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The Complete Idiot's Guide to Game Theory by Edward Rosenthal, Ph.D., Edward C. Rosenthal

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Problems with Proportionality

In Chapter 9 I raised the question of whether proportionality could be preserved in a voting system. When the state of Pennsylvania, with 4 percent of the U.S. population, would be delegated 19.6 electoral votes if we used fractions, we need to know whether to round Pennsylvania up to 20 or down to 19. But many other states would also end up with fractional numbers of electoral votes. Given that the total must remain at 538, it becomes a tricky—often impossible—task to round all of them up or down in a consistent way and stay at the necessary 538.
This problem of rounding sounds unfortunate, but not disastrously so. However, there are other problems with this kind of proportional apportionment, and these pitfalls ...

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