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Multi-person game theory introduces a concept of Shapley value which quantifies that contribution of each person having several votes to the outcome of an election.
It is equal to the probability that the election will be decided by this person.
Examples:
In the United States presidential election, each state elects several electors, whose number equals to the sum of senators (2) and representatives (1+). This means that smaller states have more electors per capita. However, their Shapley value per capita is smaller than that of the larger states (this a non-obvious result of a computer simulation). This means that larger states have a larger impact on the outcome of an election.
Is this democratic? It depends, of course, on the definition of "democracy"; US, like most other countries are not direct democracies but rather republics.
Does it make sense to use the electoral college these days? It depends, of course, what you want to accomplish.
However, one should bear in mind that the sports tournament is won by the team that won the most games, not the one whose total score is the highest.
Another point to contemplate is that deciding the presidential election by popular vote only will completely disenfranchise the rural areas.
It is equal to the probability that the election will be decided by this person.
Examples:
- everyone of the n voters has the same number of votes. then everyone has the same Shapley value (1/n)
- two persons, one has 2 votes, the other has 1. Shapley value for the first is 1, for the second is 0
- three persons, one has 1.9999 votes, the others have 1 each. Shapley value is 1/3 for each of them
In the United States presidential election, each state elects several electors, whose number equals to the sum of senators (2) and representatives (1+). This means that smaller states have more electors per capita. However, their Shapley value per capita is smaller than that of the larger states (this a non-obvious result of a computer simulation). This means that larger states have a larger impact on the outcome of an election.
Is this democratic? It depends, of course, on the definition of "democracy"; US, like most other countries are not direct democracies but rather republics.
Does it make sense to use the electoral college these days? It depends, of course, what you want to accomplish.
However, one should bear in mind that the sports tournament is won by the team that won the most games, not the one whose total score is the highest.
Another point to contemplate is that deciding the presidential election by popular vote only will completely disenfranchise the rural areas.
