The Coriolis effect in a 50 m-radius cylinder gives a velocity difference of about.4 meters/second between my head and feet. So you propose a sport that combines significant vertical position changes with balancing (on water)!
I'd be impressed to see it, but I think that's the sort of environment where you could make a sport of Extreme Standing Up Rapidly (TM).
Bush, claiming this wiretap authority is essential for national security, threatens to veto the bill to give it if it doesn't contain retroactive telecom immunity and then has the effrontery to accuse the Democrats of partisan obstruction. That's what really makes me boggle about this situation.
I would say the solution would be quite simple in a range system: if there are, say, 7 choices -- instead of letting people vote on each one, give them a set number of points, say 300. They may distribute the points as they wish but at a maximum of 100 points per choice. They would not have to use up their points if they so choose. This completely misses the point of range voting: to eliminate the spoiler effect and give third candidates the opportunity to run without people worrying about the spoiler effect, it's essential to be able to give full or near-full marks to arbitrarily many candidates.
As for the Tennessee example: what's artificial about it? Nothing would stop someone for voting 100/100 for one person and 0 for everybody else, giving that vote the same impact as it would have in a plurality system; there's just more nuance available for those who want to use it.
There is still probably some reliance on how viable voters think that most of the candidates are. If I like A the most, B second, down to E the least, E is definitely getting a 0 from me. If E has no chance of winning, I can safely give D a 0 as well. But if E has some chance of winning, I need to weigh whether giving D a slightly positive score, in case D and E are the frontrunners, is worth risking the cases where D is a frontrunner with some other candidate. That depends on an estimate of relative viability.
Instead of using absolute dollar figures for your analysis, you should use lifestyle impact.
e.g. One dollar a week == no lifestyle impact; $370MM payout == off the charts lifestyle impact.
This is why people will continue to play the lottery, even if mathematically it's a poor choice.
It's funny that you should use "lifestyle impact", because the impact of each dollar on an individual's happiness decreases drastically for a total that large.
One dollar == small impact; $370 million == large impact, but much smaller than 370 million times the impact of $1.
If you have the highest bid and the 2nd highest bid is less than you're willing to pay, you'll pay the amount of the 2nd highest no matter how far above it you bid. In this case you might as well have just bid what you were willing to pay.
If you have the highest bid and the 2nd highest bid is more than you're willing to pay, you're stuck paying more than what you were willing to give - a bad result.
The only conceivable reason to bid more than you're willing to pay is to try to screw someone else.
Since all the primes after 2 are odd, why yes, the intervals between all prime(x) and prime(y), after 2, are of even length. And this doesn't suggest to you that perhaps there are similar patterns present that aren't quite as blindingly obvious?
I always thought that the perfect random number generator would be the interval between prime numbers. If we can't predict whether or not a number will be prime then, by definition, the interval between one prime and the next should be random. Of course we can predict whether a number will be prime. It's a lot easier than finding the interval to the next prime, too. That's a somewhat tongue-in-cheek response, but primes are important, and the ways in which their distribution is nonrandom are important (for example: the probability that N is prime is about 1/ln(N) for large N); so on the face of it this seems like a fairly poor way to start trying to make a pseudorandom number generator.
100... so that by your reckoning they can have 20 idiots, 30 biased, 40 honest, and 10 liars? (Not exactly, of course.)
Nobody's trying to produce a result like "60 out of 100 subjects chose the higher bit rate, showing with p > 0.95 that there is a correlation." The question was, "These tracks cost 30% more, is the difference in bitrate going to make that worthwhile?" So they assembled a group of 10 and ran a test - crucially, a double-blind test - that gave them enough information to say, "Maybe not, sometimes we're not even sure which is which."
To be sure, there are other things I'd like to have seen in the article, but don't blame someone for doing some investigation and drawing conclusions at a level justified by their sample size.
It's misleading to say a root cellar works because of insulation: at least as important is exchanging heat freely with the ground around it, which past a few feet down stays at roughly the same temperature year-round.
See http://en.wikipedia.org/wiki/Earth_cooling_tubes for a more recent take on the same principle.
The answer to a / 0 is defined as the limit for a / x when x approaches 0. Sorry, but no.
Your limit is correct, but division by x is defined as multiplication by the multiplicative inverse of x. 0 has no multiplicative inverse, so division by 0 is undefined.
There might conceivably be a number system where it's useful to define division by 0 the way you've described, but it's not true for the real numbers.
Part of the problem with the "paper trail" issue is that the idea keeps getting transformed, by gradual steps, into something that is totally useless. The paper gets put behind glass, printed on a roll, no recourse if it's too fant to read, etc. until there's no reason to suspect that it represents the voter's intentions and not some hacker's. Not in so many words, these are some of the problems the white paper mentioned (the one used in the article to disparage paper trails) talks about. The subject "voter-verified" paper audit trail was kept using standard receipt rolls, and various printing problems compromised a lot of ballots. How they can call it voter-verified is beyond me.
(It also pointed to more traditional problems: physical security of the paper ballots, etc.)
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The Coriolis effect in a 50 m-radius cylinder gives a velocity difference of about .4 meters/second between my head and feet. So you propose a sport that combines significant vertical position changes with balancing (on water)!
I'd be impressed to see it, but I think that's the sort of environment where you could make a sport of Extreme Standing Up Rapidly (TM).
Bush, claiming this wiretap authority is essential for national security, threatens to veto the bill to give it if it doesn't contain retroactive telecom immunity and then has the effrontery to accuse the Democrats of partisan obstruction. That's what really makes me boggle about this situation.
As for the Tennessee example: what's artificial about it? Nothing would stop someone for voting 100/100 for one person and 0 for everybody else, giving that vote the same impact as it would have in a plurality system; there's just more nuance available for those who want to use it.
There is still probably some reliance on how viable voters think that most of the candidates are. If I like A the most, B second, down to E the least, E is definitely getting a 0 from me. If E has no chance of winning, I can safely give D a 0 as well. But if E has some chance of winning, I need to weigh whether giving D a slightly positive score, in case D and E are the frontrunners, is worth risking the cases where D is a frontrunner with some other candidate. That depends on an estimate of relative viability.
Because you're not willing to pay that much.
If you have the highest bid and the 2nd highest bid is less than you're willing to pay, you'll pay the amount of the 2nd highest no matter how far above it you bid. In this case you might as well have just bid what you were willing to pay.
If you have the highest bid and the 2nd highest bid is more than you're willing to pay, you're stuck paying more than what you were willing to give - a bad result.
The only conceivable reason to bid more than you're willing to pay is to try to screw someone else.
I always thought that the perfect random number generator would be the interval between prime numbers. If we can't predict whether or not a number will be prime then, by definition, the interval between one prime and the next should be random. Of course we can predict whether a number will be prime. It's a lot easier than finding the interval to the next prime, too. That's a somewhat tongue-in-cheek response, but primes are important, and the ways in which their distribution is nonrandom are important (for example: the probability that N is prime is about 1/ln(N) for large N); so on the face of it this seems like a fairly poor way to start trying to make a pseudorandom number generator.
100... so that by your reckoning they can have 20 idiots, 30 biased, 40 honest, and 10 liars? (Not exactly, of course.)
Nobody's trying to produce a result like "60 out of 100 subjects chose the higher bit rate, showing with p > 0.95 that there is a correlation." The question was, "These tracks cost 30% more, is the difference in bitrate going to make that worthwhile?" So they assembled a group of 10 and ran a test - crucially, a double-blind test - that gave them enough information to say, "Maybe not, sometimes we're not even sure which is which."
To be sure, there are other things I'd like to have seen in the article, but don't blame someone for doing some investigation and drawing conclusions at a level justified by their sample size.
1000 Km from the equator to the pole? Cue "It's A Small World"...
The meter was actually intended (back in the 1790s) to be one ten-millionth of the distance from the equator to the pole along a meridian.
It's misleading to say a root cellar works because of insulation: at least as important is exchanging heat freely with the ground around it, which past a few feet down stays at roughly the same temperature year-round.
See http://en.wikipedia.org/wiki/Earth_cooling_tubes for a more recent take on the same principle.
Your limit is correct, but division by x is defined as multiplication by the multiplicative inverse of x. 0 has no multiplicative inverse, so division by 0 is undefined.
There might conceivably be a number system where it's useful to define division by 0 the way you've described, but it's not true for the real numbers.
(It also pointed to more traditional problems: physical security of the paper ballots, etc.)