This also provides a way for constructively lower-bounding it, which doesn’t appeal to nebulous systems like weather or hard-to-estimate-quantum-contribution-to-even-in-principle things like whether leading candidates will drop dead of a heart attack or stroke or assassination before the election (surely a major consideration!). You can use quantum randomness to directly affect elections by amplifying your actions.
An example of this would be donor lotteries: pick your preferred candidate and commit $X to supporting them & affiliated groups; then take an efficient high-leverage lottery like forex options, and use a quantum random number generator to choose which one to buy, with a payoff of, say, 1000:1 (which should imply by EMH that it has roughly 1/1000 probability of paying off). You wipe out to $0 in 999 universes but then get 1000x in the last universe. In that universe, you donate it.*
Given assumptions about how much money you start with, how much leverage you choose, and the elasticity of donation for victory, this implies that there must be at least a certain amount of quantum uncertainty in who wins. I think with plausible values, you still get a quantum uncertainty which doesn’t require too many zeros after the decimal point to write down, so that’s useful: if even a single person could have that much quantum-influence if they wanted… And the more people who do this, the more the quantum-ness goes up even if the actions sometimes cancel out.
(Using made-up numbers: If I commit $1m and I believe that $1000m in donations 100% guarantees victory to my favored candidate who has a 50% chance right now and I use 1:1000 leverage, then 1/1000th of the time quantum randomness means the candidate goes from 50% to 100% (because I hit the jackpot & donate & they win), so there must be at least 1/1000 * (100-50) = 0.05% quantum randomness in who wins, where even an otherwise omniscient predictor is unsure because they can’t know if we’ll end up in the 999 baseline universes or the 1 quantum fluke universe. They may be 99.95% sure the other candidate will win for reasons not apparent to us, but not 100% sure.)
* There are a few stories floating around of people doing things like this, so it’s not necessarily even that wacky a strategy.
To the convergence to the classical probability, but it doesn’t wash away the quantumness. The quantumness doesn’t go away when you add more quantumness (barring specific setups like interference or spooky action where you’ve carefully created correlations/anti-correlations between the quantum randomness, of course). If I flip 1 classical coin for an expected 0.5 heads, that is less quantum than if I flip 1 classical coin and 1 quantum coin and average, and less quantum than if I clip 1 classical coin and 999 quantum coins and average, even though per CLT the second will be tighter around 0.5 and the third will be much tighter around 0.5.
Sure. Main thing is the election results are about the same, just a list of names of which ‘quantum die rolling organization’ supported candidate A, and who supported B, has many differences.
Or in your coin example, universe 1 might be HHTTHTHT and universe 2 might be THTHHTHT , but the totals are almost the same.
This also provides a way for constructively lower-bounding it, which doesn’t appeal to nebulous systems like weather or hard-to-estimate-quantum-contribution-to-even-in-principle things like whether leading candidates will drop dead of a heart attack or stroke or assassination before the election (surely a major consideration!). You can use quantum randomness to directly affect elections by amplifying your actions.
An example of this would be donor lotteries: pick your preferred candidate and commit $X to supporting them & affiliated groups; then take an efficient high-leverage lottery like forex options, and use a quantum random number generator to choose which one to buy, with a payoff of, say, 1000:1 (which should imply by EMH that it has roughly 1/1000 probability of paying off). You wipe out to $0 in 999 universes but then get 1000x in the last universe. In that universe, you donate it.*
Given assumptions about how much money you start with, how much leverage you choose, and the elasticity of donation for victory, this implies that there must be at least a certain amount of quantum uncertainty in who wins. I think with plausible values, you still get a quantum uncertainty which doesn’t require too many zeros after the decimal point to write down, so that’s useful: if even a single person could have that much quantum-influence if they wanted… And the more people who do this, the more the quantum-ness goes up even if the actions sometimes cancel out.
(Using made-up numbers: If I commit $1m and I believe that $1000m in donations 100% guarantees victory to my favored candidate who has a 50% chance right now and I use 1:1000 leverage, then 1/1000th of the time quantum randomness means the candidate goes from 50% to 100% (because I hit the jackpot & donate & they win), so there must be at least 1/1000 * (100-50) = 0.05% quantum randomness in who wins, where even an otherwise omniscient predictor is unsure because they can’t know if we’ll end up in the 999 baseline universes or the 1 quantum fluke universe. They may be 99.95% sure the other candidate will win for reasons not apparent to us, but not 100% sure.)
* There are a few stories floating around of people doing things like this, so it’s not necessarily even that wacky a strategy.
Gwern, this only kingmakes if there is one player able to decide the election on their own by quantum dice.
What happens when there is 100 large entities doing this? 10,000? Law of large numbers would apply here.
To the convergence to the classical probability, but it doesn’t wash away the quantumness. The quantumness doesn’t go away when you add more quantumness (barring specific setups like interference or spooky action where you’ve carefully created correlations/anti-correlations between the quantum randomness, of course). If I flip 1 classical coin for an expected 0.5 heads, that is less quantum than if I flip 1 classical coin and 1 quantum coin and average, and less quantum than if I clip 1 classical coin and 999 quantum coins and average, even though per CLT the second will be tighter around 0.5 and the third will be much tighter around 0.5.
Sure. Main thing is the election results are about the same, just a list of names of which ‘quantum die rolling organization’ supported candidate A, and who supported B, has many differences.
Or in your coin example, universe 1 might be HHTTHTHT and universe 2 might be THTHHTHT , but the totals are almost the same.