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Now, what if Republicans try to react by moving between states themselves to prevent Democrats from accomplishing their mission? Then, we have a kind of game-th

by timkam 7y ago

Now, what if Republicans try to react by moving between states themselves to prevent Democrats from accomplishing their mission? Then, we have a kind of game-theoretical knapsack problem. I could imagine that generalizing and formalizing this scenario in detail would actually be a neat scientific contribution. Any comments that point to relevant publications on this are much appreciated.

TheDong 7y ago
If you do this with perfect knowledge and both sides playing optimally, I believe that just ends up being the popular vote, so the democrats win. Whoever has the popular vote simply has more people to shuffle around. I suppose what you mean instead is that each side gets one round, and the new goal is for the democrats to create a distribution which the republicans cannot win by moving people around. I believe that ends up being identical to the knapsack problem since you now simply have the democrats wishing to maximize their margin in each state based on its number of EVs; in fact, I think that's an even more straighforward knapsack problem than the one in the article since we don't have to take the complement. Perhaps you meant something else entirely different, in which case I don't think you described it clearly enough.
- timkam 7y ago
  Agreed. I wasn't describing the problem clearly at all, it is just a rough idea. Now, I agree that the problem is only interesting if we keep some constraints, a) at least as to how people can move and possibly also on b) what information people have on the strategy of the opposing team, as well as c) how teams can coordinate among their own members. Another fun constraint would be to model mixed democrate/republican households of different sizes that can only move together.
ptah 7y ago
>Democrats win 21st century elections by relative landslides, while Republicans win by very narrow margins Republicans would need orders of magnitude more people to move

by timkam 7y ago

TheDong 7y ago

If you do this with perfect knowledge and both sides playing optimally, I believe that just ends up being the popular vote, so the democrats win. Whoever has the popular vote simply has more people to shuffle around. I suppose what you mean instead is that each side gets one round, and the new goal is for the democrats to create a distribution which the republicans cannot win by moving people around. I believe that ends up being identical to the knapsack problem since you now simply have the democrats wishing to maximize their margin in each state based on its number of EVs; in fact, I think that's an even more straighforward knapsack problem than the one in the article since we don't have to take the complement. Perhaps you meant something else entirely different, in which case I don't think you described it clearly enough.

timkam 7y ago
Agreed. I wasn't describing the problem clearly at all, it is just a rough idea. Now, I agree that the problem is only interesting if we keep some constraints, a) at least as to how people can move and possibly also on b) what information people have on the strategy of the opposing team, as well as c) how teams can coordinate among their own members. Another fun constraint would be to model mixed democrate/republican households of different sizes that can only move together.

ptah 7y ago

>Democrats win 21st century elections by relative landslides, while Republicans win by very narrow margins Republicans would need orders of magnitude more people to move