Total invested = 8670+6650+1680 = $17,000.
a. Karissa: (8670/17,000) * 34 = 17.34(18 coins).
Jane: (6650/17,000) * 34 = 13.3(13 coins).
Hillary: (1680/17,000) * 34 = 3.36(3 coins).
0.34+0.30+0.36 = 1.0 coin which goes to highest investor(Karissa).
b. Repeat part a with 35 coins.
Three people invest in a treasure dive, each investing the amount listed below. The dive results in 34 gold coins. Using Hamilton's method, apportion those coins to the investors based on their investment.
Investor
Investment
Allocation of 34 coins
Karissa
$8,670
Jane
$6,650
Hillary
$1,680
Right before the coins are distributed, the divers find one more coin they had misplaced. Redo the allocation, now with 35 coins
Investor
Investment
Allocation of 35 coins
Karissa
$8,670
Jane
$6,650
Hillary
$1,680
Does this situation illustrate any apportionment issues?
3 answers
Three people invest in a treasure dive, each investing the amount listed below. The dive results in 34 gold coins. Using Hamilton's method, apportion those coins to the investors based on their investment.
Investor:
| Investor A | Investor B | Investor C |
|------------|------------|------------|
| $8,670 | $6,650 | $1,680 |
Total investment:
Total investment = $8,670 + $6,650 + $1,680 = $17,000
Fair share per coin:
Fair share per coin = Total investment / Total coins = $17,000 / 34 = $500
Investor A share:
Investor A share = (Investor A investment / Total investment) * Total coins = ($8,670 / $17,000) * 34 = 17.34 coins
Investor B share:
Investor B share = (Investor B investment / Total investment) * Total coins = ($6,650 / $17,000) * 34 = 13.3 coins
Investor C share:
Investor C share = (Investor C investment / Total investment) * Total coins = ($1,680 / $17,000) * 34 = 3.36 coins
Final allocation:
| Investor A | Investor B | Investor C |
|------------|------------|------------|
| 17 coins | 13 coins | 3 coins |
To check if the allocation is fair:
Investor A priority = Investor A share / sqrt(Investor A share + Investor B share + Investor C share) = 17 / sqrt(17 + 13 + 3) = 0.742
Investor B priority = Investor B share / sqrt(Investor A share + Investor B share + Investor C share) = 13 / sqrt(17 + 13 + 3) = 0.579
Investor C priority = Investor C share / sqrt(Investor A share + Investor B share + Investor C share) = 3 / sqrt(17 + 13 + 3) = 0.193
Investor A priority + Investor B priority + Investor C priority = 0.742 + 0.579 + 0.193 = 1.514
The sum of priorities is larger than 1, indicating an overallocation of coins. The situation illustrates an apportionment issue known as the "Alabama paradox," where adding an extra unit can change the allocation significantly.
| Investor A | Investor B | Investor C |
|------------|------------|------------|
| $8,670 | $6,650 | $1,680 |
Total investment:
Total investment = $8,670 + $6,650 + $1,680 = $17,000
Fair share per coin:
Fair share per coin = Total investment / Total coins = $17,000 / 34 = $500
Investor A share:
Investor A share = (Investor A investment / Total investment) * Total coins = ($8,670 / $17,000) * 34 = 17.34 coins
Investor B share:
Investor B share = (Investor B investment / Total investment) * Total coins = ($6,650 / $17,000) * 34 = 13.3 coins
Investor C share:
Investor C share = (Investor C investment / Total investment) * Total coins = ($1,680 / $17,000) * 34 = 3.36 coins
Final allocation:
| Investor A | Investor B | Investor C |
|------------|------------|------------|
| 17 coins | 13 coins | 3 coins |
To check if the allocation is fair:
Investor A priority = Investor A share / sqrt(Investor A share + Investor B share + Investor C share) = 17 / sqrt(17 + 13 + 3) = 0.742
Investor B priority = Investor B share / sqrt(Investor A share + Investor B share + Investor C share) = 13 / sqrt(17 + 13 + 3) = 0.579
Investor C priority = Investor C share / sqrt(Investor A share + Investor B share + Investor C share) = 3 / sqrt(17 + 13 + 3) = 0.193
Investor A priority + Investor B priority + Investor C priority = 0.742 + 0.579 + 0.193 = 1.514
The sum of priorities is larger than 1, indicating an overallocation of coins. The situation illustrates an apportionment issue known as the "Alabama paradox," where adding an extra unit can change the allocation significantly.
1 answer