What's the point? You are taking something that is quite complex and creating a simpler model in order to make the computations easier. Fine. But, you can only take that so far. The more extreme your simplifications the less your model applies to the situation you are trying to model. The key is to balance loss of accuracy and applicability against mathematical tractability. However, your "simplifying assumptions" are so out of touch with reality that any conclusions you come to are meaningless. In fact, they are worse than meaningless because, like on-line polls and surveys, they actually subtract from the knowledge base. People see the result and implicitly, if not explicitly, apply it to the actual case and they THINK they have knowledge that they simply do not have - hence they have effectively been given negative information ("negative" as in "less-than-zero")
Peter L. Montgomery wrote in message ... > In the US presidential election, the winner is determined >by electoral vote rather than by popular vote. >What is the chance that the two will give different outcomes >in an otherwise close race? > > Make simplifying assumptions, such as an odd number >of equi-populous states.
Absurd simplification. You can't possibly take the US and assume that NY and CA are all of a sudden equi-populous with states like WY. As soon as you make this assumptions, you have dictated that your results can't apply to the real thing.
>In a two-candidate race, voters everywhere vote randomly >for one of the two candidates.
Tempting, but the most likely situation whereby the electoral college and the popular vote will not yield the same result is far removed from this. It is with non-uniformly distributed voting blocks whereby the losing candidate (and losing is defined as losing the electoral college) wins strong in lots of states with few electoral votes and the winning candidate wins weakly in a few states with many electoral votes.
>Every state has the same (odd) number of voters, >and the same number of electors --
Again, and absurd simplication that makes the model fundamentally in conflict with the reality you are trying to model.
>the winning candidate within each state gets all of that state's electors.
This is not a bad assumption. There are some sates that are not winner take all (at least in the primaries - I'm all of a sudden not positive about the general election) but a model that ignores this factor is still useful.
>What is the probability that the candidate winning >a majority of the overall vote will lose in a majority of the states?
In your mythical model or in the US? They have virtually nothing in common and what applies to one has no applicaiton to the other.
>-- >E = m c^2. Einstein = Man of the Century. Why the squaring? > > Peter-Lawrence.Montgomery@cwi.nl Home: San Rafael, California > Microsoft Research and CWI