just about every traditional test of “moral probity” in most religious traditions enjoys huge favorable ratings by the most conservative of American religious affiliations and their leaders.

The “Markov chain” social change in support of same-sex marriage was slow and steady, with religious opposition fading only slowly and still visibly present. The “Markov chain” social change that elected Donald Trump, on the other hand, was amazingly fast, religious opposition be damned.

Part Three of this series has now been posted.


  1. Two sources of data are: ​Americans Move Dramatically Toward Acceptance of Homosexuality.” NORC at the University of Chicago; and Mitchell, Travis, “Changing Attitudes on Gay Marriage.” Pew Research Center’s Religion & Public Life Project, 26 June 2017.
  2. This earlier post demonstrates how logarithmically-increasing rates, rather than linear growth, is more the norm in nature and culture rather than the exception.
  3. And of course, humans also have “XXY”, “XYY” and other chromosome variations naturally found in the species.


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