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apharIt is claimed that Voters In Wyoming Have 3.6 Times The Voting Power That [California voters] Have.
Had the author said that a WY voter elects 3.6 times more electors than a CA voter, he would have been correct - and irrelevant.
However, he said Voting Power and thus he is wrong.
Voting power is quantified by Shapley Value, which measures how often a given voter casts the decisive vote. E.g., if there are 3 voters, each of them is equally likely to cast the second (decisive) vote, so each has power 1/3. However, if two of them form a coalition, i.e., always vote the same, then the 3rd voter becomes irrelevant and thus his power is now 0, while the power of the two allied voters is now 1/2 each.
The US presidential election analogue is: suppose, for simplicity, we have just two states: CA with 10M people, which elects 10 representatives (one per 1M) and 2 senators, and WY with 10k people, which elects 1 representative (as a state, it is entitled to at least one) and 2 senators.
CA has 12 electors per 10M people - 1.2e-6 electors per person (1.2 electors per 1M).
WY has 3 electors per 10k people - 3e-4 electors per person (300 electors per 1M).
Looks like WY has 250 more power than CA!
Nope, not so fast.
When the electoral college convenes, CA elects the president without consulting WY - its 12 electors form a majority of the 15-member college.
This means that CA has electoral power 1 and WY 0.
Thus, WY is completely disenfranchised.
This is a simplistic example which shows that "electors per capita" is a worthless metric.
The question is - how does it translate into the real life?
Fortunately, almost 60 years ago this question has already been answered: table 4 shows that "large states" with 40+ electors have about 7% more "per capita power" than "small states" (5 and fewer electors).
PS. The quote in the subject comes from John McCarthy.
PPS. See also Why hasn't the US changed the Electoral College to allocate electors by proportion for each state?
Had the author said that a WY voter elects 3.6 times more electors than a CA voter, he would have been correct - and irrelevant.
However, he said Voting Power and thus he is wrong.
Voting power is quantified by Shapley Value, which measures how often a given voter casts the decisive vote. E.g., if there are 3 voters, each of them is equally likely to cast the second (decisive) vote, so each has power 1/3. However, if two of them form a coalition, i.e., always vote the same, then the 3rd voter becomes irrelevant and thus his power is now 0, while the power of the two allied voters is now 1/2 each.
The US presidential election analogue is: suppose, for simplicity, we have just two states: CA with 10M people, which elects 10 representatives (one per 1M) and 2 senators, and WY with 10k people, which elects 1 representative (as a state, it is entitled to at least one) and 2 senators.
CA has 12 electors per 10M people - 1.2e-6 electors per person (1.2 electors per 1M).
WY has 3 electors per 10k people - 3e-4 electors per person (300 electors per 1M).
Looks like WY has 250 more power than CA!
Nope, not so fast.
When the electoral college convenes, CA elects the president without consulting WY - its 12 electors form a majority of the 15-member college.
This means that CA has electoral power 1 and WY 0.
Thus, WY is completely disenfranchised.
This is a simplistic example which shows that "electors per capita" is a worthless metric.
The question is - how does it translate into the real life?
Fortunately, almost 60 years ago this question has already been answered: table 4 shows that "large states" with 40+ electors have about 7% more "per capita power" than "small states" (5 and fewer electors).
PS. The quote in the subject comes from John McCarthy.
PPS. See also Why hasn't the US changed the Electoral College to allocate electors by proportion for each state?
no subject
Date: 2018-10-11 06:33 pm (UTC)И приятно, что Маккарти сказал "арифметика", а не "математика".
no subject
Date: 2018-10-11 06:47 pm (UTC)no subject
Date: 2018-10-11 09:17 pm (UTC)Погоди, а авторы именно per capita имеют в виду, считая свои "силовые индексы" (70 секунд на IBM 7090, хе-хе)?
no subject
Date: 2018-10-12 04:16 pm (UTC)first they compute the Shapley values for states, then divide by the state population to get per capita.
otherwise the numbers are trivially wrong.