Lesson 19 of 1524
Voting and apportionment
The same ballots can name different winners under different rules.
Practice this chapterPlurality gives the win to whoever has the most first-place votes. It does not require a majority. A majority is more than half of the votes.
A Borda count awards points down each ballot. A Condorcet winner would beat every rival one against one. Apportionment, including Hamilton’s method, divides seats and can produce paradoxes when the house size changes.
Majority
more than half of the votes cast
With an even number of votes, half itself is not a majority.
Worked example
First-place totals are 40, 35, and 25. Who has a plurality, and is there a majority?
- 1Plurality means the largest first-place total. 40 is larger than 35 and larger than 25, so that candidate has a plurality.
- 2Add every vote before you test a majority: 40 + 35 + 25 = 100.
- 3A majority is more than half. Half of 100 is 50, so a majority needs at least 51 votes.
- 440 is not more than 50. The other two candidates together have 35 + 25 = 60, which is more than half.
Result: Plurality only. No majority.
Why. 40 is the most first-place votes, which is all a plurality requires. It is not a majority because a majority of these 100 votes would have to be more than 50, and 40 is not.
“Most votes” is not the same sentence as “more than half.” A plurality winner can be opposed by a majority of the voters.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.