Case st u d y: election fra u d IN FE R E N C E FOR C ATE G OR IC - - PowerPoint PPT Presentation

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Case st u d y: election fra u d IN FE R E N C E FOR C ATE G OR IC - - PowerPoint PPT Presentation

Nov 08, 2023 47 likes •627 views

Case st u d y: election fra u d IN FE R E N C E FOR C ATE G OR IC AL DATA IN R Andre w Bra y Assistant Professor of Statistics at Reed College Election fra u d Vote b uy ing Voting t w ice Altering v ote totals 1 The phrase election fra u d

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Case study: election fraud

IN FE R E N C E FOR C ATE G OR IC AL DATA IN R

Andrew Bray

Assistant Professor of Statistics at Reed College

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INFERENCE FOR CATEGORICAL DATA IN R

Election fraud

Vote buying Voting twice Altering vote totals

The phrase election fraud can mean many things including vote buying, casting two ballots in dierent locations, and stung ballot boxes with fake ballots. We're going to focus on a version of the third, when the vote

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INFERENCE FOR CATEGORICAL DATA IN R

Election fraud

Vote buying Voting twice Altering vote totals

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INFERENCE FOR CATEGORICAL DATA IN R

Benford’s Law A.K.A. "the first digit law"

library(gapminder) gapminder %>% filter(year == 2007) %>% select(country, pop) # A tibble: 142 x 2 country pop <fct> <int> 1 Afghanistan 31889923 2 Albania 3600523 3 Algeria 33333216 4 Angola 12420476 5 Argentina 40301927 6 Australia 20434176 7 Austria 8199783 8 Bahrain 708573 9 Bangladesh 150448339 10 Belgium 10392226 # … with 132 more rows

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INFERENCE FOR CATEGORICAL DATA IN R

Benford’s Law A.K.A. "the first digit law"

If the election was fair then vote counts should follow Benford’s Law. If the election was fraudulent then vote counts should not follow Benford’s Law.

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INFERENCE FOR CATEGORICAL DATA IN R

Iran election 2009

iran %>% select(city, ahmadinejad, mousavi, total_votes_cast) # A tibble: 366 x 4 city ahmadinejad mousavi total_votes_cast <chr> <dbl> <dbl> <dbl> 1 Azar Shahr 37203 18312 56712 2 Asko 32510 18799 52643 3 Ahar 47938 26220 75500 4 Bostan Abad 38610 12603 51911 5 Bonab 36395 33695 71389 6 Tabriz 435728 419983 876919 7 Jalfa 20520 14340 35295 8 Chahar o Imaq 12197 3975 16375 9 Sarab 53196 17669 72152 10 Shabestar 37099 39182 77459 # … with 356 more rows

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Let's practice!

IN FE R E N C E FOR C ATE G OR IC AL DATA IN R

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Goodness of fit

IN FE R E N C E FOR C ATE G OR IC AL DATA IN R

Andrew Bray

Assistant Professor of Statistics at Reed College

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INFERENCE FOR CATEGORICAL DATA IN R

First Digit Distribution

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INFERENCE FOR CATEGORICAL DATA IN R

First Digit Distribution

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INFERENCE FOR CATEGORICAL DATA IN R

First Digit Distribution

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INFERENCE FOR CATEGORICAL DATA IN R

First Digit Distribution

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INFERENCE FOR CATEGORICAL DATA IN R

First Digit Distribution

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INFERENCE FOR CATEGORICAL DATA IN R

Chi-squared distance

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INFERENCE FOR CATEGORICAL DATA IN R

Chi-squared distance

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INFERENCE FOR CATEGORICAL DATA IN R

Chi-squared distance

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INFERENCE FOR CATEGORICAL DATA IN R

Chi-squared distance

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INFERENCE FOR CATEGORICAL DATA IN R

Chi-squared distance

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INFERENCE FOR CATEGORICAL DATA IN R

Chi-squared distance

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INFERENCE FOR CATEGORICAL DATA IN R

Chi-squared distance

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INFERENCE FOR CATEGORICAL DATA IN R

Chi-squared distance

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INFERENCE FOR CATEGORICAL DATA IN R

Chi-squared distance

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INFERENCE FOR CATEGORICAL DATA IN R

Chi-squared distance

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INFERENCE FOR CATEGORICAL DATA IN R

First Digit Distribution

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INFERENCE FOR CATEGORICAL DATA IN R

First Digit Distribution

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INFERENCE FOR CATEGORICAL DATA IN R

First Digit Distribution

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INFERENCE FOR CATEGORICAL DATA IN R

First Digit Distribution

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INFERENCE FOR CATEGORICAL DATA IN R

Example: uniformity of party

ggplot(gss2016, aes(x = party)) + geom_bar() + geom_hline(yintercept = 149/3, color = "goldenrod", size = 2) tab <- gss2016 %>% select(party) %>% table() tab Dem Ind Rep 43 72 34 p_uniform <- c(Dem = 1/3, Ind = 1/3, Rep = 1/3) chisq.test(tab, p = p_uniform)$stat X-squared 15.87919

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INFERENCE FOR CATEGORICAL DATA IN R

Simulating the null

gss2016 %>% specify(response = party) %>% hypothesize(null = "point", p = p_uniform) %>% generate(reps = 1, type = "simulate") # A tibble: 149 x 2 # Groups: replicate [1] party replicate <fct> <fct> 1 I 1 2 D 1 3 I 1 4 I 1 5 D 1 6 R 1 7 I 1 8 R 1 9 D 1 10 I 1 # ... with 139 more rows

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INFERENCE FOR CATEGORICAL DATA IN R

Simulating the null

sim_1 <- gss2016 %>% specify(response = party) %>% hypothesize(null = “point”, p = p_uniform) %>% generate(reps = 1, type = "simulate") ggplot(sim_1, aes(x = party)) + geom_bar()

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Let's practice!

IN FE R E N C E FOR C ATE G OR IC AL DATA IN R

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And now to US

IN FE R E N C E FOR C ATE G OR IC AL DATA IN R

Andrew Bray

Assistant Professor of Statistics at Reed College

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INFERENCE FOR CATEGORICAL DATA IN R

Iran election fraud

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INFERENCE FOR CATEGORICAL DATA IN R

Iran election fraud

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INFERENCE FOR CATEGORICAL DATA IN R

Iran election fraud

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INFERENCE FOR CATEGORICAL DATA IN R

Iran election fraud

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INFERENCE FOR CATEGORICAL DATA IN R

U.S.A. 2016 election

H : the election was fair (Benford’s Law

holds)

H : the election was fraudulent (Benford’s

Law does not hold)

A

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INFERENCE FOR CATEGORICAL DATA IN R

Iowa vote totals

By TUBS [CC BY SA 3.0], from Wikimedia Commons

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INFERENCE FOR CATEGORICAL DATA IN R

Iowa vote totals

iowa # A tibble: 1,386 x 5

  • ffice candidate party county votes

<chr> <chr> <chr> <chr> <dbl> 1 President/Vice Pre… Evan McMullin / Nathan Johnson Nominated by Peti… Adair 10 2 President/Vice Pre… Under Votes NA Adair 32 3 President/Vice Pre… Gary Johnson / Bill Weld Libertarian Adair 127 4 President/Vice Pre… Over Votes NA Adair 5 5 President/Vice Pre… Gloria La Riva / Dennis J. Banks Socialism and Lib… Adair 0 6 President/Vice Pre… Darrell L. Castle / Scott N. Bra… Constitution Adair 10 7 President/Vice Pre… Hillary Clinton / Tim Kaine Democratic Adair 1133 8 President/Vice Pre… Jill Stein / Ajamu Baraka Green Adair 14 9 President/Vice Pre… Rocky Roque De La Fuente / Micha… Nominated by Peti… Adair 3 10 President/Vice Pre… Donald Trump / Mike Pence Republican Adair 2461 # … with 1,376 more rows

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Let's practice!

IN FE R E N C E FOR C ATE G OR IC AL DATA IN R

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Election fraud in Iran and Iowa: debrief

IN FE R E N C E FOR C ATE G OR IC AL DATA IN R

Andrew Bray

Assistant Professor of Statistics at Reed College

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INFERENCE FOR CATEGORICAL DATA IN R

Iowa election fraud

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INFERENCE FOR CATEGORICAL DATA IN R

Iowa election fraud

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INFERENCE FOR CATEGORICAL DATA IN R

Iowa election fraud

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INFERENCE FOR CATEGORICAL DATA IN R

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INFERENCE FOR CATEGORICAL DATA IN R

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INFERENCE FOR CATEGORICAL DATA IN R

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INFERENCE FOR CATEGORICAL DATA IN R

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INFERENCE FOR CATEGORICAL DATA IN R

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INFERENCE FOR CATEGORICAL DATA IN R

Take-home lesson

The statistical tool must be appropriate for the task.

By TUBS [CC BY SA 3.0], from Wikimedia Commons By P30Carl [GFDL] or [CC BY SA 3.0], from Wikimedia Commons

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INFERENCE FOR CATEGORICAL DATA IN R

Methods for categorical data

Condence Intervals

One proportion Dierence in proportions

Hypothesis tests

One proportion Dierence in proportions Test of independence Goodness of t

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INFERENCE FOR CATEGORICAL DATA IN R

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INFERENCE FOR CATEGORICAL DATA IN R

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INFERENCE FOR CATEGORICAL DATA IN R

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INFERENCE FOR CATEGORICAL DATA IN R

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INFERENCE FOR CATEGORICAL DATA IN R

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INFERENCE FOR CATEGORICAL DATA IN R

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Let's practice!

IN FE R E N C E FOR C ATE G OR IC AL DATA IN R