by John Allen Paulos
Voters are lazy and often pay little or no attention to numbers and facts presumably relevant to their concerns.
I remember initiating a discussion of the housing crisis in the US. I mentioned a headline I claimed to have just read, which stated “Experts Fear Annual Housing Costs in the U.S. – Rent and Mortgage Payments – Might Top $3 Billion.” I expressed my concern with, “Imagine that – more than 3 billion dollars per year.”
People to whom I related the number responded by bemoaning the mortgage crisis, foreclosures, Wall Street, immigrants, and a host of other issues. Only a couple ever really thought about the headline and noticed that 3 billion is a ludicrously low number. A population of 350 million translates to about 100 million households. Dividing 100 million into $3 billion results in about $30 per person in rent or mortgage paid annually by the average household. Just $30 a year! I’d probably run into the same numerical slothfulness and incomprehension if I initially said $3 trillion was the annual cost for housing in the US. I can imagine that if these numbers arose naturally and were not so obviously crazy, partisan differences between groups would inevitably develop.
This anecdote is not without relevance for larger issues such as Social Security, Medicaid, Health Care, immigration, climate change, and so on.
Regarding the latter and what now passes for the EPA, I note that terminating measures designed to limit climate change and replacing them with measures that encourage drilling and fracking constitute a sort of Ponzi scheme. The early investors and proponents (and everyone else) would see lower oil and gas prices for a while. Not much later, however, these same investors and proponents (and everyone else) would live in a much less pleasant and habitable world. Some of the proponents of “drill, baby, drill” have even signed on to the common, but absurd assertion that global warming is a hoax. One needn’t be able to graph y = x + sin(x) to realize that a generally upward movement of average temperatures doesn’t preclude occasional local dips. Likewise, someone with terminal cancer will feel pretty good on some days without doctors revising their prognosis. In any case the business/environmental schism is as hard as ever.
The effects of ignorance and innumeracy are ubiquitous, so I’ll just mention one more salient issue. Fentanyl coming into the United States from either Canada or Mexico is seen by some voters who are devoid of any feeling for numbers and/or truth to be problems of comparable significance. They might hear about the 20,000 grams of intercepted fentanyl coming into the US from Canada last year and become outraged, but they would not likely express more outrage about the 10 million grams of intercepted fentanyl (500 times as much) coming into the US from Mexico last year. In both cases the amount crossing the borders is no doubt much larger, although the ratio of the two countries’ contributions is likely to be the same. In any case, people’s attitudes about the importation of fentanyl from Mexico and Canada as well about the deportation of immigrants from Mexico and Central America are quite divided, but they’re nevertheless usually expressed with great certainty.
I could go on and on, but let me focus on a related question. Why is there so often a lockstep liberal versus conservative response to the soup of misinformation and disinformation that surrounds us? A complicated question, of course, but If the numbers and facts pertaining to the issues mentioned above aren’t sufficient to move individual voters to vote independently on these issues, what is? A very simple, but abstract model introduced in 1999 by Joshua Epstein formerly of the Brookings Institution, “Learning to be Thoughtless: Social Norms and Individual Computation,” suggests that a partial answer is people’s propinquity to their neighbors. (Since then Epstein and others have developed more sophisticated agent-based models that provide insight into the onset of violence, the development of economies, and a host of other phenomena.)
So what is the model? Let’s imagine that metaphorically arrayed around a big circle are millions of people who each day must decide whether they intend to vote for the conservative red or the liberal blue candidate. Assume that these people may or may not have an initial favorite candidate, but that they are very conformist, low-information voters and prefer to consult their immediate neighbors before deciding. After asking the people on either side of them, they adjust their vote to conform to that of the majority of their neighbors.
This can be done in a number of ways. One is to expand their samples of adjacent voters only as much as necessary and reduce them as much as possible, wishing always to conform with a minimum exertion. Initially they’re disengaged and relatively uninterested in issues such as the ones discussed above. A possible way to model this situation is to use the following specific rule, which, of course, can be made more realistic. If one day a voter, say George, asks about the preferences of the X people on either side of him, the next day he expands his sample to the X+1 people on either side of him. If the percentage favoring the two candidates in this expanded sample is different than it is when he asks only the X people on either side of him, he expands his sample further.
On the other hand, if the percentage favoring the two candidates is the same in the expanded sample as it is when he asks only the X people on either side of him, George might feel that he is working too hard. In this case he reduces his sample to the X-1 people on either side of him. If the percentage favoring the candidates is the same in this smaller sample, he reduces the sample further. Every voter updates his or her favorite candidate daily and interacts with other voters according to these same rules. (Incidentally these rules might remind one of John Conway’s agent-based Game of Life.)
There is a surprising consequence of Epstein’s rules, the sort of common phenomenon in which simple rules give rise to recognizable human patterns. After several days of this sequential updating of votes, there are long arcs of solid red voters and long arcs of solid blue voters and between these there are small arcs of very mixed voters. After a short while, voters in the solid arcs need to consult only their immediate neighbors to decide how to vote and almost never change their votes. Voters between the solid arcs need to consult many people on either side of them and change their vote quite frequently.
Although Epstein didn’t apply his model to voting but to automatically-followed social norms, the idea of extending it to voting is natural. People do tend to surround themselves, metaphorically at least, with others of like mind and generally only those at the borders between partisans, the so called independent swing voters, are open to much change. His major point, which I’m distorting a little here by casting his model into an electoral framework, is that social norms and electoral preferences often result from nothing more than propinquity. They make it unnecessary to think much about what to wear, which side of the road to drive on, when to eat, or whom to vote for.
To the considerable extent that voting is – at least for many people – an unthinking emulation of those with whom they associate, the model helps explain the near uniformity of the political opinions of their friends about guns, abortions, immigrants,
Also, when there’s some sort of shock to the system, Epstein’s model suggests something else rather interesting. If a large number of voters change their vote suddenly for some reason (say a pandemic, economic collapse, or environmental catastrophe), the changed voter preferences soon settle down to a new equilibrium just as stable with solid red, solid blue, and mixed border areas, but located at different places around the circle. The model thus shows how political allegiances can sometimes change suddenly, but then settle quickly into a new but different set of uni-colored arcs just as rigidly adhered to as the old.
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John Allen Paulos is an emeritus Professor of Mathematics at Temple University and the author of Innumeracy and A Mathematician Reads the Newspaper. These and his other books are available here.
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