---
title: "Presidents and States"
description: "Winfree's own statement of this exercise is lost; this reconstruction takes two famous regularities from American history, the zero-year presidents and the bellwether states, and asks whether a run of confirmations makes a pattern, an accident or a law."
type: Activity
tags: [course, student-facing, problem, section-4, patterns, induction, coincidences, bellwether-states]
status: stable
problem:
section: 4
session: 19
identification: unknown
kind: discussion
generated:
by: "claude/opus-5"
at: "2026-09-16T00:00:00Z"
sources:
- id: winfree-handout-2002
resource: "https://web.archive.org/web/20020420212713/http://eebweb.arizona.edu/Faculty/Winfree/handout_479.htm"
title: "The Art of Scientific Discovery (ECOL 479/579): course handout, archived 20 April 2002"
author: "Arthur T. Winfree"
- id: wikipedia-curse-of-tippecanoe
resource: "https://en.wikipedia.org/wiki/Curse_of_Tippecanoe"
title: "Curse of Tippecanoe"
author: "Wikipedia contributors"
- id: wikipedia-as-maine-goes
resource: "https://en.wikipedia.org/wiki/As_Maine_goes,_so_goes_the_nation"
title: "As Maine goes, so goes the nation"
author: "Wikipedia contributors"
- id: wikipedia-missouri-bellwether
resource: "https://en.wikipedia.org/wiki/Missouri_bellwether"
title: "Missouri bellwether"
author: "Wikipedia contributors"
- id: wikipedia-bellwether-politics
resource: "https://en.wikipedia.org/wiki/Bellwether_(politics)"
title: "Bellwether (politics)"
author: "Wikipedia contributors"
- id: diaconis-mosteller-1989
resource: "https://www.stat.berkeley.edu/~aldous/157/Papers/diaconis_mosteller.pdf"
title: "Methods for Studying Coincidences"
author: "Persi Diaconis and Frederick Mosteller"
- id: wikipedia-presidents-by-home-state
resource: "https://en.wikipedia.org/wiki/List_of_presidents_of_the_United_States_by_home_state"
title: "List of presidents of the United States by home state"
author: "Wikipedia contributors"
- id: judson-1980
resource: "https://archive.org/details/searchforsolutio0000juds_r0s0"
title: "The Search for Solutions"
author: "Horace Freeland Judson"
- id: aosd-syllabus
resource: "https://github.com/tyson-swetnam/aosd/blob/main/docs/assets/aosd_syllabus.pdf"
title: "The Art of Scientific Discovery: original course syllabus (PDF)"
author: "Arthur T. Winfree"
---
# Presidents and States
This work is licensed under a Creative Commons Attribution 4.0 International License.
*[Section 4](../section4.md), session 19. Discussed together with [n dots on the rim of a circle](n-dots-on-circle.md).*
!!! abstract "The problem"
Reconstructed from the syllabus: Winfree's handout for this exercise
has not survived. The two patterns below were chosen by the editors
as examples of the kind the session is about, not as his.
**Presidents.** Every president elected in a year divisible by twenty
from 1840 to 1960 died in office: Harrison, Lincoln, Garfield,
McKinley, Harding, Franklin Roosevelt and Kennedy. Only one other
president had died in office: Zachary Taylor, elected in 1848, who
died in 1850.
**States.** Maine voted for state offices in September, two months
before the presidential vote. From 1820 to 1932 that result matched
the party of the next president in 21 of 28 cycles: "As Maine goes, so
goes the nation". Missouri voted for the winner in every presidential
election from 1904 through 2004 except 1956.
**Your task.** Is each regularity a pattern, an accident or a law, and
what mechanism could produce it? Imagining it is 1970, give odds that
the president elected in 1980 will die in office, and say how you got
them. How many other rules of this shape could you have searched for?
{ width="560" }
*Drawn for this site (CC BY 4.0). Small squares mark the other elections; the filled one is Taylor's.*
## Why it is in the course
Session 19 opens Section 4, "Patterns, Empirical Generalizations", with
Judson's chapter *Pattern*, and pairs this exercise with
[n dots on the rim of a circle](n-dots-on-circle.md). The disk gives a
number pattern you can test by drawing the next case; history offers no
next case on demand. Both ask how many confirmations a generalization
needs.
Session 4 asked for "facts before explanations of facts" and for
"distinguishing things we know vs only imagine". That seven zero-year
presidents died in office is a fact. A curse is an explanation, and
accepting it is a separate step from checking the record.
## Where it comes from
*Ripley's Believe It or Not!* noted the zero-year pattern in 1931 and
again in 1948. It came to be blamed on a curse laid by the Shawnee leader
Tenskwatawa after his brother's defeat by Harrison at Tippecanoe in 1811,
hence the name "Curse of Tippecanoe".
Maine's reputation dates to 1840. In 1936 Maine voted Republican in
September, and in November Landon carried only Maine and Vermont, which
prompted James Farley's quip "As Maine goes, so goes Vermont". A 1959 law
moved Maine's elections to November. Missouri then inherited the
reputation.
{ width="560" }
*Popular Graphic Arts, "The Presidents of the United States" (1848), Library of Congress, via Wikimedia Commons. Public domain. A campaign banner for Lewis Cass.*
??? tip "Hints"
- How many presidents had there been by 1970, and how many had died in
office? Only then ask how remarkable the zero-year list is.
- State the rule so exactly that someone in 1970 could apply it.
Lincoln and Roosevelt each died in a term won in a later election.
Does the rule still count them?
- A pattern found by searching many possible rules must be judged
against the number of rules searched.
- One state has a story for why its record worked, and the story
predicts when it should stop working. Which state?
??? success "Resolution"
**The presidents.** The run broke in 1980: Reagan was shot in March
1981 and survived, and Bush (2000) and Biden (2020) served out their
terms. It should not have been very surprising. About one in five of
the presidents before Reagan had died in office. The rule was stated
after the fact, with a free choice of interval, starting year and
criterion. Let the zero year be a year of death as well as of election,
and Taylor, who died in 1850, fits too. Nobody publishes the patterns
that fail. Diaconis and Mosteller name the two traps the multiplicity
of endpoints and the law of truly large numbers: a rule that may count
many outcomes as hits is far less improbable than it looks. A rule with
no mechanism earns no credit for the next case, so honest odds in 1970
were near the base rate, not near certainty.
**The states.** Maine's record had a mechanism: its early election
sampled the same national mood as the November vote. That explains the
record and its end, since the 1936 landslide showed the sample could
mislead and the 1959 move to November removed it. Missouri had no such
mechanism beyond resembling the country for a while, and its run ended
with the 2008 election without any change in the rule.
**The moral.** Rules that survive, such as Kepler's third law in
[Paired Observations](paired-observations.md), rest on a mechanism, not
on a longer run of confirmations.
## Sources
- **Arthur T. Winfree**, *The Art of Scientific Discovery* (ECOL 479/579): course handout, archived 20 April 2002 โ [Internet Archive](https://web.archive.org/web/20020420212713/http://eebweb.arizona.edu/Faculty/Winfree/handout_479.htm){target=_blank} ๐
- **Wikipedia contributors**, "Curse of Tippecanoe" โ [Wikipedia](https://en.wikipedia.org/wiki/Curse_of_Tippecanoe){target=_blank} ๐
- **Wikipedia contributors**, "As Maine goes, so goes the nation" โ [Wikipedia](https://en.wikipedia.org/wiki/As_Maine_goes,_so_goes_the_nation){target=_blank} ๐
- **Wikipedia contributors**, "Missouri bellwether" โ [Wikipedia](https://en.wikipedia.org/wiki/Missouri_bellwether){target=_blank} ๐
- **Wikipedia contributors**, "Bellwether (politics)" โ [Wikipedia](https://en.wikipedia.org/wiki/Bellwether_(politics)){target=_blank} ๐ (the end of Missouri's run)
- **Persi Diaconis and Frederick Mosteller**, "Methods for Studying Coincidences", *Journal of the American Statistical Association* 84(408), 853โ861 (1989) โ [PDF](https://www.stat.berkeley.edu/~aldous/157/Papers/diaconis_mosteller.pdf){target=_blank} ๐
- **Wikipedia contributors**, "List of presidents of the United States by home state" โ [Wikipedia](https://en.wikipedia.org/wiki/List_of_presidents_of_the_United_States_by_home_state){target=_blank} ๐
- **Horace Freeland Judson**, *The Search for Solutions* (1980), chapter 2, "Pattern" โ [Internet Archive](https://archive.org/details/searchforsolutio0000juds_r0s0){target=_blank} ๐ *(borrow)*
- **Arthur T. Winfree**, *The Art of Scientific Discovery*: original course syllabus โ [PDF](https://github.com/tyson-swetnam/aosd/blob/main/docs/assets/aosd_syllabus.pdf){target=_blank} ๐
!!! note "How sure are we that this is Winfree's problem?"
Not sure. The syllabus and Winfree's archived handout give only the
name and the session, and no other source names the exercise.
Candidate readings:
- **Bellwether states** such as Maine and Missouri, which join both
nouns in the title.
- **The zero-year presidents**, the closest match to the disk
problem's run of confirmations followed by failure, but with no
obvious "states".
- **A table of presidents against states** to search for patterns.
Eight presidents were born in Virginia, yet by home state New York
leads with seven, so the headline depends on the column you read.
- **Two datasets side by side**, one about presidents and one about
states. The reconstruction above takes this reading.
---
*Back to [Section 4](../section4.md) ยท [All problems](index.md) ยท [The schedule](../syllabus.md#section-4-patterns-empirical-generalizations)*