People weren't born to have a natural understanding of probabilities, we didn't have any need for that expertise on the savannah. This is a huge problem in an increasingly complex world where most decisions involve many factors that must be taken into account, and where most thing aren't black or white.
Our inability to intuitively judge probabilities correctly rears its ugly head in such diverse areas as politics, eating habits, the war on terror, and here the judicial system. We're heavily biased as a species, and we consistently put the probability of terrible things happening much much higher than they really are.
The war on terror is a great example: Because terror is, well terrifying, we have a tendency to think "this is awful - and it could happen to me", even though the chance of dying by the hands of terrorists is smaller than the chance of being struck by lightning. Combined with our desire for everything to have an easy and understandable cause this is the primary problem in this case.
We need to think before we act: Sometimes things aren't as they seem, and sometimes they don't have a cause but are simply flukes of randomness passing though our lives.
Because terror is, well terrifying, we have a tendency to think "this is awful - and it could happen to me"
On the other hand, a miscarriage of justice for most people is an abstract concept. For those who directly experience such a circumstance, it can well be perplexing, devastating, and every bit as terrifying. It is indeed devastating to know that the truth is on your side, and yet the whole of society is still arrayed against you. It is the same as the ultimate insult to Winston Smith in 1984. (2+2 = 5)
And my guess is it happens way more often than you'd guess. I was quite shocked to watch a movie "Witch Hunt" http://www.imdb.com/title/tt1196112/ -- multiple people were convicted and spend many years in jail (one guy 20 years) for child molestation charges which were completely bogus (they're all now acquitted). Now you have to ask yourself, for each case where an innocent person is finally freed after 15 or 20 years, how many more just never see that justice even after a long time. What's your best guess about the fraction of people in jail that are innocent? 1%? 10%? And now think that like 1% of the population is incarcerated. How likely does it make any of us to go to jail?
Humans intuitively use probabilities all of the time, but they are not necessarily proof that a crime has occurred.
On the savannah, we did not need to establish beyond a reasonable doubt that an animal was about to eat us. We HAD to err on the side of the worst possibility. Or we'd be dead.
I think people can understand statistics if you give them a clear explanation.
EX: You can't multiply p values and think of the result as a p value, because none of them are greater than 1. So if you keep doing it you will always get a lower number.
EX2: You can't pick and chose which tests to use because if you do 100 tests you would expect several p values < .05.
The real issue is the defense need to be able to explain this stuff and jump all over a prosecution that try's to use these tricks.
It's scary how we are increasingly being judged and predicted using statistics and mathematics. It's also very sad to see it go wrong like this (whatever happened to "innocent until proven guilty"?).
Imho the most scary part is how accurate these calculations and predictions are on average and how on that base they have begun to invade our daily lives.
A court might rule me guilty because the numbers say there's a 85% probability. A company might not employ me because the analysis of my friends-graph, school and other public history suggests a 70% probability that $other_candidate would add more value than me. Health insurance might not take me in because my genes suggest a 50% probability of an expensive disease.
"whatever happened to 'innocent until proven guilty'?"
A math problem for you: Given an innumerate judge, an innumerate prosecution, an innumerate defense, and 12 innumerate jury members, what is the probability that a fundamentally-innumerate verdict will be reached?
Using statistics for decisions we don't want decided with statistics is problem, but as far as I can tell right now it is flat-out dominated by the fact nobody can use them correctly. Truthfully, having learned quite a lot of math, my feeling is that when a "normal person" starts hearing about statistics and they get the "eyes glaze over" thing going on, that's the rational answer. I wish more people understood basic physics, I wish more people understood basic finances and the principles of interest, but, honestly, when a normal person encounters a statistic they should pretty much just ignore it. The odds that a given stat either came from someone innumerate, or someone deliberately (or accidentally!) bending it to make a predetermined point (which makes the stat useless) really, truly, no sarcasm, no cynicism, are so close to 100% that simply ignoring is the best answer.
Awesome, if I ever want to murder you, I'll get two guns, one with bullets and one with blanks, recruit a friend, double blind them so I don't know who has what and we'll both shoot you at the same time.
Since it can never be ascribed to more than 50% certainty which of us shot you, we will both go free.
No, you got me wrong. I meant "you should convict somebody based on hard proof. If you want to convict somebody based on likelihood, judges and juries - like all humans - have a big problem working with big numbers. To minimize hurtful bad decisions, and overcome this human flaw, we should set a fixed, very high probability."
Our inability to intuitively judge probabilities correctly rears its ugly head in such diverse areas as politics, eating habits, the war on terror, and here the judicial system. We're heavily biased as a species, and we consistently put the probability of terrible things happening much much higher than they really are.
The war on terror is a great example: Because terror is, well terrifying, we have a tendency to think "this is awful - and it could happen to me", even though the chance of dying by the hands of terrorists is smaller than the chance of being struck by lightning. Combined with our desire for everything to have an easy and understandable cause this is the primary problem in this case.
We need to think before we act: Sometimes things aren't as they seem, and sometimes they don't have a cause but are simply flukes of randomness passing though our lives.