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Who wins when the same voters are counted differently?

Start with one fictional voter’s second choice, then follow districts, seats and national totals. At each stage mark which information survives and which questions the result can still answer.

Questions in this reading · 5
  1. Who gets onto the tally before a majority is counted?
  2. Whose cooperation does the winner still need?
  3. Does a second choice survive the ballot?
  4. Transferring a vote and drawing its district
  5. Why can ten thousand more votes buy no additional seat?

Who gets onto the tally before a majority is counted?

In the fictional three-seat district, ranking candidates changes what happens to a ballot after its first choice. The City of London example moves one step earlier: which residents or workers can receive a ballot? Keeping a counting formula fixed while changing eligibility changes what the result represents. Trace a ballot to a seat, then ask who could enter that calculation at all.

Passages and timestamps · 4
Citizens rank their
The Voting System That's Actually Too Good for Politicians to Allow · ▶ 6:03–6:04
If no winner, last place is eliminated
The Voting System That's Actually Too Good for Politicians to Allow · ▶ 6:10–6:13
The companies then give their votes to select employees
Most Cities Got More Democratic. This One Didn't. · ▶ 1:35–1:39
with the remaining 1/4th from residents
Most Cities Got More Democratic. This One Didn't. · ▶ 1:27–1:29

Whose cooperation does the winner still need?

A counting rule can assign office without identifying who can turn an order about roads or taxes into action. Alongside the winner, Grey asks us to draw the people whose cooperation is needed and the resources that sustain it. This separates two observations: obtaining office and implementing a decision. If the officeholder stays but the necessary collaborators change, which commitments can still be carried out?

Passages and timestamps · 2
The individuals needed to make the necessary things happen
Try to Rule Fairly and You'll Be Overthrown · ▶ 1:11–1:16
Control the treasure.
Try to Rule Fairly and You'll Be Overthrown · ▶ 2:11–2:13

Does a second choice survive the ballot?

In Grey’s animal kingdom seven candidates split the vote, and Leopard only has to outpoll each rival individually. Adding the losing votes tells us most voters did not put Leopard first. It cannot reveal a rival those voters would support together. A ranked ballot lets Squirrel put Turtle first and Owl second. That later preference is additional information the old totals cannot supply. Both clips use the same author’s fictional setting, making it easier to hold the electorate constant.

Passages and timestamps · 2
80% -- wanted someone else as king
Why Your Vote Doesn't Count · ▶ 1:21–1:26
Turtle as his first choice, Owl as his second
The Voting System That Should Replace Every Election · ▶ 1:25–1:29

Transferring a vote and drawing its district

In an instant runoff, a ballot for an eliminated candidate can transfer to the next remaining choice. Now keep the ballots and regroup the very same people into two districts. Grey’s other example shows that seat winners can change while individual choices stay fixed. Run each experiment on a separate sheet: alter the tally rule or the grouping, with the other held fixed.

Passages and timestamps · 2
whoever decides where the lines are drawn has enormous influence
Why Your Vote Doesn't Count · ▶ 4:31–4:38
least popular candidate is eliminated after each round
The Voting System That Should Replace Every Election · ▶ 2:08–2:11

Why can ten thousand more votes buy no additional seat?

The UK example places votes in constituencies, each electing one MP. More votes in an already safe seat add no seat. Grey constructs another extreme under the US electoral college: narrow wins in certain states can coexist with huge losses elsewhere without cancellation on a national net-vote basis. Both demonstrations are Grey’s, comparing two aggregation rules. Trace each grouping on the way from ballot to winner before interpreting a national percentage.

Passages and timestamps · 4
they're a bunch of local elections.
The UK Election Results Were the Worst in History · ▶ 0:40–0:45
each of which elects one member of parliament
The UK Election Results Were the Worst in History · ▶ 0:45–0:49
win the votes of the people who count the most
You Can Win the Presidency With 22% of the Vote · ▶ 4:28–4:32
because it's a winner take all system
You Can Win the Presidency With 22% of the Vote · ▶ 4:41–4:45

Try it on your own example

Draw six voters and give each a first and second choice. Tally first choices across the group, then award one seat in each of two districts. What changed, and which question would require information beyond the winner list?