Anirban DasGupta writes:

I thought it would be revealing and entertaining to look at the recently concluded US midterm election results and make some conclusions. Who is voting Republican? What is, really, the Republican base? And what about the Democrats? Are the bases entirely disjoint? Is the base more scattered for one of the parties compared to the other? Are the midterm voters of each party essentially the same as the voters who voted for them in the 2016 Presidential election? Or, are the two parties growing and capturing new voters? We will see…
We will also give a probability based on a stated model that the sitting US President would be reelected if elections are held now. First, the actual 2018 midterm data, which is presented in table 1.

Table 1: voting data for 2018 US midterm elections

 Group Group size Republican % Democrat % All voters 44% 50.5% All males 48% 51% 47% All females 52% 40% 59% White men 35% 60% 39% White women 37% 49% 49% White men no college 20% 66% 32% White men college 15% 51% 47% White women no college 21% 56% 42% White women college 16% 39% 60% Nonwhites no college 18% 22% 76% Nonwhites college 10% 22% 77% All 18-29 age 13% 32% 67% All 45-64 39% 50% 49% All whites 72% 54% 44% Blacks 11% 9% 90% Latinos 11% 29% 69% Asians 3% 23% 77% Black men 5% 12% 88% Black women 6% 7% 92% Gun owners 46% 61% 36% Non gun owners 53% 26% 72 % Protestants 25% 61% 38% Catholics 26% 49% 50% White evangelicals 26% 75% 22% Jewish 2% 17% 79% Married 59% 47% 51% Unmarried 41% 37% 61% Independents 30% 42 % 54% Trump strongly like 31% 94% 5% Trump like some 14% 74% 24% Trump dislike some 8% 34% 63% Trump strongly dislike 46% 4% 95% Health care main issue 41% 23% 75% Immigration main 23% 75% 23% Economy main 22% 63% 34% LGBT 6% 17% 82% Urban 32% 32% 65% Suburban 51% 49% 49% Rural 17% 57% 42%

In view of these demographic voting percentages, by an elementary application of Bayes’ theorem, we can identify subgroups of the US population that can be called the bases of the two political parties. White men form 35% of the total population, but form 48% of the Republican vote. Evangelical Christians form 26% of the total population, and yet form 44% of the Republican vote. Gun owners also form 44% of the Republican vote, and about 20% of the Republican vote are rural voters.
In contrast, women form 52% of the total population, but form 61% of the Democratic vote. White women with a college degree and blacks each form 20% of the Democratic vote, millennials form 17%, Latinos 15%, black women alone 11%, LGBT voters 10%, and urban and suburban voters form a whopping 86% of the Democratic vote. The Democratic base seems to consist of a larger number of smaller subgroups than two or three large dominating groups. The Democratic base is more uniform. It is useful to present the bases in a tabular form (see table 2 and table 3, below).

Table 2: Republican base, data for 2018 US midterm elections

 Republican Base % of population % of Rep. vote White men 35% 48% White men no college 20% 30% Evangelicals 26% 44% Gun owners 46% 44% Rural voters 17% 20%

Table 3: Democrat base, data for 2018 US midterm elections

 Democratic Base % of population % of Dem. vote Women 52% 61% Women with college degree 16% 20% Blacks 11% 20% Millennials 7% 17% Latinos 11% 15% Black women 6% 11% LGBT voters 6% 10%

We can also deduce from the midterm results and Bayes’ theorem that 83% of the Republican voters in the midterm are those that voted for the Republican nominee in the 2016 Presidential election; and 80% of the Democratic voters in the midterm are those that voted for the Democratic nominee in the 2016 Presidential election. Both parties have attracted some new voters. Political activity in the coming months will no doubt see the two parties protect and defend interests of their respective bases.
It is always a seductive idea to try to predict the future, especially for a loaded question such as, “Will the sitting US President be re-elected?” We give some sort of a probability for it based on a set of assumptions, which are that:

(a) The probability is for re-election if elections are held now.

(b) It is assumed that whether or not the sitting President wins the electoral college votes in a given state is determined by his approval rating in that state.

(c) If the approval rating is 50% or more, it is assumed that he is guaranteed to win that state, and if the approval rating is 45% or less, it is assumed that he will lose that state. If the approval rating, say $α$, is between 0.45 and 0.5, we model the probability that he will win that state as $20 × (α − 0.45).$

(d) Based on the approval ratings in each state at the 2018 midterm elections, there are then only four states that are in play: Arizona, Nevada, North Carolina, and Wisconsin. The sitting Presidents’ winning probability in these states are respectively 0.75, 0.5, 0.75, 0.5, using the formula in (c). These states carry 11, 6, 15, 10 electoral college votes, respectively. So, plainly, the probability of carrying all four states is at most 0.5.

(e) If we let $µ$ denote the expected number of electoral colleges the sitting President will win from these four states, then, by using the obvious indicator variables, $µ = 27.5$.

(f) Of the 306 electoral colleges that the sitting President won in the 2016 election, he is assured to win in 228 at this point of time, and he is assured to lose in 42 of them (PA approval 45, MI approval 44, IA approval 43). Thus, to still win an electoral college majority of at least 270 electoral colleges, he must carry all four states in play listed above.

Therefore, the probability that the sitting President will win re-election if elections are held now is approximately 14%, under the model stated in (a)–(c), and mutual independence of voters in these four states. We can give a conservative bound without assuming this mutual independence, for, by Markov’s inequality, the probability that the sitting President will win all four of the above states is at most 2.5÷4 = 0.625. If we average the 14% number and the 62.5% number, we get 38.5%, and it is humorous to notice that this is alluringly close to the betting market probability (according to PredictIt) as I write this…