A Formula For U.S. Election Outcomes


A Formula For U.S. Election Outcomes

I am wondering what the chances are for significant U.S. government action on the following ten issues, before 2022:

1. Equity of taxation
(popular/leveling vs. corporate/plutocratic),
2. Extract money from politics, kill Citizens United
(prosecute influence peddling and financial crimes),
3. climate change action (Green New Deal),
4. cut war spending, end the Yemen War
(and cut military-corporate subsidies),
5. Medicare-for-All
(versus insurance company gouging),
6. Social Security expansion
(versus general impoverishment for fat cat gains),
7. fund and staff welfare programs
(food, shelter, childcare, post-disaster assistance),
8. immigration reform and smart liberalization,
9. public school upgrades and teacher funding
(versus vouchers for resegregation; free college),
10. end subsidies for Christian xenophobia bigotry
(pursue Civil rights prosecutions, and Reparations).

This depends on what kinds of administrations we get as a result of national and state elections in 2020 and 2022. So, I devised a mathematical model of U.S. voting outcomes based on voter political affiliations and voting preferences. My aim is to have a tool to quantify my guesses about future election outcomes, so as to improve my speculations on when and to what degree desirable action will be taken on the ten issues stated. This exercise was better than being glum, dejected and confused about American politics, and this essay summarizes my findings. I based my model on voting behavior during U.S. presidential (quadrennial) elections instead of on midterm elections, but why not use it for both?

There were 7 of steps in devising this model: 1, determining the fractional composition of the American electorate by age brackets (15 of them); 2, finding the percent voter turnout by age bracket; 3, finding the party identification (both formal affiliation and casual identification) proportionally by age bracket; 4, collapsing all that data into the percent of the voting population that favors each of the three major U.S. political ideologies (from least to most amorphous): Republican, Democratic, and Independent; 5, examining the tabulated numerical date to divine the most general and instructive relationship, dependent on the fewest number of parameters, to devise a specific correlating and predictive mathematical formula; 6, calculate hypothetical results from this formula and then compare them (to the extent possible) with data on prior election outcomes; and 7, generalize the initial formula into an easily used estimating tool.

The Data

My source for population data was the U.S. Census Bureau [1]. On July 1, 2017, the US population was (officially) 325,719,178, and the voting age (18-85+) population (without considering legal barriers) was 252,018,630. I used data published by Charles Franklin on voter turnout as a function of age (https://medium.com/@PollsAndVotes/age-and-voter-turnout-52962b0884ef), [2]. I collapsed Franklin’s smooth data curve (for voter turnout, by age, to presidential elections) into 15 single values of percent turnout, one for each of the 15 age brackets: 18-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60-64, 65-69, 70-74, 75-80, 80-84, 85 and up. Turnout for teen and early 20s voters is 47%-55% (17%-25% for midterms), and turnout increases steadily with age, reaching a broad peak between 80% and 85% for voters 55 to 80 years old (70% to 73% for ages 62 to 79, for midterms). The population between 18 and 34 years (16 year span) is 75,913,971; the population between 60 and 79 years (19 year span) is 58,412,409. The population between 55 and 79 (24 year span) is 80,420,365; the population between 18 and 39 (21 year span) is 97,145,968. Voters between the ages of 18 and 29 (11 year span) contribute 17% of the presidential vote; voters between the ages of 50 and 59 (9 year span) contribute 19% of the presidential vote. Ah, poor youth, condemned to struggle and strive in a country (and world) shaped and directed by the crabbed and brittle prejudices of a smaller number of futureless self-satisfied property owners.

Party affiliation is of two types: being a reliable voter to a party you are registered with, or being an independent voter who will admit to “leaning” (in the voting booth) to the Democrats or Republicans, especially when you are alarmed or enthused about a particular election or issue. Those voters who refuse to declare a duopolistic party allegiance or even a “lean” are the staunch Independents. The Gallup organization has published data on the percent of voters who are Democrats, Republicans, and Independents, as well as leaners to the Democrats and Republicans, by age (https://news.gallup.com/poll/172439/party-identification-varies-widely-across-age-spectrum.aspx), [3]. Using this data, I lumped leaners in with declared party loyalists (respectively, for Republicans and Democrats), and then for each of the 15 age brackets assigned three numerical factors for the percentage of the age bracket voting in each of three modes: Republican, Democratic or Independent. From all the data described to this point, I was able to calculate, for each age bracket, the percent of the presidential vote that went to the Republican and Democratic parties, and to the Independent category. I summed up the results for the 15 age brackets to get an overall composition of the entire voting population, and rounded the final numbers slightly for convenience, to arrive at: 45% Democratic, 40.5% Republican, and 14.5% Independent. I will call this the “baseline.”

Note that all the data described above refers to conditions between 2014 and 2017.

The Formula (!)

If people voted consistently with their declared affiliations, we would have a continuous sequence of Democratic Party administrations; but people don’t, so we have flux and upheaval. In fact, the outcome of our national elections is driven by the surreptitious faithlessness of our tight-lipped (to pollsters at least) Independent voters. Our staunch Independent voters number between 1-in-8 (12.5%) to 1-in-5 (20%) of the voting population, and this fraction varies geographically and over time, in mysterious ways. What actually happens with Independents in the privacy of their voting booths is that they make individual choices about individual issues and candidates, and for each of these they vote in one of three ways: Democratic, Republican, or for one of the myriad of Independent options available, including abstention. So, the 14.5% (to take a fixed number for now) of the voting population that is incorrigibly Independent actually splits into three fractions during voting (quantified here as percentages of the Independent voting population only): I%D, I%R, and I%I. The label I%D represents the percentage of the Independents who voted Democratic in a particular election. Similarly, I%R corresponds to the percentage of the Independents who supplied Republican votes, and I%I corresponds to the percentage of the Independents who remained purely Independent. Note that I%D + I%R + I%I = 100%.

The 4.5% advantage Democrats have over Republicans nationally, based on my calculations (the baseline), can easily be overcome by a 5% or greater net contribution of Republican votes from the Independents. For example, if the Independent population splits: 50% Republican, 5.2% Democratic, and 44.8% staunch Independent (50% + 5.2% + 44.8% = 100% of the Independent population) then they contribute, nationally: 7.2% for Republicans (50% of the 0.145 fraction of the national vote made up of Independents), 0.8% for Democrats (5.2% of their 0.145 national fraction), and 6.5% (44.8% of their 0.145 national fraction) for Independent candidates. The result for the national election becomes: 47.7% Republican (40.5% + 7.2%), 45.8% Democratic (45% + 0.8%), and 6.5% Independent (14.5% – 7.2% – 0.8%). Note that 47.7% + 45.8% + 6.5% = 100% of the national vote. In this case the Republicans win the election with a 2.0% lead (with slight rounding).

By calculating several examples, as just shown, one can arrive at the following equation for election outcomes (for the duopoly horse race).

D-R = 4.5% + [0.145 x (I%D – I%R)].

In words: the percentage difference between Democrats and Republicans in national elections is equal to 4.5% plus the fraction 0.145 multiplied by the difference between the percentage of the Independent voting population that voted Democratic, and the percentage of the Independent voting population that voted Republican. The calculation for the previous example is as follows:

D-R = 4.5% + [0.145 x (5.2% – 50%)] =
D-R = 4.5% + [0.145 x (-44.8%)] =
D-R = 4.5% + [-6.5%]
D-R = -2%

Democrats lose, numerically, by 2%. Also, the actual vote going to Independents nationally is:

Actual Independent Vote Nationally =
14.5% (Independents) – 7.2% (to R) – 0.8% (to D) = 6.5%.

After playing a while with the duopoly horse race estimator formula, give above, I realized one can generalize it further.

D-R = D0 + [Fl x (I%D – I%R)].

D-R = percentage difference between Democrats and Republicans, from election.
D0 = percentage advantage (+) or disadvantage (-) for Democrats, based on affiliations.
FI = the fraction (not percentage) of the voting population that is Independent.
I%D = the percentage of the Independent population that chooses D (this time).
I%R = the percentage of the Independent population that chooses R (this time).
I%I = the percentage of the Independent population that remains I (this time).
Note that: I%D + I%R + I%I = 100%.

So far here, I have used D0 = 4.5%, and FI = 0.145. However, you can choose different numbers based on your own survey of population, voter turnout and party affiliation data, or on your intuition about a particular electoral contest. As mentioned earlier, estimates of FI can range between 0.125 (1/8) to 0.2 (1/5), and perhaps beyond.

Comparing To Previous Elections

I have not found data on the population sizes and voting splits of the Independent voting contingent in previous elections. It would be nice to validate the formula using such data. While the assumptions underpinning this model may not be representative of conditions in all prior US elections, we can nevertheless use prior election results to calculate inferences about what might have been the voting behavior of Independent voters in the past. To do that, we assume that the baseline (40.5% R, 14.5% I, 45% D), which was calculated from 2014-2017 data, has been constant (or nearly constant) since 1968. Here are the calculated inferences on how Independents voted in elections since 1968, based on the known national outcomes.

1968, Nixon
R. Nixon (R) 43.4% vs. H. Humphrey (D) 42.7% vs. G. Wallace (I) 13.5%
Remainder of the national vote is 0.4%
Independents contribute 14.5% of the national vote
Independents split: 77.2% (Wallace), 20% (R), 0% (D), 2.8% (I).

1972, Nixon
R. Nixon (R) 60.7% vs. G. McGovern (D) 37.5%
Remainder of the national vote is 1.8%
Independents contribute 14.5% of the national vote
Independents split: 87.6% (R), 0% (D), 12.4% (I)

1976, Carter
J. Carter (D) 50.1% vs. G. Ford (R) 48%
Remainder of the national vote is 1.9%
Independents contribute 14.5% of the national vote
Independents split: 51.7% (R), 35.2% (D), 13.1% (I)

1980, Reagan
R. Reagan (R) 50.7% vs. J. Carter (D) 41% vs. J. Anderson (I) 6.6%
Remainder of the national vote is 1.7%
Independents contribute 14.5% of the national vote
Independents split: 42.8% (R), 0% (D), 45.5% (Anderson), 11.7% (I)

1984, Reagan
R. Reagan (R) 58.8% vs. W. Mondale (D) 40.6%
Remainder of the national vote is 0.6%
Independents contribute 14.5% of the national vote
Independents split: 95.9% (R), 0% (D), 4.1% (I)

1988, Bush Sr.
G.H.W. Bush (R) 53.4% vs. M. Dukakis (D) 45.6%
Remainder of the national vote is 1.0%
Independents contribute 14.5% of the national vote
Independents split: 89% (R), 4.1% (D), 6.9% (I)

1992, Clinton
W. Clinton (D) 43% vs. G.H.W. Bush (R) 37.4% vs. R. Perot (I) 18.9%
Remainder of the national vote is 0.7%
Independents contribute 14.5% of the national vote
Independents split: 0% (R), 0% (D), 95.2% (Perot), 4.8% (I)

1996, Clinton
W. Clinton (D) 49.2% vs. R. Dole (R) 40.7% vs. R. Perot (I) 8.4%
Remainder of the national vote is 1.7%
Independents contribute 14.5% of the national vote
Independents split: 1.4% (R), 29% (D), 58% (Perot), 11.6% (I)

2000, Bush Jr.
G. Bush (R) 47.9% vs. A. Gore (D) 48.4%
Remainder of the national vote is 3.7%
Independents contribute 14.5% of the national vote
Independents split: 51% (R), 23.5% (D), 25.5% (I)
Bush appointed despite a 0.5% deficit.

2004, Bush Jr.
G. Bush (R) 50.7% vs. J. Kerry (D) 48.3%
Remainder of the national vote is 1.0%
Independents contribute 14.5% of the national vote
Independents split: 70.3% (R), 22.8% (D), 6.9% (I)

2008, Obama
B. Obama (D) 52.9% vs. J. McCain (R) 45.7%
Remainder of the national vote is 1.4%
Independents contribute 14.5% of the national vote
Independents split: 35.9% (R), 54.4% (D), 9.7% (I)

2012, Obama
B. Obama (D) 51.1% vs. M. Romney (R) 47.2%
Remainder of the national vote is 1.7%
Independents contribute 14.5% of the national vote
Independents split: 46.2% (R), 42.1% (D), 11.7% (I)

2016, Trump
D. Trump (R) 46.1% vs. H. Clinton (D) 48.2%
Remainder of the national vote is 5.7%
Independents contribute 14.5% of the national vote
Independents split: 38.6% (R), 22.1% (D), 39.3% (I)
Trump appointed despite a 2.1% deficit.

The 2.1% Republican Credit

In the 2000 election, G. Bush (R) had a 0.5% deficit and was still appointed the 43rd President of the United States of America.

In the 2016 election, H. Clinton (D) gained a 2.1% lead over D. Trump (R) – the same lead J. Carter (D) used to win in 1976 – and yet Trump was appointed the 45th President of the United States of America.

These “deficit wins” were due to a combination of nefarious factors: the Electoral College, pro-Republican judicial bias, voter suppression efforts (in both R and D varieties), vote counting sabotage, and undoubtedly other forms of creative incompetence.

So, today we must assume that because of embedded structural irregularities in the American electoral mechanism, that Democrats must gain more than a 2.1% advantage over Republicans in order to win national elections.

I easily concede that my simple clean mathematical formula does not contain the full range of rascally dirty realities in American electoral spectacles.

Dreams Of DSA Utopia

Could a significant politically leftward sentiment ever take hold among the Independent voting population, and this cause a leftward shift in electoral outcomes? The more socialist (or democratic-socialist, or progressive, of left) the legislators, executives and administrations that result from near-future elections, the more likely the ten issues I listed at the beginning would get serious attention – and action!

W. Clinton (D) won in 1996 with an 8.5% advantage. His Democratic administration was pure corporate, no different from center-right Republican policy before Reagan. I assume that if the voting population turned further away from Republicans, and more in favor of the most socialist-oriented Democratic candidates, that the resulting Democratic administrations would be less corporate-oriented (yes, I know this is magical thinking at present).

So, perhaps a Democratic victory with a 12.5% advantage would result in a Democratic administration that is a half-and-half mixture of corporate (DNC type) Democrats and socialist (DSA type) Democrats, and then some serious nibbling would occur on the ten issues. Mathematically, this could result if the hypothetical Independents split: 55.2% (D), 0% (R), and 44.8% stayed pure (I). The projected national election result would be 53% Democratic, 40.5% Republican, and 6.5% Independent.

An even better though less likely occurrence would be a socialist Democratic Party that gains a 16.5% electoral advantage, driving the Republican Party to extinction (instead of us!). Using the formula, we can infer an Independent split of: 82.8% (D), 0% (R), 17.2% pure (I). The projected national election result would be 57% Democratic, 40.5% Republican, 2.5% Independent.

The ultimate fantasy is of all Independents becoming enthusiastic DSA socialists, so they would add their 14.5% of the national vote to a socialist Democratic Party, with a projected electoral result of: 59.5% Democratic (pure DSA), 40.5% Republican, 0% Independent. An electorate that could accomplish this would empower national and state administrations that would address the ten issues listed earlier, with vigor and all the resources – human, material, and intangible – available to this rich nation.

However improbable the last scenario – of a Socialist political tsunami – appears in the United States of today, I think it is better to keep it in mind as a vision (more easily done if you are young), rather than acidly disparaging and brusquely dismissing it (more likely done by the old and bitter), because it can help motivate useful activism and kind action from those who want a better world with fairer politics and economics, and know that it is humanly possible to get it.


[1] Annual Estimates of the Resident Population for Selected Age Groups by Sex for the United States, States, Counties, and Puerto Rico Commonwealth and Municipios: April 1, [use above title to search in “2017 Population Estimates,” link below is just a start]

[2] Age and Voter Turnout (Charles Franklin)

[3] Party Identification Varies Widely Across the Age Spectrum


Richard Dedekind & Irrational Numbers

This post is entirely the work of Patrick Weidhaas, a mathematician and friend.


Patrick Weidhaas: “I recently wrote a math article on the very successful definition of the real numbers by the German mathematician Richard Dedekind (1831-1916). He came up with the “Dedekind cuts.” I learned about this in college and never fully understood it — and wasn’t that interested in it. Only lately did I fully appreciate the significance of his attempt to define the real numbers purely through arithmetic — without any help from geometry.”

Patrick Weidhaas: “This is a photo I took in Berlin on September 11, 2010. It is one of my favorite shots. I still remember the late sunny afternoon as I encountered this blue bridge and the small lake (“Königssee”) below.”


DEP Micro-device 2D Electric Field

I used to have the ambition of being an “artistic scientist,” a physicist and engineer aiming to produce scientific findings that were both useful and elegant, and which I would present in as beautiful a manner as I was able. The type of beauty I sought is a combination of logical simplicity, mathematical elegance, some range and depth of insight provided by the ideas, all communicated with visual and literary crispness in my written reports and other presentations.

I achieved this ideal, to my own satisfaction at least, a few times during my scientific career. One of those proud achievements is my model of the electric field in dielectrophoretic (DEP) micro-devices.

My original report “The 2D Electric Field Above A Planar Sequence Of Independent Strip Electrodes” is available below (a link to a PDF file). The report is dated 4 October 1999, and lists two authors; the second author is the patron who paid my salary during the months I worked on this project.

This paper was sent to a journal and subsequently published, but with egregious errors introduced by the journal’s editors, who “simplified” my math for publishing convenience. Months after I pointed this out to them, they issued an errata. The combination of the published paper and the errata (showing correct formulas) did not include many of the illustrations I had produced for my original report (Version 1), and which I think would help anyone actually thinking of using my mathematical model of DEP electrostatics.

So, this blog entry is similar to the case of a former artist who pulls out an obscure and favorite painting of theirs from storage in an attic or basement, dusts it off, and hangs it up on the wall so he can look at it again, and remember how good it felt to make.

A second report (an excerpt in PDF form) describes how use of the electrostatic model could assist in the development of DEP micro-devices (which are used in DNA sequencing technology).

DEP Device Diagram

DEP Device Diagram

DEP 2D Math Beauty

DEP 2D Math Beauty

DEP 2D Model Version-1

DEP 2D Model & micro-devices