Senate Apportionment

Logic Level 2

The United States Senate assigns states seats using the following system: regardless of the population of each state or the total number of states, every state gets two seats.

Of the criteria described in the apportionment paradox , which does this system fulfill?


An ideal assignment system would obey the following three rules:

  1. Quota rule: each group gets a number of seats equal to its proportion of the vote either rounded up or rounded down. ( ( In the example, the seats would be 5 or 6 to A A , 2 or 3 to B B , and 1 or 2 to C . ) C.)
  2. If the total number of seats is increased, the number assigned to any group doesn’t decrease.
  3. If group A A gets more votes than group B B , no seats are transferred from A A to B B .
1 and 2 1 and 3 1, 2 and 3 2 and 3 None

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2 solutions

Adam Strandberg
Mar 1, 2016

Since the number of seats assigned has nothing to do with the population of the state, criterion 1 is violated .

The only way that the number of seats can change is if states are added or removed, and in those cases the number of seats for each state stays the same, so criterion 2 is fulfilled .

No seats can be transferred between states under any circumstance, so criterion 3 is fulfilled .

Yeah, I know. I got it right too, but it's really cheaty!

Zoe Codrington - 2 years, 8 months ago
Saya Suka
Apr 3, 2021

I don't understand what this problem is about.

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