Statistical Models of Presidential Elections

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# Statistical Models of Presidential Elections
## Bayesian inference using polls and the fundamentals
### G. Elliott Morris Data journalist The Economist
### <class=‘date’>October 9, 2020 Prepared for a talk at the IU-Bloomington Workshop on Methods</class>

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# 2020 presidential election forecast*

_*as of October 8 at 7:05 PM_

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# Our model

### 1. National economic + political fundamentals

### 2. Decompose into state-level priors

### 3. Polls

Uncertainty is propogated throughout the models, incorporated via MCMC sampling in step 3.

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# National Fundamentals

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# What fundamentals?

#### i) Index of economic growth (1940 - 2016)
- eight different variables, scaled to measure the standard-deviation from average annual growth

#### ii) Presidential approval (1948 - 2016)

#### iii) Polarization (1948 - 2016)
- measured as the share of swing voters in the electorate, per the ANES --- and interacted with economic growth

#### iv) Whether an incumbent is on the ballot

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# National fundamentals

### Model formula:

vote ~ incumbent_running:economic growth:polarization + approval

### Training

Model trained on 1948-2016 using elastic net regression with leave-one-out cross-validation

RMSE = 2.6 percentage points on two-party Democratic vote share

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# State-level prior

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# State-level prior

#### i) Train a model to predict the Democratic share of the vote in a state relative to the national vote, 1948-2016
* Variables are: lean in the last election, lean two elections ago, home state effects * state size, conditional on the national vote in the state

#### ii) Use the covariates to make predictions for 2020, _conditional on the national fundamentals prediction for every day_

#### ii) Simulate state-level outcomes to extract a mean and standard deviation
* Propogates uncertainty both from the LOOCV RMSE of the national model and the state-level model

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# Pooling the polls

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# It's just a trend through points...

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# (...but with some fancy extra stuff)

```
mu_b[:,T] = cholesky_ss_cov_mu_b_T * raw_mu_b_T + mu_b_prior;  
for (i in 1:(T-1)) mu_b[:, T - i] = cholesky_ss_cov_mu_b_walk * raw_mu_b[:, T - i] + mu_b[:, T + 1 - i];
national_mu_b_average = transpose(mu_b) * state_weights;
mu_c = raw_mu_c * sigma_c;
mu_m = raw_mu_m * sigma_m;
mu_pop = raw_mu_pop * sigma_pop;
e_bias[1] = raw_e_bias[1] * sigma_e_bias;
sigma_rho = sqrt(1-square(rho_e_bias)) * sigma_e_bias;
for (t in 2:T) e_bias[t] = mu_e_bias + rho_e_bias * (e_bias[t - 1] - mu_e_bias) + raw_e_bias[t] * sigma_rho;
//*** fill pi_democrat
for (i in 1:N_state_polls){
  logit_pi_democrat_state[i] = 
    mu_b[state[i], day_state[i]] + 
    mu_c[poll_state[i]] + 
    mu_m[poll_mode_state[i]] + 
    mu_pop[poll_pop_state[i]] + 
    unadjusted_state[i] * e_bias[day_state[i]] +
    raw_measure_noise_state[i] * sigma_measure_noise_state + 
    polling_bias[state[i]];
}

```

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# Poll-level model

#### i. Latent state-level vote shares evolve as a random walk over time
* Pooling toward the state-level fundamentals more as we are further out from election day

#### ii. Polls are observations with measurement error that are debiased on the basis of:
* Pollster firm (so-called "house effects")
* Poll mode
* Poll population

#### iii. Correcting for partisan non-response
* Whether a pollster weights by party registration or past vote
* Incorporated as a residual AR process

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# Tying it all together

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# Tying it all together

## 1. 2016 election-day forecast:

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# Tying it all together

## 2. 2020 forecast*:

_*As of October 9th, 2020_

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# Q&A

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# Thank you!

#### Website: [gelliottmorris.com](https://www.gelliottmorris.com)

#### Email: [elliott@thecrosstab.com](mailto:elliott@thecrosstab.com)

#### Twitter: [@gelliottmorris](http://www.twitter.com/gelliottmorris)

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_These slides were made with the `xaringan` package for R from Yihui Xie. They are available online at https://www.gelliottmorris.com/slides/2020-10-09-indiana-bloomington-methods-workshop/_